From 374d7b3f8c091b0ed43e02676fe935d2613bf4d1 Mon Sep 17 00:00:00 2001
From: MatteoRobbiati <robbiati.matteo@gmail.com>
Date: Wed, 30 Jul 2025 10:04:56 +0200
Subject: [PATCH 01/33] chore: updating deps, expecially qmatchatea extras

---
 poetry.lock    | 1880 ++++++++++++++++++++++++++----------------------
 pyproject.toml |    4 +-
 2 files changed, 1043 insertions(+), 841 deletions(-)

diff --git a/poetry.lock b/poetry.lock
index 1d0a1c9..3b25b7e 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,4 +1,4 @@
-# This file is automatically @generated by Poetry 1.7.0 and should not be changed by hand.
+# This file is automatically @generated by Poetry 2.1.3 and should not be changed by hand.
 
 [[package]]
 name = "alabaster"
@@ -6,6 +6,7 @@ version = "0.7.16"
 description = "A light, configurable Sphinx theme"
 optional = false
 python-versions = ">=3.9"
+groups = ["docs"]
 files = [
     {file = "alabaster-0.7.16-py3-none-any.whl", hash = "sha256:b46733c07dce03ae4e150330b975c75737fa60f0a7c591b6c8bf4928a28e2c92"},
     {file = "alabaster-0.7.16.tar.gz", hash = "sha256:75a8b99c28a5dad50dd7f8ccdd447a121ddb3892da9e53d1ca5cca3106d58d65"},
@@ -13,13 +14,14 @@ files = [
 
 [[package]]
 name = "alembic"
-version = "1.15.2"
+version = "1.16.4"
 description = "A database migration tool for SQLAlchemy."
 optional = false
 python-versions = ">=3.9"
+groups = ["main"]
 files = [
-    {file = "alembic-1.15.2-py3-none-any.whl", hash = "sha256:2e76bd916d547f6900ec4bb5a90aeac1485d2c92536923d0b138c02b126edc53"},
-    {file = "alembic-1.15.2.tar.gz", hash = "sha256:1c72391bbdeffccfe317eefba686cb9a3c078005478885413b95c3b26c57a8a7"},
+    {file = "alembic-1.16.4-py3-none-any.whl", hash = "sha256:b05e51e8e82efc1abd14ba2af6392897e145930c3e0a2faf2b0da2f7f7fd660d"},
+    {file = "alembic-1.16.4.tar.gz", hash = "sha256:efab6ada0dd0fae2c92060800e0bf5c1dc26af15a10e02fb4babff164b4725e2"},
 ]
 
 [package.dependencies]
@@ -36,6 +38,7 @@ version = "4.13.2"
 description = "ANTLR 4.13.2 runtime for Python 3"
 optional = false
 python-versions = "*"
+groups = ["main"]
 files = [
     {file = "antlr4_python3_runtime-4.13.2-py3-none-any.whl", hash = "sha256:fe3835eb8d33daece0e799090eda89719dbccee7aa39ef94eed3818cafa5a7e8"},
     {file = "antlr4_python3_runtime-4.13.2.tar.gz", hash = "sha256:909b647e1d2fc2b70180ac586df3933e38919c85f98ccc656a96cd3f25ef3916"},
@@ -47,6 +50,8 @@ version = "0.1.4"
 description = "Disable App Nap on macOS >= 10.9"
 optional = false
 python-versions = ">=3.6"
+groups = ["dev"]
+markers = "sys_platform == \"darwin\""
 files = [
     {file = "appnope-0.1.4-py2.py3-none-any.whl", hash = "sha256:502575ee11cd7a28c0205f379b525beefebab9d161b7c964670864014ed7213c"},
     {file = "appnope-0.1.4.tar.gz", hash = "sha256:1de3860566df9caf38f01f86f65e0e13e379af54f9e4bee1e66b48f2efffd1ee"},
@@ -54,24 +59,26 @@ files = [
 
 [[package]]
 name = "astroid"
-version = "3.3.9"
+version = "3.3.11"
 description = "An abstract syntax tree for Python with inference support."
 optional = false
 python-versions = ">=3.9.0"
+groups = ["analysis"]
 files = [
-    {file = "astroid-3.3.9-py3-none-any.whl", hash = "sha256:d05bfd0acba96a7bd43e222828b7d9bc1e138aaeb0649707908d3702a9831248"},
-    {file = "astroid-3.3.9.tar.gz", hash = "sha256:622cc8e3048684aa42c820d9d218978021c3c3d174fb03a9f0d615921744f550"},
+    {file = "astroid-3.3.11-py3-none-any.whl", hash = "sha256:54c760ae8322ece1abd213057c4b5bba7c49818853fc901ef09719a60dbf9dec"},
+    {file = "astroid-3.3.11.tar.gz", hash = "sha256:1e5a5011af2920c7c67a53f65d536d65bfa7116feeaf2354d8b94f29573bb0ce"},
 ]
 
 [[package]]
 name = "autoray"
-version = "0.7.1"
+version = "0.7.2"
 description = "Abstract your array operations."
 optional = false
 python-versions = ">=3.9"
+groups = ["main"]
 files = [
-    {file = "autoray-0.7.1-py3-none-any.whl", hash = "sha256:36bbcac072771039073d896eb3e73cedbe41b879e247b6ec3c70781ce9afc720"},
-    {file = "autoray-0.7.1.tar.gz", hash = "sha256:e5af6c62ba7c3be8a36b2ab19e344c715f3478d39a0e47755aad365572bc90f8"},
+    {file = "autoray-0.7.2-py3-none-any.whl", hash = "sha256:f692f0f21a6f187ce877f3cc810f035d601ccd713beac02974811650bb60f580"},
+    {file = "autoray-0.7.2.tar.gz", hash = "sha256:7f8f375af12deea65736b65305b86eff2e11ebaf8c58d3e599752681772ff0d7"},
 ]
 
 [package.extras]
@@ -84,13 +91,14 @@ version = "2.17.0"
 description = "Internationalization utilities"
 optional = false
 python-versions = ">=3.8"
+groups = ["docs"]
 files = [
     {file = "babel-2.17.0-py3-none-any.whl", hash = "sha256:4d0b53093fdfb4b21c92b5213dba5a1b23885afa8383709427046b21c366e5f2"},
     {file = "babel-2.17.0.tar.gz", hash = "sha256:0c54cffb19f690cdcc52a3b50bcbf71e07a808d1c80d549f2459b9d2cf0afb9d"},
 ]
 
 [package.extras]
-dev = ["backports.zoneinfo", "freezegun (>=1.0,<2.0)", "jinja2 (>=3.0)", "pytest (>=6.0)", "pytest-cov", "pytz", "setuptools", "tzdata"]
+dev = ["backports.zoneinfo ; python_version < \"3.9\"", "freezegun (>=1.0,<2.0)", "jinja2 (>=3.0)", "pytest (>=6.0)", "pytest-cov", "pytz", "setuptools", "tzdata ; sys_platform == \"win32\""]
 
 [[package]]
 name = "backcall"
@@ -98,6 +106,7 @@ version = "0.2.0"
 description = "Specifications for callback functions passed in to an API"
 optional = false
 python-versions = "*"
+groups = ["dev"]
 files = [
     {file = "backcall-0.2.0-py2.py3-none-any.whl", hash = "sha256:fbbce6a29f263178a1f7915c1940bde0ec2b2a967566fe1c65c1dfb7422bd255"},
     {file = "backcall-0.2.0.tar.gz", hash = "sha256:5cbdbf27be5e7cfadb448baf0aa95508f91f2bbc6c6437cd9cd06e2a4c215e1e"},
@@ -105,13 +114,14 @@ files = [
 
 [[package]]
 name = "beautifulsoup4"
-version = "4.13.3"
+version = "4.13.4"
 description = "Screen-scraping library"
 optional = false
 python-versions = ">=3.7.0"
+groups = ["docs"]
 files = [
-    {file = "beautifulsoup4-4.13.3-py3-none-any.whl", hash = "sha256:99045d7d3f08f91f0d656bc9b7efbae189426cd913d830294a15eefa0ea4df16"},
-    {file = "beautifulsoup4-4.13.3.tar.gz", hash = "sha256:1bd32405dacc920b42b83ba01644747ed77456a65760e285fbc47633ceddaf8b"},
+    {file = "beautifulsoup4-4.13.4-py3-none-any.whl", hash = "sha256:9bbbb14bfde9d79f38b8cd5f8c7c85f4b8f2523190ebed90e950a8dea4cb1c4b"},
+    {file = "beautifulsoup4-4.13.4.tar.gz", hash = "sha256:dbb3c4e1ceae6aefebdaf2423247260cd062430a410e38c66f2baa50a8437195"},
 ]
 
 [package.dependencies]
@@ -127,114 +137,116 @@ lxml = ["lxml"]
 
 [[package]]
 name = "certifi"
-version = "2025.1.31"
+version = "2025.7.14"
 description = "Python package for providing Mozilla's CA Bundle."
 optional = false
-python-versions = ">=3.6"
+python-versions = ">=3.7"
+groups = ["docs"]
 files = [
-    {file = "certifi-2025.1.31-py3-none-any.whl", hash = "sha256:ca78db4565a652026a4db2bcdf68f2fb589ea80d0be70e03929ed730746b84fe"},
-    {file = "certifi-2025.1.31.tar.gz", hash = "sha256:3d5da6925056f6f18f119200434a4780a94263f10d1c21d032a6f6b2baa20651"},
+    {file = "certifi-2025.7.14-py3-none-any.whl", hash = "sha256:6b31f564a415d79ee77df69d757bb49a5bb53bd9f756cbbe24394ffd6fc1f4b2"},
+    {file = "certifi-2025.7.14.tar.gz", hash = "sha256:8ea99dbdfaaf2ba2f9bac77b9249ef62ec5218e7c2b2e903378ed5fccf765995"},
 ]
 
 [[package]]
 name = "charset-normalizer"
-version = "3.4.1"
+version = "3.4.2"
 description = "The Real First Universal Charset Detector. Open, modern and actively maintained alternative to Chardet."
 optional = false
 python-versions = ">=3.7"
+groups = ["docs"]
 files = [
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 ]
 
 [[package]]
@@ -243,6 +255,7 @@ version = "3.4.0"
 description = "CMA-ES, Covariance Matrix Adaptation Evolution Strategy for non-linear numerical optimization in Python"
 optional = false
 python-versions = "*"
+groups = ["main"]
 files = [
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@@ -261,10 +274,12 @@ version = "0.4.6"
 description = "Cross-platform colored terminal text."
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,!=3.5.*,!=3.6.*,>=2.7"
+groups = ["main", "analysis", "dev", "docs", "tests"]
 files = [
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 ]
+markers = {main = "sys_platform == \"win32\" or platform_system == \"Windows\"", analysis = "sys_platform == \"win32\"", dev = "sys_platform == \"win32\"", docs = "sys_platform == \"win32\"", tests = "sys_platform == \"win32\""}
 
 [[package]]
 name = "colorlog"
@@ -272,6 +287,7 @@ version = "6.9.0"
 description = "Add colours to the output of Python's logging module."
 optional = false
 python-versions = ">=3.6"
+groups = ["main"]
 files = [
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@@ -285,86 +301,106 @@ development = ["black", "flake8", "mypy", "pytest", "types-colorama"]
 
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-version = "1.3.1"
+version = "1.3.3"
 description = "Python library for calculating contours of 2D quadrilateral grids"
 optional = false
-python-versions = ">=3.10"
+python-versions = ">=3.11"
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 ]
 
 [package.dependencies]
-numpy = ">=1.23"
+numpy = ">=1.25"
 
 [package.extras]
 bokeh = ["bokeh", "selenium"]
 docs = ["furo", "sphinx (>=7.2)", "sphinx-copybutton"]
-mypy = ["contourpy[bokeh,docs]", "docutils-stubs", "mypy (==1.11.1)", "types-Pillow"]
+mypy = ["bokeh", "contourpy[bokeh,docs]", "docutils-stubs", "mypy (==1.17.0)", "types-Pillow"]
 test = ["Pillow", "contourpy[test-no-images]", "matplotlib"]
 test-no-images = ["pytest", "pytest-cov", "pytest-rerunfailures", "pytest-xdist", "wurlitzer"]
 
 [[package]]
 name = "cotengra"
-version = "0.7.2"
+version = "0.7.5"
 description = "Hyper optimized contraction trees for large tensor networks and einsums."
 optional = false
 python-versions = ">=3.8"
+groups = ["main"]
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 ]
 
 [package.dependencies]
@@ -377,78 +413,104 @@ test = ["altair", "baytune", "chocolate", "cmaes", "dask", "distributed", "kahyp
 
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 [package.extras]
-toml = ["tomli"]
+toml = ["tomli ; python_full_version <= \"3.11.0a6\""]
 
 [[package]]
 name = "cudensitymat-cu11"
@@ -456,6 +518,8 @@ version = "0.0.5"
 description = "cuDensityMat - a component of NVIDIA cuQuantum SDK"
 optional = true
 python-versions = "*"
+groups = ["main"]
+markers = "extra == \"cuda\""
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+    {file = "cupy_cuda11x-13.5.1-cp39-cp39-manylinux2014_x86_64.whl", hash = "sha256:dd93d3079b1f20faead594af8e6680817ce6a0858b4898dfa4976becfa5ba55c"},
+    {file = "cupy_cuda11x-13.5.1-cp39-cp39-win_amd64.whl", hash = "sha256:db17d70b7445ddc34c2a33adbaf897cc337345f2b6ee90e8b5e2c207ab7deca8"},
 ]
 
 [package.dependencies]
 fastrlock = ">=0.5"
-numpy = ">=1.22,<2.3"
+numpy = ">=1.22,<2.6"
 
 [package.extras]
 all = ["Cython (>=3)", "optuna (>=2.0)", "scipy (>=1.7,<1.17)"]
@@ -502,6 +568,8 @@ version = "24.11.0"
 description = "NVIDIA cuQuantum Python"
 optional = true
 python-versions = ">=3.10"
+groups = ["main"]
+markers = "extra == \"cuda\""
 files = [
     {file = "cuquantum_python_cu11-24.11.0-cp310-cp310-manylinux2014_aarch64.whl", hash = "sha256:0c0af65796f3d897cd52188309517407b1f1b57863435caaf2e999b1661c86a6"},
     {file = "cuquantum_python_cu11-24.11.0-cp310-cp310-manylinux2014_x86_64.whl", hash = "sha256:1d49cc700e18e3a456cfd1c49a43adce5935b97dfc23b330be46e5e1a294363f"},
@@ -523,13 +591,15 @@ test = ["cffi (>=1.0.0)", "cirq-core", "jsonschema (==4.17.3)", "nbconvert", "nb
 
 [[package]]
 name = "custatevec-cu11"
-version = "1.8.0"
+version = "1.9.0.post0"
 description = "cuStateVec - a component of NVIDIA cuQuantum SDK"
 optional = true
 python-versions = "*"
+groups = ["main"]
+markers = "extra == \"cuda\""
 files = [
-    {file = "custatevec_cu11-1.8.0-py3-none-manylinux2014_aarch64.whl", hash = "sha256:80c5f88e9df30c9d1622d957699ade2395b89f2af2ff2820b45e5ef1599f1cf9"},
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+    {file = "custatevec_cu11-1.9.0.post0-py3-none-manylinux2014_aarch64.whl", hash = "sha256:e627f11e38296a2f7061f2b2dec98e5f952ebd10e97dd34380a9cd2a62bef2c9"},
+    {file = "custatevec_cu11-1.9.0.post0-py3-none-manylinux2014_x86_64.whl", hash = "sha256:c3caa642752da7d7d8605f2864f418e5bc33ff21f12bd27b658cbca4684d76f1"},
 ]
 
 [[package]]
@@ -538,6 +608,8 @@ version = "2.2.0"
 description = "NVIDIA cuTENSOR"
 optional = true
 python-versions = "*"
+groups = ["main"]
+markers = "extra == \"cuda\""
 files = [
     {file = "cutensor_cu11-2.2.0-py3-none-manylinux2014_aarch64.whl", hash = "sha256:b2623e556bdb228a7cb3031d1391f17a7ab965430687e9491b4e15dd47f7da8a"},
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@@ -546,13 +618,15 @@ files = [
 
 [[package]]
 name = "cutensornet-cu11"
-version = "2.7.0"
+version = "2.8.0"
 description = "cuTensorNet - a component of NVIDIA cuQuantum SDK"
 optional = true
 python-versions = "*"
+groups = ["main"]
+markers = "extra == \"cuda\""
 files = [
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+    {file = "cutensornet_cu11-2.8.0-py3-none-manylinux2014_aarch64.whl", hash = "sha256:d98d2b14dbf8486760bc06d6ef47ff4153dc9be54ca95c107deddd4b41d3cb62"},
+    {file = "cutensornet_cu11-2.8.0-py3-none-manylinux2014_x86_64.whl", hash = "sha256:8bd49dd9a8c0fb6fb07f0bfe196b7e555eae744e3e0a4c2e49c6c07eaf41c4de"},
 ]
 
 [package.dependencies]
@@ -564,6 +638,7 @@ version = "0.12.1"
 description = "Composable style cycles"
 optional = false
 python-versions = ">=3.8"
+groups = ["main"]
 files = [
     {file = "cycler-0.12.1-py3-none-any.whl", hash = "sha256:85cef7cff222d8644161529808465972e51340599459b8ac3ccbac5a854e0d30"},
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@@ -579,6 +654,7 @@ version = "1.0.1"
 description = "Cython implementation of Toolz: High performance functional utilities"
 optional = false
 python-versions = ">=3.8"
+groups = ["main"]
 files = [
     {file = "cytoolz-1.0.1-cp310-cp310-macosx_10_9_x86_64.whl", hash = "sha256:cec9af61f71fc3853eb5dca3d42eb07d1f48a4599fa502cbe92adde85f74b042"},
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@@ -694,6 +770,7 @@ version = "5.2.1"
 description = "Decorators for Humans"
 optional = false
 python-versions = ">=3.8"
+groups = ["dev"]
 files = [
     {file = "decorator-5.2.1-py3-none-any.whl", hash = "sha256:d316bb415a2d9e2d2b3abcc4084c6502fc09240e292cd76a76afc106a1c8e04a"},
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@@ -701,14 +778,16 @@ files = [
 
 [[package]]
 name = "dill"
-version = "0.3.9"
+version = "0.4.0"
 description = "serialize all of Python"
 optional = false
 python-versions = ">=3.8"
+groups = ["main", "analysis"]
 files = [
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-    {file = "dill-0.3.9.tar.gz", hash = "sha256:81aa267dddf68cbfe8029c42ca9ec6a4ab3b22371d1c450abc54422577b4512c"},
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+    {file = "dill-0.4.0.tar.gz", hash = "sha256:0633f1d2df477324f53a895b02c901fb961bdbf65a17122586ea7019292cbcf0"},
 ]
+markers = {main = "extra == \"qmatchatea\""}
 
 [package.extras]
 graph = ["objgraph (>=1.7.2)"]
@@ -716,13 +795,14 @@ profile = ["gprof2dot (>=2022.7.29)"]
 
 [[package]]
 name = "docutils"
-version = "0.19"
+version = "0.17.1"
 description = "Docutils -- Python Documentation Utilities"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+groups = ["docs"]
 files = [
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+    {file = "docutils-0.17.1.tar.gz", hash = "sha256:686577d2e4c32380bb50cbb22f575ed742d58168cee37e99117a854bcd88f125"},
 ]
 
 [[package]]
@@ -731,6 +811,8 @@ version = "0.8.3"
 description = "Fast, re-entrant optimistic lock implemented in Cython"
 optional = true
 python-versions = "*"
+groups = ["main"]
+markers = "extra == \"cuda\""
 files = [
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@@ -805,76 +887,68 @@ files = [
 
 [[package]]
 name = "fonttools"
-version = "4.57.0"
+version = "4.59.0"
 description = "Tools to manipulate font files"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
+groups = ["main"]
 files = [
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 name = "furo"
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 description = "A clean customisable Sphinx documentation theme."
 optional = false
 python-versions = ">=3.7"
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 [package.extras]
@@ -981,37 +1039,39 @@ test = ["objgraph", "psutil"]
 
 [[package]]
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+version = "3.14.0"
 description = "Read and write HDF5 files from Python"
 optional = true
 python-versions = ">=3.9"
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 ]
 
 [package.dependencies]
@@ -1023,6 +1083,7 @@ version = "3.10"
 description = "Internationalized Domain Names in Applications (IDNA)"
 optional = false
 python-versions = ">=3.6"
+groups = ["docs"]
 files = [
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@@ -1037,6 +1098,7 @@ version = "1.4.1"
 description = "Getting image size from png/jpeg/jpeg2000/gif file"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+groups = ["docs"]
 files = [
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@@ -1048,6 +1110,7 @@ version = "2.1.0"
 description = "brain-dead simple config-ini parsing"
 optional = false
 python-versions = ">=3.8"
+groups = ["tests"]
 files = [
     {file = "iniconfig-2.1.0-py3-none-any.whl", hash = "sha256:9deba5723312380e77435581c6bf4935c94cbfab9b1ed33ef8d238ea168eb760"},
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@@ -1059,6 +1122,7 @@ version = "7.34.0"
 description = "IPython: Productive Interactive Computing"
 optional = false
 python-versions = ">=3.7"
+groups = ["dev"]
 files = [
     {file = "ipython-7.34.0-py3-none-any.whl", hash = "sha256:c175d2440a1caff76116eb719d40538fbb316e214eda85c5515c303aacbfb23e"},
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@@ -1095,6 +1159,7 @@ version = "6.0.1"
 description = "A Python utility / library to sort Python imports."
 optional = false
 python-versions = ">=3.9.0"
+groups = ["analysis"]
 files = [
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@@ -1110,6 +1175,7 @@ version = "0.19.2"
 description = "An autocompletion tool for Python that can be used for text editors."
 optional = false
 python-versions = ">=3.6"
+groups = ["dev"]
 files = [
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@@ -1129,6 +1195,7 @@ version = "3.1.6"
 description = "A very fast and expressive template engine."
 optional = false
 python-versions = ">=3.7"
+groups = ["docs"]
 files = [
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@@ -1142,13 +1209,14 @@ i18n = ["Babel (>=2.7)"]
 
 [[package]]
 name = "joblib"
-version = "1.4.2"
+version = "1.5.1"
 description = "Lightweight pipelining with Python functions"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
+groups = ["main"]
 files = [
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 ]
 
 [[package]]
@@ -1157,6 +1225,7 @@ version = "1.4.8"
 description = "A fast implementation of the Cassowary constraint solver"
 optional = false
 python-versions = ">=3.10"
+groups = ["main"]
 files = [
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@@ -1242,13 +1311,14 @@ files = [
 
 [[package]]
 name = "latexcodec"
-version = "3.0.0"
+version = "3.0.1"
 description = "A lexer and codec to work with LaTeX code in Python."
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.9"
+groups = ["docs"]
 files = [
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+    {file = "latexcodec-3.0.1.tar.gz", hash = "sha256:e78a6911cd72f9dec35031c6ec23584de6842bfbc4610a9678868d14cdfb0357"},
 ]
 
 [[package]]
@@ -1257,6 +1327,7 @@ version = "0.44.0"
 description = "lightweight wrapper around basic LLVM functionality"
 optional = false
 python-versions = ">=3.10"
+groups = ["main"]
 files = [
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@@ -1287,6 +1358,7 @@ version = "1.3.10"
 description = "A super-fast templating language that borrows the best ideas from the existing templating languages."
 optional = false
 python-versions = ">=3.8"
+groups = ["main"]
 files = [
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@@ -1306,6 +1378,7 @@ version = "3.0.2"
 description = "Safely add untrusted strings to HTML/XML markup."
 optional = false
 python-versions = ">=3.9"
+groups = ["main", "docs"]
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 ]
 
 [package.dependencies]
@@ -1433,6 +1507,7 @@ version = "0.1.7"
 description = "Inline Matplotlib backend for Jupyter"
 optional = false
 python-versions = ">=3.8"
+groups = ["dev"]
 files = [
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@@ -1447,6 +1522,7 @@ version = "0.7.0"
 description = "McCabe checker, plugin for flake8"
 optional = false
 python-versions = ">=3.6"
+groups = ["analysis"]
 files = [
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@@ -1458,6 +1534,7 @@ version = "1.3.0"
 description = "Python library for arbitrary-precision floating-point arithmetic"
 optional = false
 python-versions = "*"
+groups = ["main"]
 files = [
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@@ -1466,27 +1543,29 @@ files = [
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 docs = ["sphinx"]
-gmpy = ["gmpy2 (>=2.1.0a4)"]
+gmpy = ["gmpy2 (>=2.1.0a4) ; platform_python_implementation != \"PyPy\""]
 tests = ["pytest (>=4.6)"]
 
 [[package]]
 name = "networkx"
-version = "3.4.2"
+version = "3.5"
 description = "Python package for creating and manipulating graphs and networks"
 optional = false
-python-versions = ">=3.10"
+python-versions = ">=3.11"
+groups = ["main"]
 files = [
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 ]
 
 [package.extras]
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+default = ["matplotlib (>=3.8)", "numpy (>=1.25)", "pandas (>=2.0)", "scipy (>=1.11.2)"]
+developer = ["mypy (>=1.15)", "pre-commit (>=4.1)"]
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-test = ["pytest (>=7.2)", "pytest-cov (>=4.0)"]
+test = ["pytest (>=7.2)", "pytest-cov (>=4.0)", "pytest-xdist (>=3.0)"]
+test-extras = ["pytest-mpl", "pytest-randomly"]
 
 [[package]]
 name = "numba"
@@ -1494,6 +1573,7 @@ version = "0.61.2"
 description = "compiling Python code using LLVM"
 optional = false
 python-versions = ">=3.10"
+groups = ["main"]
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 [[package]]
@@ -1592,6 +1673,7 @@ version = "1.0.1"
 description = "Reference OpenQASM AST in Python"
 optional = false
 python-versions = "*"
+groups = ["main"]
 files = [
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 [package.extras]
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-parser = ["antlr4_python3_runtime (>=4.7,<4.14)", "importlib_metadata"]
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+parser = ["antlr4_python3_runtime (>=4.7,<4.14)", "importlib_metadata ; python_version < \"3.10\""]
 tests = ["pytest (>=6.0)", "pyyaml"]
 
 [[package]]
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+version = "4.4.0"
 description = "A hyperparameter optimization framework"
 optional = false
 python-versions = ">=3.8"
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 [package.dependencies]
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 [[package]]
 name = "packaging"
-version = "24.2"
+version = "25.0"
 description = "Core utilities for Python packages"
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 python-versions = ">=3.8"
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 [[package]]
@@ -1649,6 +1733,7 @@ version = "0.8.4"
 description = "A Python Parser"
 optional = false
 python-versions = ">=3.6"
+groups = ["dev"]
 files = [
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@@ -1664,6 +1749,8 @@ version = "6.1.1"
 description = "Python Build Reasonableness"
 optional = true
 python-versions = ">=2.6"
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+markers = "extra == \"qmatchatea\""
 files = [
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 description = "Pexpect allows easy control of interactive console applications."
 optional = false
 python-versions = "*"
+groups = ["dev"]
+markers = "sys_platform != \"win32\""
 files = [
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 optional = false
 python-versions = "*"
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 ]
 
 [package.extras]
-docs = ["furo", "olefile", "sphinx (>=8.1)", "sphinx-copybutton", "sphinx-inline-tabs", "sphinxext-opengraph"]
+docs = ["furo", "olefile", "sphinx (>=8.2)", "sphinx-autobuild", "sphinx-copybutton", "sphinx-inline-tabs", "sphinxext-opengraph"]
 fpx = ["olefile"]
 mic = ["olefile"]
-tests = ["check-manifest", "coverage (>=7.4.2)", "defusedxml", "markdown2", "olefile", "packaging", "pyroma", "pytest", "pytest-cov", "pytest-timeout", "trove-classifiers (>=2024.10.12)"]
-typing = ["typing-extensions"]
+test-arrow = ["pyarrow"]
+tests = ["check-manifest", "coverage (>=7.4.2)", "defusedxml", "markdown2", "olefile", "packaging", "pyroma", "pytest", "pytest-cov", "pytest-timeout", "pytest-xdist", "trove-classifiers (>=2024.10.12)"]
+typing = ["typing-extensions ; python_version < \"3.10\""]
 xmp = ["defusedxml"]
 
 [[package]]
 name = "platformdirs"
-version = "4.3.7"
+version = "4.3.8"
 description = "A small Python package for determining appropriate platform-specific dirs, e.g. a `user data dir`."
 optional = false
 python-versions = ">=3.9"
+groups = ["analysis"]
 files = [
-    {file = "platformdirs-4.3.7-py3-none-any.whl", hash = "sha256:a03875334331946f13c549dbd8f4bac7a13a50a895a0eb1e8c6a8ace80d40a94"},
-    {file = "platformdirs-4.3.7.tar.gz", hash = "sha256:eb437d586b6a0986388f0d6f74aa0cde27b48d0e3d66843640bfb6bdcdb6e351"},
+    {file = "platformdirs-4.3.8-py3-none-any.whl", hash = "sha256:ff7059bb7eb1179e2685604f4aaf157cfd9535242bd23742eadc3c13542139b4"},
+    {file = "platformdirs-4.3.8.tar.gz", hash = "sha256:3d512d96e16bcb959a814c9f348431070822a6496326a4be0911c40b5a74c2bc"},
 ]
 
 [package.extras]
@@ -1803,28 +1931,30 @@ type = ["mypy (>=1.14.1)"]
 
 [[package]]
 name = "pluggy"
-version = "1.5.0"
+version = "1.6.0"
 description = "plugin and hook calling mechanisms for python"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
+groups = ["tests"]
 files = [
-    {file = "pluggy-1.5.0-py3-none-any.whl", hash = "sha256:44e1ad92c8ca002de6377e165f3e0f1be63266ab4d554740532335b9d75ea669"},
-    {file = "pluggy-1.5.0.tar.gz", hash = "sha256:2cffa88e94fdc978c4c574f15f9e59b7f4201d439195c3715ca9e2486f1d0cf1"},
+    {file = "pluggy-1.6.0-py3-none-any.whl", hash = "sha256:e920276dd6813095e9377c0bc5566d94c932c33b27a3e3945d8389c374dd4746"},
+    {file = "pluggy-1.6.0.tar.gz", hash = "sha256:7dcc130b76258d33b90f61b658791dede3486c3e6bfb003ee5c9bfb396dd22f3"},
 ]
 
 [package.extras]
 dev = ["pre-commit", "tox"]
-testing = ["pytest", "pytest-benchmark"]
+testing = ["coverage", "pytest", "pytest-benchmark"]
 
 [[package]]
 name = "prompt-toolkit"
-version = "3.0.50"
+version = "3.0.51"
 description = "Library for building powerful interactive command lines in Python"
 optional = false
-python-versions = ">=3.8.0"
+python-versions = ">=3.8"
+groups = ["dev"]
 files = [
-    {file = "prompt_toolkit-3.0.50-py3-none-any.whl", hash = "sha256:9b6427eb19e479d98acff65196a307c555eb567989e6d88ebbb1b509d9779198"},
-    {file = "prompt_toolkit-3.0.50.tar.gz", hash = "sha256:544748f3860a2623ca5cd6d2795e7a14f3d0e1c3c9728359013f79877fc89bab"},
+    {file = "prompt_toolkit-3.0.51-py3-none-any.whl", hash = "sha256:52742911fde84e2d423e2f9a4cf1de7d7ac4e51958f648d9540e0fb8db077b07"},
+    {file = "prompt_toolkit-3.0.51.tar.gz", hash = "sha256:931a162e3b27fc90c86f1b48bb1fb2c528c2761475e57c9c06de13311c7b54ed"},
 ]
 
 [package.dependencies]
@@ -1836,6 +1966,7 @@ version = "7.0.0"
 description = "Cross-platform lib for process and system monitoring in Python.  NOTE: the syntax of this script MUST be kept compatible with Python 2.7."
 optional = false
 python-versions = ">=3.6"
+groups = ["main"]
 files = [
     {file = "psutil-7.0.0-cp36-abi3-macosx_10_9_x86_64.whl", hash = "sha256:101d71dc322e3cffd7cea0650b09b3d08b8e7c4109dd6809fe452dfd00e58b25"},
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@@ -1859,6 +1990,8 @@ version = "0.7.0"
 description = "Run a subprocess in a pseudo terminal"
 optional = false
 python-versions = "*"
+groups = ["dev"]
+markers = "sys_platform != \"win32\""
 files = [
     {file = "ptyprocess-0.7.0-py2.py3-none-any.whl", hash = "sha256:4b41f3967fce3af57cc7e94b888626c18bf37a083e3651ca8feeb66d492fef35"},
     {file = "ptyprocess-0.7.0.tar.gz", hash = "sha256:5c5d0a3b48ceee0b48485e0c26037c0acd7d29765ca3fbb5cb3831d347423220"},
@@ -1866,21 +1999,22 @@ files = [
 
 [[package]]
 name = "pybtex"
-version = "0.24.0"
+version = "0.25.1"
 description = "A BibTeX-compatible bibliography processor in Python"
 optional = false
-python-versions = ">=2.7,!=3.0.*,!=3.1.*,!=3.2.*"
+python-versions = ">=3.6"
+groups = ["docs"]
 files = [
-    {file = "pybtex-0.24.0-py2.py3-none-any.whl", hash = "sha256:e1e0c8c69998452fea90e9179aa2a98ab103f3eed894405b7264e517cc2fcc0f"},
-    {file = "pybtex-0.24.0.tar.gz", hash = "sha256:818eae35b61733e5c007c3fcd2cfb75ed1bc8b4173c1f70b56cc4c0802d34755"},
+    {file = "pybtex-0.25.1-py2.py3-none-any.whl", hash = "sha256:9053b0d619409a0a83f38abad5d9921de5f7b3ede00742beafcd9f10ad0d8c5c"},
+    {file = "pybtex-0.25.1.tar.gz", hash = "sha256:9eaf90267c7e83e225af89fea65c370afbf65f458220d3946a9e3049e1eca491"},
 ]
 
 [package.dependencies]
 latexcodec = ">=1.0.4"
 PyYAML = ">=3.01"
-six = "*"
 
 [package.extras]
+doc = ["sphinx"]
 test = ["pytest"]
 
 [[package]]
@@ -1889,6 +2023,7 @@ version = "1.0.3"
 description = "A docutils backend for pybtex."
 optional = false
 python-versions = ">=3.7"
+groups = ["docs"]
 files = [
     {file = "pybtex-docutils-1.0.3.tar.gz", hash = "sha256:3a7ebdf92b593e00e8c1c538aa9a20bca5d92d84231124715acc964d51d93c6b"},
     {file = "pybtex_docutils-1.0.3-py3-none-any.whl", hash = "sha256:8fd290d2ae48e32fcb54d86b0efb8d573198653c7e2447d5bec5847095f430b9"},
@@ -1900,13 +2035,14 @@ pybtex = ">=0.16"
 
 [[package]]
 name = "pygments"
-version = "2.19.1"
+version = "2.19.2"
 description = "Pygments is a syntax highlighting package written in Python."
 optional = false
 python-versions = ">=3.8"
+groups = ["dev", "docs", "tests"]
 files = [
-    {file = "pygments-2.19.1-py3-none-any.whl", hash = "sha256:9ea1544ad55cecf4b8242fab6dd35a93bbce657034b0611ee383099054ab6d8c"},
-    {file = "pygments-2.19.1.tar.gz", hash = "sha256:61c16d2a8576dc0649d9f39e089b5f02bcd27fba10d8fb4dcc28173f7a45151f"},
+    {file = "pygments-2.19.2-py3-none-any.whl", hash = "sha256:86540386c03d588bb81d44bc3928634ff26449851e99741617ecb9037ee5ec0b"},
+    {file = "pygments-2.19.2.tar.gz", hash = "sha256:636cb2477cec7f8952536970bc533bc43743542f70392ae026374600add5b887"},
 ]
 
 [package.extras]
@@ -1914,13 +2050,14 @@ windows-terminal = ["colorama (>=0.4.6)"]
 
 [[package]]
 name = "pylint"
-version = "3.3.6"
+version = "3.3.7"
 description = "python code static checker"
 optional = false
 python-versions = ">=3.9.0"
+groups = ["analysis"]
 files = [
-    {file = "pylint-3.3.6-py3-none-any.whl", hash = "sha256:8b7c2d3e86ae3f94fb27703d521dd0b9b6b378775991f504d7c3a6275aa0a6a6"},
-    {file = "pylint-3.3.6.tar.gz", hash = "sha256:b634a041aac33706d56a0d217e6587228c66427e20ec21a019bc4cdee48c040a"},
+    {file = "pylint-3.3.7-py3-none-any.whl", hash = "sha256:43860aafefce92fca4cf6b61fe199cdc5ae54ea28f9bf4cd49de267b5195803d"},
+    {file = "pylint-3.3.7.tar.gz", hash = "sha256:2b11de8bde49f9c5059452e0c310c079c746a0a8eeaa789e5aa966ecc23e4559"},
 ]
 
 [package.dependencies]
@@ -1928,7 +2065,7 @@ astroid = ">=3.3.8,<=3.4.0.dev0"
 colorama = {version = ">=0.4.5", markers = "sys_platform == \"win32\""}
 dill = [
     {version = ">=0.3.7", markers = "python_version >= \"3.12\""},
-    {version = ">=0.3.6", markers = "python_version >= \"3.11\" and python_version < \"3.12\""},
+    {version = ">=0.3.6", markers = "python_version == \"3.11\""},
 ]
 isort = ">=4.2.5,<5.13 || >5.13,<7"
 mccabe = ">=0.6,<0.8"
@@ -1945,6 +2082,7 @@ version = "3.2.3"
 description = "pyparsing module - Classes and methods to define and execute parsing grammars"
 optional = false
 python-versions = ">=3.9"
+groups = ["main"]
 files = [
     {file = "pyparsing-3.2.3-py3-none-any.whl", hash = "sha256:a749938e02d6fd0b59b356ca504a24982314bb090c383e3cf201c95ef7e2bfcf"},
     {file = "pyparsing-3.2.3.tar.gz", hash = "sha256:b9c13f1ab8b3b542f72e28f634bad4de758ab3ce4546e4301970ad6fa77c38be"},
@@ -1955,23 +2093,25 @@ diagrams = ["jinja2", "railroad-diagrams"]
 
 [[package]]
 name = "pytest"
-version = "8.3.5"
+version = "8.4.1"
 description = "pytest: simple powerful testing with Python"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
+groups = ["tests"]
 files = [
-    {file = "pytest-8.3.5-py3-none-any.whl", hash = "sha256:c69214aa47deac29fad6c2a4f590b9c4a9fdb16a403176fe154b79c0b4d4d820"},
-    {file = "pytest-8.3.5.tar.gz", hash = "sha256:f4efe70cc14e511565ac476b57c279e12a855b11f48f212af1080ef2263d3845"},
+    {file = "pytest-8.4.1-py3-none-any.whl", hash = "sha256:539c70ba6fcead8e78eebbf1115e8b589e7565830d7d006a8723f19ac8a0afb7"},
+    {file = "pytest-8.4.1.tar.gz", hash = "sha256:7c67fd69174877359ed9371ec3af8a3d2b04741818c51e5e99cc1742251fa93c"},
 ]
 
 [package.dependencies]
-colorama = {version = "*", markers = "sys_platform == \"win32\""}
-iniconfig = "*"
-packaging = "*"
+colorama = {version = ">=0.4", markers = "sys_platform == \"win32\""}
+iniconfig = ">=1"
+packaging = ">=20"
 pluggy = ">=1.5,<2"
+pygments = ">=2.7.2"
 
 [package.extras]
-dev = ["argcomplete", "attrs (>=19.2)", "hypothesis (>=3.56)", "mock", "pygments (>=2.7.2)", "requests", "setuptools", "xmlschema"]
+dev = ["argcomplete", "attrs (>=19.2)", "hypothesis (>=3.56)", "mock", "requests", "setuptools", "xmlschema"]
 
 [[package]]
 name = "pytest-cov"
@@ -1979,6 +2119,7 @@ version = "4.1.0"
 description = "Pytest plugin for measuring coverage."
 optional = false
 python-versions = ">=3.7"
+groups = ["tests"]
 files = [
     {file = "pytest-cov-4.1.0.tar.gz", hash = "sha256:3904b13dfbfec47f003b8e77fd5b589cd11904a21ddf1ab38a64f204d6a10ef6"},
     {file = "pytest_cov-4.1.0-py3-none-any.whl", hash = "sha256:6ba70b9e97e69fcc3fb45bfeab2d0a138fb65c4d0d6a41ef33983ad114be8c3a"},
@@ -1997,6 +2138,7 @@ version = "1.1.5"
 description = "pytest plugin that allows you to add environment variables."
 optional = false
 python-versions = ">=3.8"
+groups = ["tests"]
 files = [
     {file = "pytest_env-1.1.5-py3-none-any.whl", hash = "sha256:ce90cf8772878515c24b31cd97c7fa1f4481cd68d588419fd45f10ecaee6bc30"},
     {file = "pytest_env-1.1.5.tar.gz", hash = "sha256:91209840aa0e43385073ac464a554ad2947cc2fd663a9debf88d03b01e0cc1cf"},
@@ -2014,6 +2156,7 @@ version = "2.9.0.post0"
 description = "Extensions to the standard Python datetime module"
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,>=2.7"
+groups = ["main"]
 files = [
     {file = "python-dateutil-2.9.0.post0.tar.gz", hash = "sha256:37dd54208da7e1cd875388217d5e00ebd4179249f90fb72437e91a35459a0ad3"},
     {file = "python_dateutil-2.9.0.post0-py2.py3-none-any.whl", hash = "sha256:a8b2bc7bffae282281c8140a97d3aa9c14da0b136dfe83f850eea9a5f7470427"},
@@ -2028,6 +2171,7 @@ version = "6.0.2"
 description = "YAML parser and emitter for Python"
 optional = false
 python-versions = ">=3.8"
+groups = ["main", "docs"]
 files = [
     {file = "PyYAML-6.0.2-cp310-cp310-macosx_10_9_x86_64.whl", hash = "sha256:0a9a2848a5b7feac301353437eb7d5957887edbf81d56e903999a75a3d743086"},
     {file = "PyYAML-6.0.2-cp310-cp310-macosx_11_0_arm64.whl", hash = "sha256:29717114e51c84ddfba879543fb232a6ed60086602313ca38cce623c1d62cfbf"},
@@ -2086,13 +2230,14 @@ files = [
 
 [[package]]
 name = "qibo"
-version = "0.2.17"
+version = "0.2.20"
 description = "A framework for quantum computing with hardware acceleration."
 optional = false
 python-versions = "<3.14,>=3.10"
+groups = ["main"]
 files = [
-    {file = "qibo-0.2.17-py3-none-any.whl", hash = "sha256:c1585c2c61969408863b8fac090999e9b0ad79bf74ca329fc611e6073a7a2792"},
-    {file = "qibo-0.2.17.tar.gz", hash = "sha256:0cc9e5bfb0d11bd84dee49f6f05d348f80eaed141d3ff572435d0bacc51007df"},
+    {file = "qibo-0.2.20-py3-none-any.whl", hash = "sha256:240b4fb8913abd7b419311f4daddd067187c630324d13b6d6e6068163c8cad46"},
+    {file = "qibo-0.2.20.tar.gz", hash = "sha256:dfbe6b5851cf1f481cb14903c40185cd3dbf8069b0d2ed371f074b1df5d794a6"},
 ]
 
 [package.dependencies]
@@ -2103,29 +2248,31 @@ numpy = ">=2.0.0,<3.0.0"
 openqasm3 = {version = ">=1.0.1,<2.0.0", extras = ["parser"]}
 optuna = ">=4.2.1,<5.0.0"
 scipy = ">=1.15.2,<2.0.0"
-sympy = ">=1.13.3,<2.0.0"
+sympy = ">=1.13.1,<2.0.0"
 tabulate = ">=0.9.0,<0.10.0"
 
 [package.extras]
-qulacs = ["qulacs (>=0.6.4,<0.7.0)"]
+qulacs = ["qulacs (>=0.6.4,<0.7.0) ; python_version < \"3.13\""]
 
 [[package]]
 name = "qiskit"
-version = "1.4.2"
+version = "1.4.3"
 description = "An open-source SDK for working with quantum computers at the level of extended quantum circuits, operators, and primitives."
 optional = true
 python-versions = ">=3.9"
+groups = ["main"]
+markers = "extra == \"qmatchatea\""
 files = [
-    {file = "qiskit-1.4.2-cp39-abi3-macosx_10_12_x86_64.whl", hash = "sha256:310d0fa8a3fbb8f6f0e09ba61602e28cf49d084f2b28a20fc965ee966ed79e4e"},
-    {file = "qiskit-1.4.2-cp39-abi3-macosx_11_0_arm64.whl", hash = "sha256:e079f49557b46e7bef42294477aa16d790d16d4feb6841ed440022e8055ea128"},
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-    {file = "qiskit-1.4.2-cp39-abi3-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl", hash = "sha256:ced4c2229bcf5c47f83f9a5003a97ad5fb69bbb2e7cc9b93ac8b9d2023e79c85"},
-    {file = "qiskit-1.4.2-cp39-abi3-manylinux_2_17_s390x.manylinux2014_s390x.whl", hash = "sha256:d7b8e6850d806ab56316e64292b099885677ffc0ccdde3c3aafd48096cbb620a"},
-    {file = "qiskit-1.4.2-cp39-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:8ca3a5b7b7b8079d91daafa60f5f1283cc0dfddc86a78e8fbcd47efbebbfd5ad"},
-    {file = "qiskit-1.4.2-cp39-abi3-win32.whl", hash = "sha256:57c4922863d50109da28ba5de0fc720c16c8b47ed20c69fe51cfa9919d1d22b2"},
-    {file = "qiskit-1.4.2-cp39-abi3-win_amd64.whl", hash = "sha256:4d8043ac40302470fd9c275091a4cd11fd70108f4b70e89fe2764da6281299e1"},
-    {file = "qiskit-1.4.2.tar.gz", hash = "sha256:3cc75cd39d524dfff695d72c7589dfaf945d112ab9e4d4e6a4c06d6ffd439d2f"},
+    {file = "qiskit-1.4.3-cp39-abi3-macosx_10_12_x86_64.whl", hash = "sha256:65caf291bbe93f136b85281cb4a807c138fc4315fc17bdda9382cb4bfa18abdf"},
+    {file = "qiskit-1.4.3-cp39-abi3-macosx_11_0_arm64.whl", hash = "sha256:6e9f41eca2f4d522f59e48a47eb8b81ed3fdd35f56cefb41cc0db47768ccde47"},
+    {file = "qiskit-1.4.3-cp39-abi3-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:a04c6baca379bae8e6fc626bd06f0dda3f2ee7961205839b5a431b7f8d1e3978"},
+    {file = "qiskit-1.4.3-cp39-abi3-manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:4ca6eeaf29ae2cf3789e7474b062845c59c6e4164276569949f9170cfcaec6b1"},
+    {file = "qiskit-1.4.3-cp39-abi3-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl", hash = "sha256:bc82934e5b5192a75adca57bfa8194166e6bce1023da3b82e02db6c279a5d0fc"},
+    {file = "qiskit-1.4.3-cp39-abi3-manylinux_2_17_s390x.manylinux2014_s390x.whl", hash = "sha256:03355819fb9747a937bfffb0aba59d44c4654536b87c62dcd00d4e4e1550190f"},
+    {file = "qiskit-1.4.3-cp39-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:8d90b25ad017839b0bf1b5d05d8bd4066b7f83e3c14839947994f5fd56a5f5e2"},
+    {file = "qiskit-1.4.3-cp39-abi3-win32.whl", hash = "sha256:74cb30e34189ca9c1263994705a0cf8d97cead5f7375dedab3be4e783173785d"},
+    {file = "qiskit-1.4.3-cp39-abi3-win_amd64.whl", hash = "sha256:554b5ad8c6198881923998fd0124660eec534c985c731d1e3c09c6421377c29e"},
+    {file = "qiskit-1.4.3.tar.gz", hash = "sha256:e4e311190c159578f253d219dc860241ccb71955ca08725bb092c74cf7fbdac5"},
 ]
 
 [package.dependencies]
@@ -2152,6 +2299,8 @@ version = "1.4.3"
 description = "Quantum matcha TEA python library for tensor network emulation of quantum circuits."
 optional = true
 python-versions = ">=3.11"
+groups = ["main"]
+markers = "extra == \"qmatchatea\""
 files = [
     {file = "qmatchatea-1.4.3-py3-none-any.whl", hash = "sha256:11712e476604844536879ee7d96362a84458d1ad9c74d4cbf5925fe06f8945bd"},
     {file = "qmatchatea-1.4.3.tar.gz", hash = "sha256:3aea3d2508cb8a1e592d2de008d2994bb7a38b42fb6bfc8e0512ff5b2b252919"},
@@ -2169,13 +2318,15 @@ scipy = ">=1.4.1"
 
 [[package]]
 name = "qredtea"
-version = "0.2.4"
+version = "0.2.5"
 description = "Quantum TEA's python tensor library beyond numpy/cupy"
 optional = true
 python-versions = ">=3.11"
+groups = ["main"]
+markers = "extra == \"qmatchatea\""
 files = [
-    {file = "qredtea-0.2.4-py3-none-any.whl", hash = "sha256:f64325936ec09870a155bcd84556e6c967cfdbe6996f2bfb964cdfe0d8e133af"},
-    {file = "qredtea-0.2.4.tar.gz", hash = "sha256:0055e8c3efdb985c0ca9f9d111c45a4f6feeab083e709b0c3ccda9d0f31f5ec5"},
+    {file = "qredtea-0.2.5-py3-none-any.whl", hash = "sha256:13b7316045cb837a635ac3a13f4fb684b21c6a9a7bff1e7cb623281778979a72"},
+    {file = "qredtea-0.2.5.tar.gz", hash = "sha256:13663b59616b4c44e3b1c3cdd3af5803b713e38212fd60156fbcac514162dbdc"},
 ]
 
 [package.dependencies]
@@ -2184,18 +2335,20 @@ joblib = "*"
 matplotlib = "*"
 mpmath = "*"
 numpy = "*"
-qtealeaves = ">=1.5.8,<1.6.0"
+qtealeaves = ">=1.5.21,<1.6.0"
 scipy = "*"
 
 [[package]]
 name = "qtealeaves"
-version = "1.5.18"
+version = "1.5.21"
 description = "Quantum TEA's python tensor network library"
 optional = true
 python-versions = ">=3.11"
+groups = ["main"]
+markers = "extra == \"qmatchatea\""
 files = [
-    {file = "qtealeaves-1.5.18-py3-none-any.whl", hash = "sha256:6f01fdc9d74b0b55166aa1bcf962b272f5a6c7f661cd25208d57cf8ec1f4d813"},
-    {file = "qtealeaves-1.5.18.tar.gz", hash = "sha256:5f38a8f240e74c7d23c753765061bd812a7cf30ec101fcff35b5e7626f43eb1c"},
+    {file = "qtealeaves-1.5.21-py3-none-any.whl", hash = "sha256:b81a773a6d2665868c9293385aac506ab5f923c335d5a55b1560241b70db04b8"},
+    {file = "qtealeaves-1.5.21.tar.gz", hash = "sha256:9f20d406ad0280bad923d1e624ad5dc4237c104aafb1807a3b1e7aa2b23c3f79"},
 ]
 
 [package.dependencies]
@@ -2208,18 +2361,19 @@ scipy = "*"
 
 [[package]]
 name = "quimb"
-version = "1.10.0"
+version = "1.11.1"
 description = "Quantum information and many-body library."
 optional = false
 python-versions = ">=3.9"
+groups = ["main"]
 files = [
-    {file = "quimb-1.10.0-py3-none-any.whl", hash = "sha256:4d270e71c9f03a4a41862682fbffcd076c61d7e40c4b3785a31ae869ce8830c4"},
-    {file = "quimb-1.10.0.tar.gz", hash = "sha256:e79f1be2f9895d966479ccabbd5ec087fc047baad83d3fb08fed264e2d7cc3ff"},
+    {file = "quimb-1.11.1-py3-none-any.whl", hash = "sha256:232f7db08436fc05d86111d863458c4659ace0e5949c63f5e5f9248064c15c9d"},
+    {file = "quimb-1.11.1.tar.gz", hash = "sha256:8f3ff7630c4a2b50781d068bfe55dfbb58cf694886707ce95c245a21e7126ee8"},
 ]
 
 [package.dependencies]
 autoray = ">=0.6.12"
-cotengra = ">=0.6.1"
+cotengra = ">=0.7.1"
 cytoolz = ">=0.8.0"
 matplotlib = {version = ">=2.0", optional = true, markers = "extra == \"tensor\""}
 networkx = {version = ">=2.3", optional = true, markers = "extra == \"tensor\""}
@@ -2231,24 +2385,25 @@ tqdm = ">=4"
 
 [package.extras]
 advanced-solvers = ["mpi4py", "petsc4py", "slepc4py"]
-docs = ["astroid (<3.0.0)", "autoray (>=0.6.12)", "cotengra (>=0.6.1)", "doc2dash (>=2.4.1)", "furo", "ipython (!=8.7.0)", "myst-nb", "setuptools-scm", "sphinx (>=2.0)", "sphinx-autoapi", "sphinx-copybutton", "sphinx-design"]
+docs = ["astroid (<3.0.0)", "autoray (>=0.6.12)", "cotengra (>=0.7.1)", "doc2dash (>=2.4.1)", "furo", "ipython (!=8.7.0)", "myst-nb", "setuptools-scm", "sphinx (>=2.0)", "sphinx-autoapi", "sphinx-copybutton", "sphinx-design"]
 tensor = ["matplotlib (>=2.0)", "networkx (>=2.3)"]
 tests = ["coverage", "pytest", "pytest-cov"]
 
 [[package]]
 name = "requests"
-version = "2.32.3"
+version = "2.32.4"
 description = "Python HTTP for Humans."
 optional = false
 python-versions = ">=3.8"
+groups = ["docs"]
 files = [
-    {file = "requests-2.32.3-py3-none-any.whl", hash = "sha256:70761cfe03c773ceb22aa2f671b4757976145175cdfca038c02654d061d6dcc6"},
-    {file = "requests-2.32.3.tar.gz", hash = "sha256:55365417734eb18255590a9ff9eb97e9e1da868d4ccd6402399eaf68af20a760"},
+    {file = "requests-2.32.4-py3-none-any.whl", hash = "sha256:27babd3cda2a6d50b30443204ee89830707d396671944c998b5975b031ac2b2c"},
+    {file = "requests-2.32.4.tar.gz", hash = "sha256:27d0316682c8a29834d3264820024b62a36942083d52caf2f14c0591336d3422"},
 ]
 
 [package.dependencies]
 certifi = ">=2017.4.17"
-charset-normalizer = ">=2,<4"
+charset_normalizer = ">=2,<4"
 idna = ">=2.5,<4"
 urllib3 = ">=1.21.1,<3"
 
@@ -2262,6 +2417,8 @@ version = "0.16.0"
 description = "A python graph library implemented in Rust"
 optional = true
 python-versions = ">=3.9"
+groups = ["main"]
+markers = "extra == \"qmatchatea\""
 files = [
     {file = "rustworkx-0.16.0-cp39-abi3-macosx_10_12_x86_64.whl", hash = "sha256:476a6c67b0142acd941691943750cc6737a48372304489969c2b62d30aaf4c27"},
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@@ -2286,86 +2443,98 @@ mpl = ["matplotlib (>=3.0)"]
 
 [[package]]
 name = "scipy"
-version = "1.15.2"
+version = "1.16.1"
 description = "Fundamental algorithms for scientific computing in Python"
 optional = false
-python-versions = ">=3.10"
+python-versions = ">=3.11"
+groups = ["main"]
 files = [
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 doc = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "pygments-github-lexers (==0.0.5)", "pyproject-hooks (!=1.1)", "rst.linker (>=1.9)", "sphinx (>=3.5)", "sphinx-favicon", "sphinx-inline-tabs", "sphinx-lint", "sphinx-notfound-page (>=1,<2)", "sphinx-reredirects", "sphinxcontrib-towncrier", "towncrier (<24.7)"]
 enabler = ["pytest-enabler (>=2.2)"]
-test = ["build[virtualenv] (>=1.0.3)", "filelock (>=3.4.0)", "ini2toml[lite] (>=0.14)", "jaraco.develop (>=7.21)", "jaraco.envs (>=2.2)", "jaraco.path (>=3.7.2)", "jaraco.test (>=5.5)", "packaging (>=24.2)", "pip (>=19.1)", "pyproject-hooks (!=1.1)", "pytest (>=6,!=8.1.*)", "pytest-home (>=0.5)", "pytest-perf", "pytest-subprocess", "pytest-timeout", "pytest-xdist (>=3)", "tomli-w (>=1.0.0)", "virtualenv (>=13.0.0)", "wheel (>=0.44.0)"]
-type = ["importlib_metadata (>=7.0.2)", "jaraco.develop (>=7.21)", "mypy (==1.14.*)", "pytest-mypy"]
+test = ["build[virtualenv] (>=1.0.3)", "filelock (>=3.4.0)", "ini2toml[lite] (>=0.14)", "jaraco.develop (>=7.21) ; python_version >= \"3.9\" and sys_platform != \"cygwin\"", "jaraco.envs (>=2.2)", "jaraco.path (>=3.7.2)", "jaraco.test (>=5.5)", "packaging (>=24.2)", "pip (>=19.1)", "pyproject-hooks (!=1.1)", "pytest (>=6,!=8.1.*)", "pytest-home (>=0.5)", "pytest-perf ; sys_platform != \"cygwin\"", "pytest-subprocess", "pytest-timeout", "pytest-xdist (>=3)", "tomli-w (>=1.0.0)", "virtualenv (>=13.0.0)", "wheel (>=0.44.0)"]
+type = ["importlib_metadata (>=7.0.2) ; python_version < \"3.10\"", "jaraco.develop (>=7.21) ; sys_platform != \"cygwin\"", "mypy (==1.14.*)", "pytest-mypy"]
 
 [[package]]
 name = "six"
@@ -2373,6 +2542,7 @@ version = "1.17.0"
 description = "Python 2 and 3 compatibility utilities"
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,>=2.7"
+groups = ["main"]
 files = [
     {file = "six-1.17.0-py2.py3-none-any.whl", hash = "sha256:4721f391ed90541fddacab5acf947aa0d3dc7d27b2e1e8eda2be8970586c3274"},
     {file = "six-1.17.0.tar.gz", hash = "sha256:ff70335d468e7eb6ec65b95b99d3a2836546063f63acc5171de367e834932a81"},
@@ -2380,24 +2550,26 @@ files = [
 
 [[package]]
 name = "snowballstemmer"
-version = "2.2.0"
-description = "This package provides 29 stemmers for 28 languages generated from Snowball algorithms."
+version = "3.0.1"
+description = "This package provides 32 stemmers for 30 languages generated from Snowball algorithms."
 optional = false
-python-versions = "*"
+python-versions = "!=3.0.*,!=3.1.*,!=3.2.*"
+groups = ["docs"]
 files = [
-    {file = "snowballstemmer-2.2.0-py2.py3-none-any.whl", hash = "sha256:c8e1716e83cc398ae16824e5572ae04e0d9fc2c6b985fb0f900f5f0c96ecba1a"},
-    {file = "snowballstemmer-2.2.0.tar.gz", hash = "sha256:09b16deb8547d3412ad7b590689584cd0fe25ec8db3be37788be3810cbf19cb1"},
+    {file = "snowballstemmer-3.0.1-py3-none-any.whl", hash = "sha256:6cd7b3897da8d6c9ffb968a6781fa6532dce9c3618a4b127d920dab764a19064"},
+    {file = "snowballstemmer-3.0.1.tar.gz", hash = "sha256:6d5eeeec8e9f84d4d56b847692bacf79bc2c8e90c7f80ca4444ff8b6f2e52895"},
 ]
 
 [[package]]
 name = "soupsieve"
-version = "2.6"
+version = "2.7"
 description = "A modern CSS selector implementation for Beautiful Soup."
 optional = false
 python-versions = ">=3.8"
+groups = ["docs"]
 files = [
-    {file = "soupsieve-2.6-py3-none-any.whl", hash = "sha256:e72c4ff06e4fb6e4b5a9f0f55fe6e81514581fca1515028625d0f299c602ccc9"},
-    {file = "soupsieve-2.6.tar.gz", hash = "sha256:e2e68417777af359ec65daac1057404a3c8a5455bb8abc36f1a9866ab1a51abb"},
+    {file = "soupsieve-2.7-py3-none-any.whl", hash = "sha256:6e60cc5c1ffaf1cebcc12e8188320b72071e922c2e897f737cadce79ad5d30c4"},
+    {file = "soupsieve-2.7.tar.gz", hash = "sha256:ad282f9b6926286d2ead4750552c8a6142bc4c783fd66b0293547c8fe6ae126a"},
 ]
 
 [[package]]
@@ -2406,6 +2578,7 @@ version = "5.3.0"
 description = "Python documentation generator"
 optional = false
 python-versions = ">=3.6"
+groups = ["docs"]
 files = [
     {file = "Sphinx-5.3.0.tar.gz", hash = "sha256:51026de0a9ff9fc13c05d74913ad66047e104f56a129ff73e174eb5c3ee794b5"},
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@@ -2432,7 +2605,7 @@ sphinxcontrib-serializinghtml = ">=1.1.5"
 [package.extras]
 docs = ["sphinxcontrib-websupport"]
 lint = ["docutils-stubs", "flake8 (>=3.5.0)", "flake8-bugbear", "flake8-comprehensions", "flake8-simplify", "isort", "mypy (>=0.981)", "sphinx-lint", "types-requests", "types-typed-ast"]
-test = ["cython", "html5lib", "pytest (>=4.6)", "typed_ast"]
+test = ["cython", "html5lib", "pytest (>=4.6)", "typed_ast ; python_version < \"3.8\""]
 
 [[package]]
 name = "sphinx-basic-ng"
@@ -2440,6 +2613,7 @@ version = "1.0.0b2"
 description = "A modern skeleton for Sphinx themes."
 optional = false
 python-versions = ">=3.7"
+groups = ["docs"]
 files = [
     {file = "sphinx_basic_ng-1.0.0b2-py3-none-any.whl", hash = "sha256:eb09aedbabfb650607e9b4b68c9d240b90b1e1be221d6ad71d61c52e29f7932b"},
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@@ -2457,6 +2631,7 @@ version = "0.5.2"
 description = "Add a copy button to each of your code cells."
 optional = false
 python-versions = ">=3.7"
+groups = ["docs"]
 files = [
     {file = "sphinx-copybutton-0.5.2.tar.gz", hash = "sha256:4cf17c82fb9646d1bc9ca92ac280813a3b605d8c421225fd9913154103ee1fbd"},
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@@ -2475,6 +2650,7 @@ version = "2.0.0"
 description = "sphinxcontrib-applehelp is a Sphinx extension which outputs Apple help books"
 optional = false
 python-versions = ">=3.9"
+groups = ["docs"]
 files = [
     {file = "sphinxcontrib_applehelp-2.0.0-py3-none-any.whl", hash = "sha256:4cd3f0ec4ac5dd9c17ec65e9ab272c9b867ea77425228e68ecf08d6b28ddbdb5"},
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@@ -2487,20 +2663,24 @@ test = ["pytest"]
 
 [[package]]
 name = "sphinxcontrib-bibtex"
-version = "2.5.0"
+version = "2.6.5"
 description = "Sphinx extension for BibTeX style citations."
 optional = false
-python-versions = ">=3.6"
+python-versions = ">=3.9"
+groups = ["docs"]
 files = [
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+    {file = "sphinxcontrib_bibtex-2.6.5-py3-none-any.whl", hash = "sha256:455ea4509642ea0b28ede3721550273626f85af65af01f161bfd8e19dc1edd7d"},
+    {file = "sphinxcontrib_bibtex-2.6.5.tar.gz", hash = "sha256:9b3224dd6fece9268ebd8c905dc0a83ff2f6c54148a9235fe70e9d1e9ff149c0"},
 ]
 
 [package.dependencies]
-docutils = ">=0.8"
-pybtex = ">=0.24"
+docutils = ">=0.8,<0.18.dev0 || >=0.20.dev0"
+pybtex = ">=0.25"
 pybtex-docutils = ">=1.0.0"
-Sphinx = ">=2.1"
+Sphinx = ">=3.5"
+
+[package.extras]
+test = ["pytest", "pytest-cov", "sphinx-autoapi"]
 
 [[package]]
 name = "sphinxcontrib-devhelp"
@@ -2508,6 +2688,7 @@ version = "2.0.0"
 description = "sphinxcontrib-devhelp is a sphinx extension which outputs Devhelp documents"
 optional = false
 python-versions = ">=3.9"
+groups = ["docs"]
 files = [
     {file = "sphinxcontrib_devhelp-2.0.0-py3-none-any.whl", hash = "sha256:aefb8b83854e4b0998877524d1029fd3e6879210422ee3780459e28a1f03a8a2"},
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@@ -2524,6 +2705,7 @@ version = "2.1.0"
 description = "sphinxcontrib-htmlhelp is a sphinx extension which renders HTML help files"
 optional = false
 python-versions = ">=3.9"
+groups = ["docs"]
 files = [
     {file = "sphinxcontrib_htmlhelp-2.1.0-py3-none-any.whl", hash = "sha256:166759820b47002d22914d64a075ce08f4c46818e17cfc9470a9786b759b19f8"},
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@@ -2540,6 +2722,7 @@ version = "1.0.1"
 description = "A sphinx extension which renders display math in HTML via JavaScript"
 optional = false
 python-versions = ">=3.5"
+groups = ["docs"]
 files = [
     {file = "sphinxcontrib-jsmath-1.0.1.tar.gz", hash = "sha256:a9925e4a4587247ed2191a22df5f6970656cb8ca2bd6284309578f2153e0c4b8"},
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@@ -2550,13 +2733,14 @@ test = ["flake8", "mypy", "pytest"]
 
 [[package]]
 name = "sphinxcontrib-katex"
-version = "0.9.10"
+version = "0.9.11"
 description = "A Sphinx extension for rendering math in HTML pages"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.9"
+groups = ["docs"]
 files = [
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+    {file = "sphinxcontrib_katex-0.9.11-py3-none-any.whl", hash = "sha256:b0a318d86b8f43314ccdd481ce0db90283ac51f51afd9479969f36a0c291f44e"},
+    {file = "sphinxcontrib_katex-0.9.11.tar.gz", hash = "sha256:2d32b210d20bbee451a51d19645f6fef5f5568b9a54e2813affb96efa661238a"},
 ]
 
 [package.dependencies]
@@ -2568,6 +2752,7 @@ version = "2.0.0"
 description = "sphinxcontrib-qthelp is a sphinx extension which outputs QtHelp documents"
 optional = false
 python-versions = ">=3.9"
+groups = ["docs"]
 files = [
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@@ -2584,6 +2769,7 @@ version = "2.0.0"
 description = "sphinxcontrib-serializinghtml is a sphinx extension which outputs \"serialized\" HTML files (json and pickle)"
 optional = false
 python-versions = ">=3.9"
+groups = ["docs"]
 files = [
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@@ -2596,68 +2782,69 @@ test = ["pytest"]
 
 [[package]]
 name = "sqlalchemy"
-version = "2.0.40"
+version = "2.0.42"
 description = "Database Abstraction Library"
 optional = false
 python-versions = ">=3.7"
+groups = ["main"]
 files = [
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 [package.dependencies]
@@ -2695,6 +2882,8 @@ version = "5.4.1"
 description = "Manage dynamic plugins for Python applications"
 optional = true
 python-versions = ">=3.9"
+groups = ["main"]
+markers = "extra == \"qmatchatea\""
 files = [
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@@ -2709,6 +2898,8 @@ version = "0.13.0"
 description = "Python library providing wrappers to SymEngine"
 optional = true
 python-versions = "<4,>=3.8"
+groups = ["main"]
+markers = "extra == \"qmatchatea\""
 files = [
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@@ -2756,13 +2947,14 @@ files = [
 
 [[package]]
 name = "sympy"
-version = "1.13.3"
+version = "1.14.0"
 description = "Computer algebra system (CAS) in Python"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
+groups = ["main"]
 files = [
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 [package.dependencies]
@@ -2777,6 +2969,7 @@ version = "0.9.0"
 description = "Pretty-print tabular data"
 optional = false
 python-versions = ">=3.7"
+groups = ["main"]
 files = [
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@@ -2787,13 +2980,14 @@ widechars = ["wcwidth"]
 
 [[package]]
 name = "tomlkit"
-version = "0.13.2"
+version = "0.13.3"
 description = "Style preserving TOML library"
 optional = false
 python-versions = ">=3.8"
+groups = ["analysis"]
 files = [
-    {file = "tomlkit-0.13.2-py3-none-any.whl", hash = "sha256:7a974427f6e119197f670fbbbeae7bef749a6c14e793db934baefc1b5f03efde"},
-    {file = "tomlkit-0.13.2.tar.gz", hash = "sha256:fff5fe59a87295b278abd31bec92c15d9bc4a06885ab12bcea52c71119392e79"},
+    {file = "tomlkit-0.13.3-py3-none-any.whl", hash = "sha256:c89c649d79ee40629a9fda55f8ace8c6a1b42deb912b2a8fd8d942ddadb606b0"},
+    {file = "tomlkit-0.13.3.tar.gz", hash = "sha256:430cf247ee57df2b94ee3fbe588e71d362a941ebb545dec29b53961d61add2a1"},
 ]
 
 [[package]]
@@ -2802,6 +2996,7 @@ version = "1.0.0"
 description = "List processing tools and functional utilities"
 optional = false
 python-versions = ">=3.8"
+groups = ["main"]
 files = [
     {file = "toolz-1.0.0-py3-none-any.whl", hash = "sha256:292c8f1c4e7516bf9086f8850935c799a874039c8bcf959d47b600e4c44a6236"},
     {file = "toolz-1.0.0.tar.gz", hash = "sha256:2c86e3d9a04798ac556793bced838816296a2f085017664e4995cb40a1047a02"},
@@ -2813,6 +3008,7 @@ version = "4.67.1"
 description = "Fast, Extensible Progress Meter"
 optional = false
 python-versions = ">=3.7"
+groups = ["main"]
 files = [
     {file = "tqdm-4.67.1-py3-none-any.whl", hash = "sha256:26445eca388f82e72884e0d580d5464cd801a3ea01e63e5601bdff9ba6a48de2"},
     {file = "tqdm-4.67.1.tar.gz", hash = "sha256:f8aef9c52c08c13a65f30ea34f4e5aac3fd1a34959879d7e59e63027286627f2"},
@@ -2834,6 +3030,7 @@ version = "5.14.3"
 description = "Traitlets Python configuration system"
 optional = false
 python-versions = ">=3.8"
+groups = ["dev"]
 files = [
     {file = "traitlets-5.14.3-py3-none-any.whl", hash = "sha256:b74e89e397b1ed28cc831db7aea759ba6640cb3de13090ca145426688ff1ac4f"},
     {file = "traitlets-5.14.3.tar.gz", hash = "sha256:9ed0579d3502c94b4b3732ac120375cda96f923114522847de4b3bb98b96b6b7"},
@@ -2845,28 +3042,30 @@ test = ["argcomplete (>=3.0.3)", "mypy (>=1.7.0)", "pre-commit", "pytest (>=7.0,
 
 [[package]]
 name = "typing-extensions"
-version = "4.13.2"
-description = "Backported and Experimental Type Hints for Python 3.8+"
+version = "4.14.1"
+description = "Backported and Experimental Type Hints for Python 3.9+"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
+groups = ["main", "docs"]
 files = [
-    {file = "typing_extensions-4.13.2-py3-none-any.whl", hash = "sha256:a439e7c04b49fec3e5d3e2beaa21755cadbbdc391694e28ccdd36ca4a1408f8c"},
-    {file = "typing_extensions-4.13.2.tar.gz", hash = "sha256:e6c81219bd689f51865d9e372991c540bda33a0379d5573cddb9a3a23f7caaef"},
+    {file = "typing_extensions-4.14.1-py3-none-any.whl", hash = "sha256:d1e1e3b58374dc93031d6eda2420a48ea44a36c2b4766a4fdeb3710755731d76"},
+    {file = "typing_extensions-4.14.1.tar.gz", hash = "sha256:38b39f4aeeab64884ce9f74c94263ef78f3c22467c8724005483154c26648d36"},
 ]
 
 [[package]]
 name = "urllib3"
-version = "2.3.0"
+version = "2.5.0"
 description = "HTTP library with thread-safe connection pooling, file post, and more."
 optional = false
 python-versions = ">=3.9"
+groups = ["docs"]
 files = [
-    {file = "urllib3-2.3.0-py3-none-any.whl", hash = "sha256:1cee9ad369867bfdbbb48b7dd50374c0967a0bb7710050facf0dd6911440e3df"},
-    {file = "urllib3-2.3.0.tar.gz", hash = "sha256:f8c5449b3cf0861679ce7e0503c7b44b5ec981bec0d1d3795a07f1ba96f0204d"},
+    {file = "urllib3-2.5.0-py3-none-any.whl", hash = "sha256:e6b01673c0fa6a13e374b50871808eb3bf7046c4b125b216f6bf1cc604cff0dc"},
+    {file = "urllib3-2.5.0.tar.gz", hash = "sha256:3fc47733c7e419d4bc3f6b3dc2b4f890bb743906a30d56ba4a5bfa4bbff92760"},
 ]
 
 [package.extras]
-brotli = ["brotli (>=1.0.9)", "brotlicffi (>=0.8.0)"]
+brotli = ["brotli (>=1.0.9) ; platform_python_implementation == \"CPython\"", "brotlicffi (>=0.8.0) ; platform_python_implementation != \"CPython\""]
 h2 = ["h2 (>=4,<5)"]
 socks = ["pysocks (>=1.5.6,!=1.5.7,<2.0)"]
 zstd = ["zstandard (>=0.18.0)"]
@@ -2877,6 +3076,7 @@ version = "0.2.13"
 description = "Measures the displayed width of unicode strings in a terminal"
 optional = false
 python-versions = "*"
+groups = ["dev"]
 files = [
     {file = "wcwidth-0.2.13-py2.py3-none-any.whl", hash = "sha256:3da69048e4540d84af32131829ff948f1e022c1c6bdb8d6102117aac784f6859"},
     {file = "wcwidth-0.2.13.tar.gz", hash = "sha256:72ea0c06399eb286d978fdedb6923a9eb47e1c486ce63e9b4e64fc18303972b5"},
@@ -2884,9 +3084,9 @@ files = [
 
 [extras]
 cuda = ["cupy-cuda11x", "cuquantum-python-cu11"]
-qmatchatea = ["qmatchatea"]
+qmatchatea = ["qiskit", "qmatchatea", "qtealeaves"]
 
 [metadata]
-lock-version = "2.0"
+lock-version = "2.1"
 python-versions = ">=3.11,<3.14"
-content-hash = "b568f966fb6f195f89aecd8583582ab7b801784dacbea947c65634cb643918cf"
+content-hash = "fa9982c6a663449880e90e3a0d7ec5782283d27a324d9b41c42d4616ded66048"
diff --git a/pyproject.toml b/pyproject.toml
index 7133e6b..efb39ca 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -26,11 +26,13 @@ quimb = { version = "^1.10.0", extras = ["tensor"] }
 cupy-cuda11x = { version = "^13.1.0", optional = true }
 cuquantum-python-cu11 = { version = "^24.1.0", optional = true }
 qmatchatea = { version = "^1.4.3", optional = true }
+qiskit = { version = "^1.4.0", optional = true }
+qtealeaves = { version = "^1.5.20", optional = true }
 
 
 [tool.poetry.extras]
 cuda = ["cupy-cuda11x", "cuquantum-python-cu11", "mpi4py"]
-qmatchatea = ["qmatchatea"]
+qmatchatea = ["qmatchatea", "qtealeaves", "qiskit"]
 
 [tool.poetry.group.docs]
 optional = true

From f0b28d87c409997fe67e5901a362ccbefdadd678 Mon Sep 17 00:00:00 2001
From: MatteoRobbiati <robbiati.matteo@gmail.com>
Date: Wed, 30 Jul 2025 10:05:45 +0200
Subject: [PATCH 02/33] fix: remove runcard argument from qmatchatea backend
 and fix self.precision in the same backend

---
 src/qibotn/backends/__init__.py   | 2 +-
 src/qibotn/backends/qmatchatea.py | 4 +++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/qibotn/backends/__init__.py b/src/qibotn/backends/__init__.py
index 1547a3d..416a384 100644
--- a/src/qibotn/backends/__init__.py
+++ b/src/qibotn/backends/__init__.py
@@ -26,7 +26,7 @@ class MetaBackend:
         if platform == "cutensornet":  # pragma: no cover
             return CuTensorNet(runcard)
         elif platform == "quimb":  # pragma: no cover
-            return QuimbBackend(runcard)
+            return QuimbBackend()
         elif platform == "qmatchatea":  # pragma: no cover
             from qibotn.backends.qmatchatea import QMatchaTeaBackend
 
diff --git a/src/qibotn/backends/qmatchatea.py b/src/qibotn/backends/qmatchatea.py
index 27239ec..a5261f4 100644
--- a/src/qibotn/backends/qmatchatea.py
+++ b/src/qibotn/backends/qmatchatea.py
@@ -23,6 +23,9 @@ class QMatchaTeaBackend(QibotnBackend, NumpyBackend):
         self.name = "qibotn"
         self.platform = "qmatchatea"
 
+        # Default precision
+        self.precision = "double"
+
         # Set default configurations
         self.configure_tn_simulation()
         self._setup_backend_specifics()
@@ -87,7 +90,6 @@ class QMatchaTeaBackend(QibotnBackend, NumpyBackend):
 
         # TODO: once MPI is available for Python, integrate it here
         self.qmatchatea_backend = qmatchatea.QCBackend(
-            backend="PY",  # The only alternative is Fortran, but we use Python here
             precision=qmatchatea_precision,
             device=qmatchatea_device,
             ansatz=self.ansatz,

From 1fa1730fb3e69f6d03b2f9e28c6ab92231448622 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Fri, 5 Sep 2025 17:18:18 +0200
Subject: [PATCH 03/33] fix: prevent error when nshots=None. In that case
 frequencies and probabilities are set to None

---
 src/qibotn/backends/quimb.py | 30 ++++++++++++++++++------------
 1 file changed, 18 insertions(+), 12 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index fdbb387..6f6826d 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -112,18 +112,24 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             circuit.to_qasm(), psi0=initial_state
         )
 
-        frequencies = Counter(circ_quimb.sample(nshots)) if nshots is not None else None
-        main_frequencies = {
-            state: count
-            for state, count in frequencies.most_common(self.n_most_frequent_states)
-        }
-        computational_states = [state for state in main_frequencies.keys()]
-        amplitudes = {
-            state: circ_quimb.amplitude(state) for state in computational_states
-        }
-        measured_probabilities = {
-            state: abs(amplitude) ** 2 for state, amplitude in amplitudes.items()
-        }
+        if nshots:
+            frequencies = Counter(circ_quimb.sample(nshots))
+            main_frequencies = {
+                state: count
+                for state, count in frequencies.most_common(
+                    self.n_most_frequent_states
+                )
+            }
+            computational_states = list(main_frequencies.keys())
+            amplitudes = {
+                state: circ_quimb.amplitude(state) for state in computational_states
+            }
+            measured_probabilities = {
+                state: abs(amplitude) ** 2 for state, amplitude in amplitudes.items()
+            }
+        else:
+            frequencies = None
+            measured_probabilities = None
 
         statevector = circ_quimb.to_dense() if return_array else None
         return TensorNetworkResult(

From 5e141b200aea728565983cdaee5582f4db5a29d7 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Mon, 8 Sep 2025 18:25:08 +0200
Subject: [PATCH 04/33] feat: added expectiation function to compute
 expectation value of a symbolic hamiltonian using quimb backend. Added
 function to convers Qibo symbolic hamiltonian in Quimb compatible list of
 observables. Added a grouping function to combine in a single list local
 observables acting on the same qubits, to allow Quimb to compute them all in
 a single contraction (not working for MPS ansatz). Also added argument in
 setup_backend_specifics to specify an optimizer.

---
 src/qibotn/backends/quimb.py | 156 ++++++++++++++++++++++++++++++++---
 1 file changed, 146 insertions(+), 10 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 6f6826d..f9fe009 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -1,12 +1,16 @@
-from collections import Counter
+import re
+from collections import Counter, defaultdict
 
+import numpy as np
 import quimb.tensor as qtn
+import quimb as qu
 from qibo.backends import NumpyBackend
 from qibo.config import raise_error
 from qibo.result import QuantumState
 
 from qibotn.backends.abstract import QibotnBackend
 from qibotn.result import TensorNetworkResult
+import warnings
 
 
 class QuimbBackend(QibotnBackend, NumpyBackend):
@@ -22,7 +26,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
 
     def configure_tn_simulation(
         self,
-        ansatz: str = "MPS",
+        ansatz: str = "any",
         max_bond_dimension: int = 10,
         n_most_frequent_states: int = 100,
     ):
@@ -31,7 +35,8 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
 
         Args:
             ansatz : str, optional
-                The tensor network ansatz to use. Currently, only "MPS" is supported. Default is "MPS".
+                The tensor network ansatz to use. Currently, only "MPS" or "any" is supported. In the second case
+                the generic Circuit Quimb class is used.
             max_bond_dimension : int, optional
                 The maximum bond dimension for the MPS ansatz. Default is 10.
 
@@ -43,13 +48,16 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         self.max_bond_dimension = max_bond_dimension
         self.n_most_frequent_states = n_most_frequent_states
 
-    def setup_backend_specifics(self, qimb_backend="numpy"):
+    def setup_backend_specifics(self, qimb_backend="numpy", optimizer='auto-hq'):
         """Setup backend specifics.
         Args:
             qimb_backend: str
                 The backend to use for the quimb tensor network simulation.
+            optimizer: str, optional
+                The optimizer to use for the quimb tensor network simulation.
         """
         self.backend = qimb_backend
+        self.optimizer = optimizer
 
     def execute_circuit(
         self,
@@ -57,7 +65,6 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         initial_state=None,
         nshots=None,
         return_array=False,
-        **prob_kwargs,
     ):
         """
         Execute a quantum circuit using the specified tensor network ansatz and initial state.
@@ -71,10 +78,6 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
                 The number of shots for sampling the circuit. If None, no sampling is performed, and the full statevector is used.
             return_array : bool, optional
                 If True, returns the statevector as a dense array. Default is False.
-            n_most_frequent_states : int, optional
-                The number of most frequent computational basis states to return. Default is 100.
-            **prob_kwargs : dict, optional
-                Additional keyword arguments for probability computation (currently unused).
 
         Returns:
             TensorNetworkResult
@@ -131,7 +134,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             frequencies = None
             measured_probabilities = None
 
-        statevector = circ_quimb.to_dense() if return_array else None
+        statevector = circ_quimb.to_dense(backend=self.backend, optimize=self.optimizer) if return_array else None
         return TensorNetworkResult(
             nqubits=circuit.nqubits,
             backend=self,
@@ -140,3 +143,136 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             prob_type="default",
             statevector=statevector,
         )
+
+    def expectation(self, circuit, observable):
+        """Compute the expectation value of a Qibo-friendly ``observable`` on the Tensor Network constructed from a Qibo ``circuit``.
+
+        This method takes a Qibo-style symbolic Hamiltonian (e.g., `X(0)*Z(1) + 2.0*Y(2)*Z(0)`)
+        as the observable, converts it into a Quimb observable and computes its expectation
+        value using the provided circuit. In case of multiple terms on the same group of qubits, they can be computed in a single contraction.
+        A grouping procedure is applied to optimize the number of contractions performed.
+
+        Args:
+            circuit: A Qibo quantum circuit object on which the expectation value
+                is computed.
+            observable: The observable whose expectation value we want to compute.
+                This must be provided in the symbolic Hamiltonian form supported by Qibo
+                (e.g., `X(0)*Y(1)` or `Z(0)*Z(1) + 1.5*Y(2)`).
+
+        Returns:
+            float: The expectation value (real part).
+        """
+
+        # Map the Qibo observable to Quimb operators and group local operators on the same sites
+        # for computing them in a single contraction. This does not work with CircuitMPS for some now
+        # for Quimb 1.11.1
+        operators_list, sites_list, coeffs_list = self._qiboobs_to_quimbobs(observable)
+        sites_list_grouped, operators_list_grouped, coeffs_list_grouped = self._group_by_tuples(sites_list, operators_list, coeffs_list)
+
+        if self.ansatz == "MPS":
+            if len(sites_list)-len(sites_list_grouped) > 10:
+                warnings.warn(
+                    "More than 10 local operators on the same sites are not being grouped as this is not compatible with CircuitMPS. Expected value computation can be more efficient without an MPS ansatz."
+                )
+            circ_ansatz = (qtn.circuit.CircuitMPS)
+            circ = circ_ansatz.from_openqasm2_str(circuit.to_qasm())
+            expectation_value = 0.0
+            for ops, sites, coeffs in zip(operators_list, sites_list, coeffs_list):
+                exp_values = circ.local_expectation(ops, where=sites, backend=self.backend, optimize=self.optimizer)
+                expectation_value += np.dot(coeffs, exp_values)
+            return np.real(expectation_value)
+        
+        else:
+            circ_ansatz = qtn.circuit.Circuit
+            circ = circ_ansatz.from_openqasm2_str(circuit.to_qasm())
+            expectation_value = 0.0
+            for ops, sites, coeffs in zip(operators_list_grouped, sites_list_grouped, coeffs_list_grouped):
+                exp_values = circ.local_expectation(ops, where=sites, backend=self.backend, optimize=self.optimizer)
+                expectation_value += np.dot(coeffs, exp_values)
+            return np.real(expectation_value)
+
+    def _qiboobs_to_quimbobs(
+        self, 
+        hamiltonian
+    ):
+        """
+        Convert a Qibo SymbolicHamiltonian into a Quimb-compatible decomposition.
+
+        Returns three lists:
+        - operators_list: Quimb operators (tensor products of Pauli matrices).
+        - sites_list: tuples of qubit indices the operators act on.
+        - coeffs_list: coefficients for each term.
+        """
+
+        factor_pattern = re.compile(r"([^\d]+)(\d+)")
+
+        operators_list = []
+        sites_list = []
+        coeffs_list = []
+
+        for term in hamiltonian.terms:
+            coeff = term.coefficient
+            term_ops = []
+            term_sites = []
+
+            for factor in term.factors:
+                match = factor_pattern.match(str(factor))
+                if not match:
+                    raise ValueError(
+                        f"Factor '{str(factor)}' does not match the expected format."
+                    )
+
+                operator_name = match.group(1)
+                qubit_index = int(match.group(2))
+
+                # Build the single-qubit operator
+                if operator_name not in {"X", "Y", "Z", "I"}:
+                    raise ValueError(f"Unsupported operator {operator_name}")
+                op = qu.pauli(operator_name)
+
+                term_ops.append(op)
+                term_sites.append(qubit_index)
+
+            # Build the tensor product if more than one factor
+            if term_ops:
+                full_op = term_ops[0]
+                for op in term_ops[1:]:
+                    full_op = full_op & op
+            else:
+                # Identity term (just coefficient)
+                full_op = qu.eye(2)
+
+            operators_list.append(full_op)
+            sites_list.append(tuple(term_sites))
+            coeffs_list.append(coeff)
+
+        return operators_list, sites_list, coeffs_list
+    
+    def _group_by_tuples(self, A, B, C):
+        """
+        Groups the elements of B and C by the unique tuples in A.
+        
+        Parameters:
+            A (list of tuples): key tuples (can contain duplicates)
+            B (list): values aligned with A
+            C (list): values aligned with A
+        
+        Returns:
+            (A_new, B_new, C_new):
+                A_new: list of unique tuples
+                B_new: list of lists of grouped values from B
+                C_new: list of lists of grouped values from C
+        """
+
+        grouped_B = defaultdict(list)
+        grouped_C = defaultdict(list)
+
+        for a, b, c in zip(A, B, C):
+            grouped_B[a].append(b)
+            grouped_C[a].append(c)
+
+        A_new = list(grouped_B.keys())
+        B_new = list(grouped_B.values())
+        C_new = list(grouped_C.values())
+
+        return A_new, B_new, C_new

From b7c26f5a2ada9b7c322b346038780f628a5c3ae0 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Mon, 8 Sep 2025 18:26:54 +0200
Subject: [PATCH 05/33] added cotengra cash exclusion

---
 .gitignore | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/.gitignore b/.gitignore
index 7f051b8..39fb956 100644
--- a/.gitignore
+++ b/.gitignore
@@ -160,3 +160,6 @@ cython_debug/
 #  option (not recommended) you can uncomment the following to ignore the entire idea folder.
 #.idea/
 .devenv
+
+# Cotengra cache
+examples/quimb_intro/ctg_cache/
\ No newline at end of file

From 641277c62b21e3770be9cb48282b3879309118c0 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Mon, 8 Sep 2025 18:28:00 +0200
Subject: [PATCH 06/33] added tests for quimb backend

---
 .gitignore                                    |   3 -
 examples/quimb_intro/quimb_introduction.ipynb | 779 ++++++++++++++++++
 2 files changed, 779 insertions(+), 3 deletions(-)
 create mode 100644 examples/quimb_intro/quimb_introduction.ipynb

diff --git a/.gitignore b/.gitignore
index 39fb956..7f051b8 100644
--- a/.gitignore
+++ b/.gitignore
@@ -160,6 +160,3 @@ cython_debug/
 #  option (not recommended) you can uncomment the following to ignore the entire idea folder.
 #.idea/
 .devenv
-
-# Cotengra cache
-examples/quimb_intro/ctg_cache/
\ No newline at end of file
diff --git a/examples/quimb_intro/quimb_introduction.ipynb b/examples/quimb_intro/quimb_introduction.ipynb
new file mode 100644
index 0000000..6153e90
--- /dev/null
+++ b/examples/quimb_intro/quimb_introduction.ipynb
@@ -0,0 +1,779 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "656bb283-ac6d-48d2-a029-3c417c9961f8",
+   "metadata": {},
+   "source": [
+    "## Introduction to Quimb backend in QiboTN\n",
+    "\n",
+    "#### Some imports"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "6722d94e-e311-48f9-b6df-c6d829bf67fb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import time\n",
+    "import numpy as np\n",
+    "from scipy import stats\n",
+    "\n",
+    "import qibo\n",
+    "from qibo import Circuit, gates, hamiltonians\n",
+    "from qibo.backends import construct_backend"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a009a5e0-cfd4-4a49-9f7c-e82f252c6147",
+   "metadata": {},
+   "source": [
+    "#### Some hyper parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "b0a1da82",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import cotengra as ctg\n",
+    "ctg_opt = ctg.ReusableHyperOptimizer(\n",
+    "    max_time=10,\n",
+    "    minimize='combo',\n",
+    "    slicing_opts=None,\n",
+    "    parallel=True,\n",
+    "    progbar=True\n",
+    ")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "64162116-1555-4a68-811c-01593739d622",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# construct qibotn backend\n",
+    "quimb_backend = construct_backend(backend=\"qibotn\", platform=\"quimb\")\n",
+    "\n",
+    "# set number of qubits\n",
+    "nqubits = 25\n",
+    "\n",
+    "# set numpy random seed\n",
+    "np.random.seed(42)\n",
+    "\n",
+    "quimb_backend.setup_backend_specifics(\n",
+    "    qimb_backend=\"jax\", \n",
+    "    optimizer='auto-hq'\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "252f5cd1-5932-4de6-8076-4a357d50ebad",
+   "metadata": {},
+   "source": [
+    "#### Constructing a parametric quantum circuit"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "4a22a172-f50d-411d-afa3-fa61937c7b3a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def build_circuit(nqubits, nlayers):\n",
+    "    \"\"\"Construct a parametric quantum circuit.\"\"\"\n",
+    "    circ = Circuit(nqubits)\n",
+    "    for _ in range(nlayers):\n",
+    "        for q in range(nqubits):\n",
+    "            circ.add(gates.RY(q=q, theta=0.))\n",
+    "            circ.add(gates.RZ(q=q, theta=0.))\n",
+    "        [circ.add(gates.CNOT(q%nqubits, (q+1)%nqubits) for q in range(nqubits))]\n",
+    "    circ.add(gates.M(*range(nqubits)))\n",
+    "    return circ"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "76f23c57-6d08-496b-9a27-52fb63bbfcb1",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 :     ─RY─RZ─o───────────────────────────────────────────────X─RY─RZ─o────── ...\n",
+      "1 :     ─RY─RZ─X─o─────────────────────────────────────────────|─RY─RZ─X─o──── ...\n",
+      "2 :     ─RY─RZ───X─o───────────────────────────────────────────|─RY─RZ───X─o── ...\n",
+      "3 :     ─RY─RZ─────X─o─────────────────────────────────────────|─RY─RZ─────X─o ...\n",
+      "4 :     ─RY─RZ───────X─o───────────────────────────────────────|─RY─RZ───────X ...\n",
+      "5 :     ─RY─RZ─────────X─o─────────────────────────────────────|─RY─RZ──────── ...\n",
+      "6 :     ─RY─RZ───────────X─o───────────────────────────────────|─RY─RZ──────── ...\n",
+      "7 :     ─RY─RZ─────────────X─o─────────────────────────────────|─RY─RZ──────── ...\n",
+      "8 :     ─RY─RZ───────────────X─o───────────────────────────────|─RY─RZ──────── ...\n",
+      "9 :     ─RY─RZ─────────────────X─o─────────────────────────────|─RY─RZ──────── ...\n",
+      "10:     ─RY─RZ───────────────────X─o───────────────────────────|─RY─RZ──────── ...\n",
+      "11:     ─RY─RZ─────────────────────X─o─────────────────────────|─RY─RZ──────── ...\n",
+      "12:     ─RY─RZ───────────────────────X─o───────────────────────|─RY─RZ──────── ...\n",
+      "13:     ─RY─RZ─────────────────────────X─o─────────────────────|─RY─RZ──────── ...\n",
+      "14:     ─RY─RZ───────────────────────────X─o───────────────────|─RY─RZ──────── ...\n",
+      "15:     ─RY─RZ─────────────────────────────X─o─────────────────|─RY─RZ──────── ...\n",
+      "16:     ─RY─RZ───────────────────────────────X─o───────────────|─RY─RZ──────── ...\n",
+      "17:     ─RY─RZ─────────────────────────────────X─o─────────────|─RY─RZ──────── ...\n",
+      "18:     ─RY─RZ───────────────────────────────────X─o───────────|─RY─RZ──────── ...\n",
+      "19:     ─RY─RZ─────────────────────────────────────X─o─────────|─RY─RZ──────── ...\n",
+      "20:     ─RY─RZ───────────────────────────────────────X─o───────|─RY─RZ──────── ...\n",
+      "21:     ─RY─RZ─────────────────────────────────────────X─o─────|─RY─RZ──────── ...\n",
+      "22:     ─RY─RZ───────────────────────────────────────────X─o───|─RY─RZ──────── ...\n",
+      "23:     ─RY─RZ─────────────────────────────────────────────X─o─|─RY─RZ──────── ...\n",
+      "24:     ─RY─RZ───────────────────────────────────────────────X─o─RY─RZ──────── ...\n",
+      "\n",
+      "0 : ... ─────────────────────────────────────────X─RY─RZ─o──────────────────── ...\n",
+      "1 : ... ─────────────────────────────────────────|─RY─RZ─X─o────────────────── ...\n",
+      "2 : ... ─────────────────────────────────────────|─RY─RZ───X─o──────────────── ...\n",
+      "3 : ... ─────────────────────────────────────────|─RY─RZ─────X─o────────────── ...\n",
+      "4 : ... ─o───────────────────────────────────────|─RY─RZ───────X─o──────────── ...\n",
+      "5 : ... ─X─o─────────────────────────────────────|─RY─RZ─────────X─o────────── ...\n",
+      "6 : ... ───X─o───────────────────────────────────|─RY─RZ───────────X─o──────── ...\n",
+      "7 : ... ─────X─o─────────────────────────────────|─RY─RZ─────────────X─o────── ...\n",
+      "8 : ... ───────X─o───────────────────────────────|─RY─RZ───────────────X─o──── ...\n",
+      "9 : ... ─────────X─o─────────────────────────────|─RY─RZ─────────────────X─o── ...\n",
+      "10: ... ───────────X─o───────────────────────────|─RY─RZ───────────────────X─o ...\n",
+      "11: ... ─────────────X─o─────────────────────────|─RY─RZ─────────────────────X ...\n",
+      "12: ... ───────────────X─o───────────────────────|─RY─RZ────────────────────── ...\n",
+      "13: ... ─────────────────X─o─────────────────────|─RY─RZ────────────────────── ...\n",
+      "14: ... ───────────────────X─o───────────────────|─RY─RZ────────────────────── ...\n",
+      "15: ... ─────────────────────X─o─────────────────|─RY─RZ────────────────────── ...\n",
+      "16: ... ───────────────────────X─o───────────────|─RY─RZ────────────────────── ...\n",
+      "17: ... ─────────────────────────X─o─────────────|─RY─RZ────────────────────── ...\n",
+      "18: ... ───────────────────────────X─o───────────|─RY─RZ────────────────────── ...\n",
+      "19: ... ─────────────────────────────X─o─────────|─RY─RZ────────────────────── ...\n",
+      "20: ... ───────────────────────────────X─o───────|─RY─RZ────────────────────── ...\n",
+      "21: ... ─────────────────────────────────X─o─────|─RY─RZ────────────────────── ...\n",
+      "22: ... ───────────────────────────────────X─o───|─RY─RZ────────────────────── ...\n",
+      "23: ... ─────────────────────────────────────X─o─|─RY─RZ────────────────────── ...\n",
+      "24: ... ───────────────────────────────────────X─o─RY─RZ────────────────────── ...\n",
+      "\n",
+      "0 : ... ───────────────────────────X─M─\n",
+      "1 : ... ───────────────────────────|─M─\n",
+      "2 : ... ───────────────────────────|─M─\n",
+      "3 : ... ───────────────────────────|─M─\n",
+      "4 : ... ───────────────────────────|─M─\n",
+      "5 : ... ───────────────────────────|─M─\n",
+      "6 : ... ───────────────────────────|─M─\n",
+      "7 : ... ───────────────────────────|─M─\n",
+      "8 : ... ───────────────────────────|─M─\n",
+      "9 : ... ───────────────────────────|─M─\n",
+      "10: ... ───────────────────────────|─M─\n",
+      "11: ... ─o─────────────────────────|─M─\n",
+      "12: ... ─X─o───────────────────────|─M─\n",
+      "13: ... ───X─o─────────────────────|─M─\n",
+      "14: ... ─────X─o───────────────────|─M─\n",
+      "15: ... ───────X─o─────────────────|─M─\n",
+      "16: ... ─────────X─o───────────────|─M─\n",
+      "17: ... ───────────X─o─────────────|─M─\n",
+      "18: ... ─────────────X─o───────────|─M─\n",
+      "19: ... ───────────────X─o─────────|─M─\n",
+      "20: ... ─────────────────X─o───────|─M─\n",
+      "21: ... ───────────────────X─o─────|─M─\n",
+      "22: ... ─────────────────────X─o───|─M─\n",
+      "23: ... ───────────────────────X─o─|─M─\n",
+      "24: ... ─────────────────────────X─o─M─\n"
+     ]
+    }
+   ],
+   "source": [
+    "circuit = build_circuit(nqubits=nqubits, nlayers=3)\n",
+    "circuit.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "07b2c097-cea2-42ec-8f1d-b4bbb5b71d98",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Setting random parameters\n",
+    "circuit.set_parameters(\n",
+    "    parameters=np.random.uniform(-np.pi, np.pi, len(circuit.get_parameters())),\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fd0cea52-03f5-4366-a01a-a5a84aa8ebc7",
+   "metadata": {},
+   "source": [
+    "#### Setting up the tensor network simulator\n",
+    "\n",
+    "Depending on the simulator, various parameters can be set. One can customize the tensor network execution via the `backend.configure_tn_simulation` function, whose face depends on the specific backend provider."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "2ee03e94-d794-4a51-9e76-01e8d8a259ba",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Customization of the tensor network simulation in the case of quimb backend\n",
+    "# Here we use only some of the possible arguments\n",
+    "quimb_backend.configure_tn_simulation(\n",
+    "    #ansatz=\"MPS\",\n",
+    "    max_bond_dimension=10\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "648d85b8-445d-4081-aeed-1691fbae67be",
+   "metadata": {},
+   "source": [
+    "#### Executing through the backend\n",
+    "\n",
+    "The `backend.execute_circuit` method can be used then. We can simulate results in three ways:\n",
+    "1. reconstruction of the final state only if `return_array` is set to `True`;\n",
+    "2. computation of the relevant probabilities of the final state.\n",
+    "3. reconstruction of the relevant state's frequencies (only if `nshots` is not `None`)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "35a244c3-adba-4b8b-b28c-0ab592b0f7cf",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'nqubits': 25,\n",
+       " 'backend': qibotn (quimb),\n",
+       " 'measures': Counter({'0010101100100011101100110': 1,\n",
+       "          '1101010011101101100010011': 1,\n",
+       "          '0100010101110001100001001': 1,\n",
+       "          '1100001000000010101011101': 1,\n",
+       "          '0100101000100110010010000': 1,\n",
+       "          '0100000111111100111001100': 1,\n",
+       "          '0010101100000111100000000': 1,\n",
+       "          '0101111100011000101100111': 1,\n",
+       "          '0111111001101110011000111': 1,\n",
+       "          '1111011100010111101010110': 1,\n",
+       "          '1001000111111111111000000': 1,\n",
+       "          '1110010011010011000010000': 1,\n",
+       "          '1001101011101101100000000': 1,\n",
+       "          '1010101100011110001110111': 1,\n",
+       "          '0111010110011101010101010': 1,\n",
+       "          '1000110100110010010011101': 1,\n",
+       "          '0010010001010110000011100': 1,\n",
+       "          '1110110010010000110100101': 1,\n",
+       "          '1110010110011111101110101': 1,\n",
+       "          '0101001000011111100010111': 1,\n",
+       "          '0111011101111111101101111': 1,\n",
+       "          '0011111111100001011000010': 1,\n",
+       "          '0110001100010001000101011': 1,\n",
+       "          '0100101101000010101101111': 1,\n",
+       "          '0101010010010010000111001': 1,\n",
+       "          '0000000011111101101011110': 1,\n",
+       "          '0000100100100001101011010': 1,\n",
+       "          '1010111100000101010101110': 1,\n",
+       "          '0110011011000001010101100': 1,\n",
+       "          '1111001101101001111111111': 1,\n",
+       "          '0011001011011110000010000': 1,\n",
+       "          '1001100100010000010010000': 1,\n",
+       "          '1011111101100001111110011': 1,\n",
+       "          '0011101011101010010111001': 1,\n",
+       "          '1111100010010010101100110': 1,\n",
+       "          '0101100001011110010100010': 1,\n",
+       "          '0100101110010011000011000': 1,\n",
+       "          '1011001011101011101000101': 1,\n",
+       "          '0000101111101100010100010': 1,\n",
+       "          '1101000010100000011000110': 1,\n",
+       "          '1100110110101111110010001': 1,\n",
+       "          '1100001011010011010111101': 1,\n",
+       "          '1000101011010011111001101': 1,\n",
+       "          '1100001001010101110010100': 1,\n",
+       "          '0110101101110000001100110': 1,\n",
+       "          '0111110111010101101000110': 1,\n",
+       "          '1110010111101010101000101': 1,\n",
+       "          '1000110010011010000110000': 1,\n",
+       "          '1001011101010100010010001': 1,\n",
+       "          '0100110100010001000101000': 1,\n",
+       "          '0000100010100010010100010': 1,\n",
+       "          '1010110110011100011000101': 1,\n",
+       "          '0000110010100001101001010': 1,\n",
+       "          '0100101000111100110010111': 1,\n",
+       "          '1011101011011110000001011': 1,\n",
+       "          '1010011111111101011110110': 1,\n",
+       "          '1100110111100010000011110': 1,\n",
+       "          '0100110100100000101100111': 1,\n",
+       "          '1110111100011110001011101': 1,\n",
+       "          '0011001100110011101000110': 1,\n",
+       "          '1000110000111001101011101': 1,\n",
+       "          '0100101101000010101011111': 1,\n",
+       "          '0101010000000110010101001': 1,\n",
+       "          '0110111101101010010111000': 1,\n",
+       "          '0010010010100010101010101': 1,\n",
+       "          '1100001000101011101100101': 1,\n",
+       "          '1010101000011101101101011': 1,\n",
+       "          '1000010111001110010011110': 1,\n",
+       "          '0000010001110001100000011': 1,\n",
+       "          '0011010000101101111101100': 1,\n",
+       "          '1011010000100011000010000': 1,\n",
+       "          '1110100011001010000110000': 1,\n",
+       "          '1101000111110111001100101': 1,\n",
+       "          '0110001101010001110011010': 1,\n",
+       "          '1001011000100110101010101': 1,\n",
+       "          '0000110010100000000110111': 1,\n",
+       "          '1111001000001000111001000': 1,\n",
+       "          '0011100011100010010100001': 1,\n",
+       "          '0111111110010000001010111': 1,\n",
+       "          '1011100100101101101011110': 1,\n",
+       "          '0111001011100110001000001': 1,\n",
+       "          '0111001000110000111101111': 1,\n",
+       "          '1101111011001110000000000': 1,\n",
+       "          '0010111101011101010010100': 1,\n",
+       "          '1100100010010001111101000': 1,\n",
+       "          '0101011111100010101010100': 1,\n",
+       "          '1110100111011111111000001': 1,\n",
+       "          '1100000010101100001000110': 1,\n",
+       "          '0111011011010001011001011': 1,\n",
+       "          '0111000000100001101010011': 1,\n",
+       "          '1001111100110001111101000': 1,\n",
+       "          '0011010010100101010101100': 1,\n",
+       "          '1010111011011001101100011': 1,\n",
+       "          '1001000100001110000110000': 1,\n",
+       "          '1011011110100101010100101': 1,\n",
+       "          '0101100010011101111111001': 1,\n",
+       "          '0000100000101110000001000': 1,\n",
+       "          '1110010111000010111001000': 1,\n",
+       "          '1011011101101101111011101': 1,\n",
+       "          '0111100010010001111001011': 1}),\n",
+       " 'measured_probabilities': {'0010101100100011101100110': np.float64(1.4287479948554065e-07),\n",
+       "  '1101010011101101100010011': np.float64(6.840535900713192e-07),\n",
+       "  '0100010101110001100001001': np.float64(2.4297656493808975e-08),\n",
+       "  '1100001000000010101011101': np.float64(8.093409548935148e-07),\n",
+       "  '0100101000100110010010000': np.float64(4.2843525768921185e-07),\n",
+       "  '0100000111111100111001100': np.float64(5.4788880664882446e-08),\n",
+       "  '0010101100000111100000000': np.float64(6.350945339007582e-09),\n",
+       "  '0101111100011000101100111': np.float64(1.6189384309546533e-09),\n",
+       "  '0111111001101110011000111': np.float64(4.231070771736262e-07),\n",
+       "  '1111011100010111101010110': np.float64(8.809840523521098e-08),\n",
+       "  '1001000111111111111000000': np.float64(2.2649917694883763e-09),\n",
+       "  '1110010011010011000010000': np.float64(2.9400450442747213e-06),\n",
+       "  '1001101011101101100000000': np.float64(3.564993949972801e-07),\n",
+       "  '1010101100011110001110111': np.float64(2.0353895972901936e-07),\n",
+       "  '0111010110011101010101010': np.float64(9.272342830457222e-08),\n",
+       "  '1000110100110010010011101': np.float64(1.0554195999421195e-07),\n",
+       "  '0010010001010110000011100': np.float64(4.926758473909799e-08),\n",
+       "  '1110110010010000110100101': np.float64(3.6907560113556863e-07),\n",
+       "  '1110010110011111101110101': np.float64(1.0912695706428317e-07),\n",
+       "  '0101001000011111100010111': np.float64(2.3749237133846456e-07),\n",
+       "  '0111011101111111101101111': np.float64(4.4313847930510314e-07),\n",
+       "  '0011111111100001011000010': np.float64(2.879407202649115e-09),\n",
+       "  '0110001100010001000101011': np.float64(2.2970898298927726e-08),\n",
+       "  '0100101101000010101101111': np.float64(1.2403396951734157e-06),\n",
+       "  '0101010010010010000111001': np.float64(3.2580433289301146e-06),\n",
+       "  '0000000011111101101011110': np.float64(7.551781140278402e-07),\n",
+       "  '0000100100100001101011010': np.float64(7.342186380985404e-06),\n",
+       "  '1010111100000101010101110': np.float64(2.0803417549284257e-07),\n",
+       "  '0110011011000001010101100': np.float64(6.536548485677532e-09),\n",
+       "  '1111001101101001111111111': np.float64(6.662093312934175e-08),\n",
+       "  '0011001011011110000010000': np.float64(9.152885414596061e-07),\n",
+       "  '1001100100010000010010000': np.float64(1.1822334160129414e-06),\n",
+       "  '1011111101100001111110011': np.float64(1.2742285932601216e-05),\n",
+       "  '0011101011101010010111001': np.float64(8.001218354241628e-07),\n",
+       "  '1111100010010010101100110': np.float64(9.3255563882172e-07),\n",
+       "  '0101100001011110010100010': np.float64(1.0626891034969866e-06),\n",
+       "  '0100101110010011000011000': np.float64(1.5652631724013031e-07),\n",
+       "  '1011001011101011101000101': np.float64(1.025423997199104e-06),\n",
+       "  '0000101111101100010100010': np.float64(6.003473256257238e-07),\n",
+       "  '1101000010100000011000110': np.float64(1.085658621941692e-06),\n",
+       "  '1100110110101111110010001': np.float64(4.659708973943698e-09),\n",
+       "  '1100001011010011010111101': np.float64(5.295910969809775e-07),\n",
+       "  '1000101011010011111001101': np.float64(3.6779048150728553e-07),\n",
+       "  '1100001001010101110010100': np.float64(4.92126869361337e-09),\n",
+       "  '0110101101110000001100110': np.float64(7.741427610734003e-08),\n",
+       "  '0111110111010101101000110': np.float64(2.399267980010788e-07),\n",
+       "  '1110010111101010101000101': np.float64(5.667518009732859e-07),\n",
+       "  '1000110010011010000110000': np.float64(2.084260073059544e-06),\n",
+       "  '1001011101010100010010001': np.float64(2.6571545078690544e-08),\n",
+       "  '0100110100010001000101000': np.float64(3.079779061777933e-08),\n",
+       "  '0000100010100010010100010': np.float64(6.929792821857359e-06),\n",
+       "  '1010110110011100011000101': np.float64(4.630180771716902e-08),\n",
+       "  '0000110010100001101001010': np.float64(9.116530823953186e-07),\n",
+       "  '0100101000111100110010111': np.float64(1.3249324853060952e-07),\n",
+       "  '1011101011011110000001011': np.float64(1.1907229585114808e-06),\n",
+       "  '1010011111111101011110110': np.float64(4.56149319722231e-09),\n",
+       "  '1100110111100010000011110': np.float64(5.257006816629565e-07),\n",
+       "  '0100110100100000101100111': np.float64(5.776773429581827e-07),\n",
+       "  '1110111100011110001011101': np.float64(1.9990466754187882e-07),\n",
+       "  '0011001100110011101000110': np.float64(4.3593985418091113e-08),\n",
+       "  '1000110000111001101011101': np.float64(3.6389888110895923e-07),\n",
+       "  '0100101101000010101011111': np.float64(7.622087666902094e-07),\n",
+       "  '0101010000000110010101001': np.float64(2.994365575033701e-07),\n",
+       "  '0110111101101010010111000': np.float64(3.147129865281865e-08),\n",
+       "  '0010010010100010101010101': np.float64(3.7955795123562516e-07),\n",
+       "  '1100001000101011101100101': np.float64(2.483089067956661e-07),\n",
+       "  '1010101000011101101101011': np.float64(3.09860035910458e-07),\n",
+       "  '1000010111001110010011110': np.float64(4.718847603022761e-08),\n",
+       "  '0000010001110001100000011': np.float64(1.618347020880399e-08),\n",
+       "  '0011010000101101111101100': np.float64(2.307864975407703e-07),\n",
+       "  '1011010000100011000010000': np.float64(1.604607088007449e-07),\n",
+       "  '1110100011001010000110000': np.float64(5.735844296703352e-07),\n",
+       "  '1101000111110111001100101': np.float64(7.018930935740711e-10),\n",
+       "  '0110001101010001110011010': np.float64(1.426676825693035e-07),\n",
+       "  '1001011000100110101010101': np.float64(1.3658924161666397e-07),\n",
+       "  '0000110010100000000110111': np.float64(7.127088059066376e-07),\n",
+       "  '1111001000001000111001000': np.float64(9.382957208112125e-08),\n",
+       "  '0011100011100010010100001': np.float64(1.5633352068001958e-07),\n",
+       "  '0111111110010000001010111': np.float64(6.24916842986095e-07),\n",
+       "  '1011100100101101101011110': np.float64(5.277053774965453e-08),\n",
+       "  '0111001011100110001000001': np.float64(2.706733332328552e-07),\n",
+       "  '0111001000110000111101111': np.float64(8.740290927759748e-07),\n",
+       "  '1101111011001110000000000': np.float64(1.1390459236761492e-07),\n",
+       "  '0010111101011101010010100': np.float64(2.851294124498577e-06),\n",
+       "  '1100100010010001111101000': np.float64(8.627935077391886e-06),\n",
+       "  '0101011111100010101010100': np.float64(6.937375172146743e-08),\n",
+       "  '1110100111011111111000001': np.float64(2.517698486277455e-07),\n",
+       "  '1100000010101100001000110': np.float64(2.1300563007206324e-07),\n",
+       "  '0111011011010001011001011': np.float64(5.8246768046662493e-08),\n",
+       "  '0111000000100001101010011': np.float64(3.123499806377365e-07),\n",
+       "  '1001111100110001111101000': np.float64(4.777318918055056e-07),\n",
+       "  '0011010010100101010101100': np.float64(5.494449035514909e-07),\n",
+       "  '1010111011011001101100011': np.float64(1.1425290362328705e-06),\n",
+       "  '1001000100001110000110000': np.float64(3.266349767666358e-08),\n",
+       "  '1011011110100101010100101': np.float64(5.947082800379298e-07),\n",
+       "  '0101100010011101111111001': np.float64(3.5373491729489938e-06),\n",
+       "  '0000100000101110000001000': np.float64(3.041450478019988e-07),\n",
+       "  '1110010111000010111001000': np.float64(2.0041305331234744e-07),\n",
+       "  '1011011101101101111011101': np.float64(2.701698118830075e-07),\n",
+       "  '0111100010010001111001011': np.float64(1.3996687152906713e-06)},\n",
+       " 'prob_type': 'default',\n",
+       " 'statevector': Array([[-5.8646699e-05-1.0826049e-04j],\n",
+       "        [-1.9374731e-05+8.6432210e-06j],\n",
+       "        [ 7.7656114e-05-3.3436768e-04j],\n",
+       "        ...,\n",
+       "        [ 1.4206149e-05+6.0087572e-05j],\n",
+       "        [ 1.2372108e-04-1.6373204e-05j],\n",
+       "        [ 3.0789568e-05+3.2571501e-05j]], dtype=complex64)}"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Simple execution (defaults)\n",
+    "outcome = quimb_backend.execute_circuit(circuit=circuit, nshots=100, return_array=True)\n",
+    "\n",
+    "# Print outcome\n",
+    "vars(outcome)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "84ec0b48-f6b4-495c-93b8-8e42d1a8b0df",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "\n",
+    "One can access to the specific contents of the simulation outcome."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "c0443efc-21ef-4ed5-9cf4-785d204a1881",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "[Qibo 0.2.20|ERROR|2025-09-08 17:57:29]: Tensor network simulation cannot be used to reconstruct statevector for >= 20 .\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Probabilities:\n",
+      " {'0010101100100011101100110': np.float64(1.4287479948554065e-07), '1101010011101101100010011': np.float64(6.840535900713192e-07), '0100010101110001100001001': np.float64(2.4297656493808975e-08), '1100001000000010101011101': np.float64(8.093409548935148e-07), '0100101000100110010010000': np.float64(4.2843525768921185e-07), '0100000111111100111001100': np.float64(5.4788880664882446e-08), '0010101100000111100000000': np.float64(6.350945339007582e-09), '0101111100011000101100111': np.float64(1.6189384309546533e-09), '0111111001101110011000111': np.float64(4.231070771736262e-07), '1111011100010111101010110': np.float64(8.809840523521098e-08), '1001000111111111111000000': np.float64(2.2649917694883763e-09), '1110010011010011000010000': np.float64(2.9400450442747213e-06), '1001101011101101100000000': np.float64(3.564993949972801e-07), '1010101100011110001110111': np.float64(2.0353895972901936e-07), '0111010110011101010101010': np.float64(9.272342830457222e-08), '1000110100110010010011101': np.float64(1.0554195999421195e-07), '0010010001010110000011100': np.float64(4.926758473909799e-08), '1110110010010000110100101': np.float64(3.6907560113556863e-07), '1110010110011111101110101': np.float64(1.0912695706428317e-07), '0101001000011111100010111': np.float64(2.3749237133846456e-07), '0111011101111111101101111': np.float64(4.4313847930510314e-07), '0011111111100001011000010': np.float64(2.879407202649115e-09), '0110001100010001000101011': np.float64(2.2970898298927726e-08), '0100101101000010101101111': np.float64(1.2403396951734157e-06), '0101010010010010000111001': np.float64(3.2580433289301146e-06), '0000000011111101101011110': np.float64(7.551781140278402e-07), '0000100100100001101011010': np.float64(7.342186380985404e-06), '1010111100000101010101110': np.float64(2.0803417549284257e-07), '0110011011000001010101100': np.float64(6.536548485677532e-09), '1111001101101001111111111': np.float64(6.662093312934175e-08), '0011001011011110000010000': np.float64(9.152885414596061e-07), '1001100100010000010010000': np.float64(1.1822334160129414e-06), '1011111101100001111110011': np.float64(1.2742285932601216e-05), '0011101011101010010111001': np.float64(8.001218354241628e-07), '1111100010010010101100110': np.float64(9.3255563882172e-07), '0101100001011110010100010': np.float64(1.0626891034969866e-06), '0100101110010011000011000': np.float64(1.5652631724013031e-07), '1011001011101011101000101': np.float64(1.025423997199104e-06), '0000101111101100010100010': np.float64(6.003473256257238e-07), '1101000010100000011000110': np.float64(1.085658621941692e-06), '1100110110101111110010001': np.float64(4.659708973943698e-09), '1100001011010011010111101': np.float64(5.295910969809775e-07), '1000101011010011111001101': np.float64(3.6779048150728553e-07), '1100001001010101110010100': np.float64(4.92126869361337e-09), '0110101101110000001100110': np.float64(7.741427610734003e-08), '0111110111010101101000110': np.float64(2.399267980010788e-07), '1110010111101010101000101': np.float64(5.667518009732859e-07), '1000110010011010000110000': np.float64(2.084260073059544e-06), '1001011101010100010010001': np.float64(2.6571545078690544e-08), '0100110100010001000101000': np.float64(3.079779061777933e-08), '0000100010100010010100010': np.float64(6.929792821857359e-06), '1010110110011100011000101': np.float64(4.630180771716902e-08), '0000110010100001101001010': np.float64(9.116530823953186e-07), '0100101000111100110010111': np.float64(1.3249324853060952e-07), '1011101011011110000001011': np.float64(1.1907229585114808e-06), '1010011111111101011110110': np.float64(4.56149319722231e-09), '1100110111100010000011110': np.float64(5.257006816629565e-07), '0100110100100000101100111': np.float64(5.776773429581827e-07), '1110111100011110001011101': np.float64(1.9990466754187882e-07), '0011001100110011101000110': np.float64(4.3593985418091113e-08), '1000110000111001101011101': np.float64(3.6389888110895923e-07), '0100101101000010101011111': np.float64(7.622087666902094e-07), '0101010000000110010101001': np.float64(2.994365575033701e-07), '0110111101101010010111000': np.float64(3.147129865281865e-08), '0010010010100010101010101': np.float64(3.7955795123562516e-07), '1100001000101011101100101': np.float64(2.483089067956661e-07), '1010101000011101101101011': np.float64(3.09860035910458e-07), '1000010111001110010011110': np.float64(4.718847603022761e-08), '0000010001110001100000011': np.float64(1.618347020880399e-08), '0011010000101101111101100': np.float64(2.307864975407703e-07), '1011010000100011000010000': np.float64(1.604607088007449e-07), '1110100011001010000110000': np.float64(5.735844296703352e-07), '1101000111110111001100101': np.float64(7.018930935740711e-10), '0110001101010001110011010': np.float64(1.426676825693035e-07), '1001011000100110101010101': np.float64(1.3658924161666397e-07), '0000110010100000000110111': np.float64(7.127088059066376e-07), '1111001000001000111001000': np.float64(9.382957208112125e-08), '0011100011100010010100001': np.float64(1.5633352068001958e-07), '0111111110010000001010111': np.float64(6.24916842986095e-07), '1011100100101101101011110': np.float64(5.277053774965453e-08), '0111001011100110001000001': np.float64(2.706733332328552e-07), '0111001000110000111101111': np.float64(8.740290927759748e-07), '1101111011001110000000000': np.float64(1.1390459236761492e-07), '0010111101011101010010100': np.float64(2.851294124498577e-06), '1100100010010001111101000': np.float64(8.627935077391886e-06), '0101011111100010101010100': np.float64(6.937375172146743e-08), '1110100111011111111000001': np.float64(2.517698486277455e-07), '1100000010101100001000110': np.float64(2.1300563007206324e-07), '0111011011010001011001011': np.float64(5.8246768046662493e-08), '0111000000100001101010011': np.float64(3.123499806377365e-07), '1001111100110001111101000': np.float64(4.777318918055056e-07), '0011010010100101010101100': np.float64(5.494449035514909e-07), '1010111011011001101100011': np.float64(1.1425290362328705e-06), '1001000100001110000110000': np.float64(3.266349767666358e-08), '1011011110100101010100101': np.float64(5.947082800379298e-07), '0101100010011101111111001': np.float64(3.5373491729489938e-06), '0000100000101110000001000': np.float64(3.041450478019988e-07), '1110010111000010111001000': np.float64(2.0041305331234744e-07), '1011011101101101111011101': np.float64(2.701698118830075e-07), '0111100010010001111001011': np.float64(1.3996687152906713e-06)}\n",
+      "\n"
+     ]
+    },
+    {
+     "ename": "NotImplementedError",
+     "evalue": "Tensor network simulation cannot be used to reconstruct statevector for >= 20 .",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
+      "\u001b[0;32m/tmp/ipykernel_44825/1053899561.py\u001b[0m in \u001b[0;36m<cell line: 0>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"\u001b[0m\u001b[0;34mProbabilities:\\n \u001b[0m\u001b[0;34m{\u001b[0m\u001b[0moutcome\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprobabilities\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\\n\u001b[0m\u001b[0;34m\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"\u001b[0m\u001b[0;34mState:\\n \u001b[0m\u001b[0;34m{\u001b[0m\u001b[0moutcome\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\\n\u001b[0m\u001b[0;34m\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m~/repo/qibotn/src/qibotn/result.py\u001b[0m in \u001b[0;36mstate\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     61\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnqubits\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatevector\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 63\u001b[0;31m         raise_error(\n\u001b[0m\u001b[1;32m     64\u001b[0m             \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     65\u001b[0m             \u001b[0;34mf\"\u001b[0m\u001b[0;34mTensor network simulation cannot be used to reconstruct statevector for >= 20 .\u001b[0m\u001b[0;34m\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/main_env/lib/python3.12/site-packages/qibo/config.py\u001b[0m in \u001b[0;36mraise_error\u001b[0;34m(exception, message)\u001b[0m\n\u001b[1;32m     44\u001b[0m     \"\"\"\n\u001b[1;32m     45\u001b[0m     \u001b[0mlog\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0merror\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 46\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mexception\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     47\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     48\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mNotImplementedError\u001b[0m: Tensor network simulation cannot be used to reconstruct statevector for >= 20 ."
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"Probabilities:\\n {outcome.probabilities()}\\n\")\n",
+    "print(f\"State:\\n {outcome.state()}\\n\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dd84f1f3-7aa5-4ad1-ae09-81e0aff75b5b",
+   "metadata": {},
+   "source": [
+    "### Compute expectation values\n",
+    "\n",
+    "Another important feature of this backend is the `expectation` function. In fact, we can compute expectation values of given observables thorugh a Qibo-friendly interface.\n",
+    "\n",
+    "---\n",
+    "\n",
+    "Let's start by importing some symbols, thanks to which we can build our observable."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "37385485-e8a3-4ab0-ad44-bcc4e9da24ca",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0 :     ─RY─RZ─o───────────────────────────────────────────────X─RY─RZ─o────── ...\n",
+      "1 :     ─RY─RZ─X─o─────────────────────────────────────────────|─RY─RZ─X─o──── ...\n",
+      "2 :     ─RY─RZ───X─o───────────────────────────────────────────|─RY─RZ───X─o── ...\n",
+      "3 :     ─RY─RZ─────X─o─────────────────────────────────────────|─RY─RZ─────X─o ...\n",
+      "4 :     ─RY─RZ───────X─o───────────────────────────────────────|─RY─RZ───────X ...\n",
+      "5 :     ─RY─RZ─────────X─o─────────────────────────────────────|─RY─RZ──────── ...\n",
+      "6 :     ─RY─RZ───────────X─o───────────────────────────────────|─RY─RZ──────── ...\n",
+      "7 :     ─RY─RZ─────────────X─o─────────────────────────────────|─RY─RZ──────── ...\n",
+      "8 :     ─RY─RZ───────────────X─o───────────────────────────────|─RY─RZ──────── ...\n",
+      "9 :     ─RY─RZ─────────────────X─o─────────────────────────────|─RY─RZ──────── ...\n",
+      "10:     ─RY─RZ───────────────────X─o───────────────────────────|─RY─RZ──────── ...\n",
+      "11:     ─RY─RZ─────────────────────X─o─────────────────────────|─RY─RZ──────── ...\n",
+      "12:     ─RY─RZ───────────────────────X─o───────────────────────|─RY─RZ──────── ...\n",
+      "13:     ─RY─RZ─────────────────────────X─o─────────────────────|─RY─RZ──────── ...\n",
+      "14:     ─RY─RZ───────────────────────────X─o───────────────────|─RY─RZ──────── ...\n",
+      "15:     ─RY─RZ─────────────────────────────X─o─────────────────|─RY─RZ──────── ...\n",
+      "16:     ─RY─RZ───────────────────────────────X─o───────────────|─RY─RZ──────── ...\n",
+      "17:     ─RY─RZ─────────────────────────────────X─o─────────────|─RY─RZ──────── ...\n",
+      "18:     ─RY─RZ───────────────────────────────────X─o───────────|─RY─RZ──────── ...\n",
+      "19:     ─RY─RZ─────────────────────────────────────X─o─────────|─RY─RZ──────── ...\n",
+      "20:     ─RY─RZ───────────────────────────────────────X─o───────|─RY─RZ──────── ...\n",
+      "21:     ─RY─RZ─────────────────────────────────────────X─o─────|─RY─RZ──────── ...\n",
+      "22:     ─RY─RZ───────────────────────────────────────────X─o───|─RY─RZ──────── ...\n",
+      "23:     ─RY─RZ─────────────────────────────────────────────X─o─|─RY─RZ──────── ...\n",
+      "24:     ─RY─RZ───────────────────────────────────────────────X─o─RY─RZ──────── ...\n",
+      "\n",
+      "0 : ... ─────────────────────────────────────────X─RY─RZ─o──────────────────── ...\n",
+      "1 : ... ─────────────────────────────────────────|─RY─RZ─X─o────────────────── ...\n",
+      "2 : ... ─────────────────────────────────────────|─RY─RZ───X─o──────────────── ...\n",
+      "3 : ... ─────────────────────────────────────────|─RY─RZ─────X─o────────────── ...\n",
+      "4 : ... ─o───────────────────────────────────────|─RY─RZ───────X─o──────────── ...\n",
+      "5 : ... ─X─o─────────────────────────────────────|─RY─RZ─────────X─o────────── ...\n",
+      "6 : ... ───X─o───────────────────────────────────|─RY─RZ───────────X─o──────── ...\n",
+      "7 : ... ─────X─o─────────────────────────────────|─RY─RZ─────────────X─o────── ...\n",
+      "8 : ... ───────X─o───────────────────────────────|─RY─RZ───────────────X─o──── ...\n",
+      "9 : ... ─────────X─o─────────────────────────────|─RY─RZ─────────────────X─o── ...\n",
+      "10: ... ───────────X─o───────────────────────────|─RY─RZ───────────────────X─o ...\n",
+      "11: ... ─────────────X─o─────────────────────────|─RY─RZ─────────────────────X ...\n",
+      "12: ... ───────────────X─o───────────────────────|─RY─RZ────────────────────── ...\n",
+      "13: ... ─────────────────X─o─────────────────────|─RY─RZ────────────────────── ...\n",
+      "14: ... ───────────────────X─o───────────────────|─RY─RZ────────────────────── ...\n",
+      "15: ... ─────────────────────X─o─────────────────|─RY─RZ────────────────────── ...\n",
+      "16: ... ───────────────────────X─o───────────────|─RY─RZ────────────────────── ...\n",
+      "17: ... ─────────────────────────X─o─────────────|─RY─RZ────────────────────── ...\n",
+      "18: ... ───────────────────────────X─o───────────|─RY─RZ────────────────────── ...\n",
+      "19: ... ─────────────────────────────X─o─────────|─RY─RZ────────────────────── ...\n",
+      "20: ... ───────────────────────────────X─o───────|─RY─RZ────────────────────── ...\n",
+      "21: ... ─────────────────────────────────X─o─────|─RY─RZ────────────────────── ...\n",
+      "22: ... ───────────────────────────────────X─o───|─RY─RZ────────────────────── ...\n",
+      "23: ... ─────────────────────────────────────X─o─|─RY─RZ────────────────────── ...\n",
+      "24: ... ───────────────────────────────────────X─o─RY─RZ────────────────────── ...\n",
+      "\n",
+      "0 : ... ───────────────────────────X─M─\n",
+      "1 : ... ───────────────────────────|─M─\n",
+      "2 : ... ───────────────────────────|─M─\n",
+      "3 : ... ───────────────────────────|─M─\n",
+      "4 : ... ───────────────────────────|─M─\n",
+      "5 : ... ───────────────────────────|─M─\n",
+      "6 : ... ───────────────────────────|─M─\n",
+      "7 : ... ───────────────────────────|─M─\n",
+      "8 : ... ───────────────────────────|─M─\n",
+      "9 : ... ───────────────────────────|─M─\n",
+      "10: ... ───────────────────────────|─M─\n",
+      "11: ... ─o─────────────────────────|─M─\n",
+      "12: ... ─X─o───────────────────────|─M─\n",
+      "13: ... ───X─o─────────────────────|─M─\n",
+      "14: ... ─────X─o───────────────────|─M─\n",
+      "15: ... ───────X─o─────────────────|─M─\n",
+      "16: ... ─────────X─o───────────────|─M─\n",
+      "17: ... ───────────X─o─────────────|─M─\n",
+      "18: ... ─────────────X─o───────────|─M─\n",
+      "19: ... ───────────────X─o─────────|─M─\n",
+      "20: ... ─────────────────X─o───────|─M─\n",
+      "21: ... ───────────────────X─o─────|─M─\n",
+      "22: ... ─────────────────────X─o───|─M─\n",
+      "23: ... ───────────────────────X─o─|─M─\n",
+      "24: ... ─────────────────────────X─o─M─\n"
+     ]
+    }
+   ],
+   "source": [
+    "# We are going to compute the expval of an Hamiltonian\n",
+    "# On the state prepared by the following circuit\n",
+    "circuit.draw()\n",
+    "\n",
+    "circuit.set_parameters(\n",
+    "    np.random.randn(len(circuit.get_parameters()))\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "ddecc910-7804-4199-8577-a7db38a16db8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle 3.6 X_{0} + 3.6 X_{1} + 3.6 X_{10} + 3.6 X_{11} + 3.6 X_{12} + 3.6 X_{13} + 3.6 X_{14} + 3.6 X_{15} + 3.6 X_{16} + 3.6 X_{17} + 3.6 X_{18} + 3.6 X_{19} + 3.6 X_{2} + 3.6 X_{20} + 3.6 X_{21} + 3.6 X_{22} + 3.6 X_{23} + 3.6 X_{24} + 3.6 X_{3} + 3.6 X_{4} + 3.6 X_{5} + 3.6 X_{6} + 3.6 X_{7} + 3.6 X_{8} + 3.6 X_{9} + 8.4 Z_{0} + 8.4 Z_{1} + 8.4 Z_{10} + 8.4 Z_{11} + 8.4 Z_{12} + 8.4 Z_{13} + 8.4 Z_{14} + 8.4 Z_{15} + 8.4 Z_{16} + 8.4 Z_{17} + 8.4 Z_{18} + 8.4 Z_{19} + 8.4 Z_{2} + 8.4 Z_{20} + 8.4 Z_{21} + 8.4 Z_{22} + 8.4 Z_{23} + 8.4 Z_{24} + 8.4 Z_{3} + 8.4 Z_{4} + 8.4 Z_{5} + 8.4 Z_{6} + 8.4 Z_{7} + 8.4 Z_{8} + 8.4 Z_{9}$"
+      ],
+      "text/plain": [
+       "3.6*X0 + 3.6*X1 + 3.6*X10 + 3.6*X11 + 3.6*X12 + 3.6*X13 + 3.6*X14 + 3.6*X15 + 3.6*X16 + 3.6*X17 + 3.6*X18 + 3.6*X19 + 3.6*X2 + 3.6*X20 + 3.6*X21 + 3.6*X22 + 3.6*X23 + 3.6*X24 + 3.6*X3 + 3.6*X4 + 3.6*X5 + 3.6*X6 + 3.6*X7 + 3.6*X8 + 3.6*X9 + 8.4*Z0 + 8.4*Z1 + 8.4*Z10 + 8.4*Z11 + 8.4*Z12 + 8.4*Z13 + 8.4*Z14 + 8.4*Z15 + 8.4*Z16 + 8.4*Z17 + 8.4*Z18 + 8.4*Z19 + 8.4*Z2 + 8.4*Z20 + 8.4*Z21 + 8.4*Z22 + 8.4*Z23 + 8.4*Z24 + 8.4*Z3 + 8.4*Z4 + 8.4*Z5 + 8.4*Z6 + 8.4*Z7 + 8.4*Z8 + 8.4*Z9"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from qibo.symbols import Z, X, I\n",
+    "\n",
+    "form = 0\n",
+    "for i in range(nqubits):\n",
+    "    for _ in range(12):\n",
+    "        form += 0.7 * Z(i)\n",
+    "        form += 0.3 * X(i)\n",
+    "\n",
+    "hamiltonian = hamiltonians.SymbolicHamiltonian(form)\n",
+    "\n",
+    "hamiltonian.form\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "163b70a3-814a-4a62-a98a-2ffca933a544",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mattia/main_env/lib/python3.12/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: creg\n",
+      "  warnings.warn(\n",
+      "/home/mattia/main_env/lib/python3.12/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: measure\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Expectation value: -0.9053105195111129\n",
+      "Elapsed time: 20.0296 seconds\n"
+     ]
+    }
+   ],
+   "source": [
+    "start = time.time()\n",
+    "expval = quimb_backend.expectation(\n",
+    "    circuit=circuit,\n",
+    "    observable=hamiltonian,\n",
+    ")\n",
+    "elapsed = time.time() - start\n",
+    "print(f\"Expectation value: {expval}\")\n",
+    "print(f\"Elapsed time: {elapsed:.4f} seconds\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "90663e28",
+   "metadata": {},
+   "source": [
+    "Try with Qibo (which is by default using the Qibojit backend)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "e2d05707",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Expectation value: -0.9053096709847108\n",
+      "Elapsed time: 319.1915 seconds\n"
+     ]
+    }
+   ],
+   "source": [
+    "start = time.time()\n",
+    "result = hamiltonian.expectation(circuit().state())\n",
+    "elapsed = time.time() - start\n",
+    "print(f\"Expectation value: {result}\")\n",
+    "print(f\"Elapsed time: {elapsed:.4f} seconds\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "94df291c-9ddc-4b2e-8442-5fca00784bd8",
+   "metadata": {},
+   "source": [
+    "They match! 🥳"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "main_env",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From 064cff6b331dfb0978c0f547d9ea97c0fc73fd9a Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 9 Sep 2025 11:17:49 +0000
Subject: [PATCH 07/33] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 src/qibotn/backends/quimb.py | 49 ++++++++++++++++++++----------------
 1 file changed, 28 insertions(+), 21 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index f9fe009..e024528 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -1,16 +1,16 @@
 import re
+import warnings
 from collections import Counter, defaultdict
 
 import numpy as np
-import quimb.tensor as qtn
 import quimb as qu
+import quimb.tensor as qtn
 from qibo.backends import NumpyBackend
 from qibo.config import raise_error
 from qibo.result import QuantumState
 
 from qibotn.backends.abstract import QibotnBackend
 from qibotn.result import TensorNetworkResult
-import warnings
 
 
 class QuimbBackend(QibotnBackend, NumpyBackend):
@@ -48,7 +48,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         self.max_bond_dimension = max_bond_dimension
         self.n_most_frequent_states = n_most_frequent_states
 
-    def setup_backend_specifics(self, qimb_backend="numpy", optimizer='auto-hq'):
+    def setup_backend_specifics(self, qimb_backend="numpy", optimizer="auto-hq"):
         """Setup backend specifics.
         Args:
             qimb_backend: str
@@ -119,9 +119,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             frequencies = Counter(circ_quimb.sample(nshots))
             main_frequencies = {
                 state: count
-                for state, count in frequencies.most_common(
-                    self.n_most_frequent_states
-                )
+                for state, count in frequencies.most_common(self.n_most_frequent_states)
             }
             computational_states = list(main_frequencies.keys())
             amplitudes = {
@@ -134,7 +132,11 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             frequencies = None
             measured_probabilities = None
 
-        statevector = circ_quimb.to_dense(backend=self.backend, optimize=self.optimizer) if return_array else None
+        statevector = (
+            circ_quimb.to_dense(backend=self.backend, optimize=self.optimizer)
+            if return_array
+            else None
+        )
         return TensorNetworkResult(
             nqubits=circuit.nqubits,
             backend=self,
@@ -167,34 +169,39 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         # for computing them in a single contraction. This does not work with CircuitMPS for some now
         # for Quimb 1.11.1
         operators_list, sites_list, coeffs_list = self._qiboobs_to_quimbobs(observable)
-        sites_list_grouped, operators_list_grouped, coeffs_list_grouped = self._group_by_tuples(sites_list, operators_list, coeffs_list)
+        sites_list_grouped, operators_list_grouped, coeffs_list_grouped = (
+            self._group_by_tuples(sites_list, operators_list, coeffs_list)
+        )
 
         if self.ansatz == "MPS":
-            if len(sites_list)-len(sites_list_grouped) > 10:
+            if len(sites_list) - len(sites_list_grouped) > 10:
                 warnings.warn(
                     "More than 10 local operators on the same sites are not being grouped as this is not compatible with CircuitMPS. Expected value computation can be more efficient without an MPS ansatz."
                 )
-            circ_ansatz = (qtn.circuit.CircuitMPS)
+            circ_ansatz = qtn.circuit.CircuitMPS
             circ = circ_ansatz.from_openqasm2_str(circuit.to_qasm())
             expectation_value = 0.0
             for ops, sites, coeffs in zip(operators_list, sites_list, coeffs_list):
-                exp_values = circ.local_expectation(ops, where=sites, backend=self.backend, optimize=self.optimizer)
+                exp_values = circ.local_expectation(
+                    ops, where=sites, backend=self.backend, optimize=self.optimizer
+                )
                 expectation_value += np.dot(coeffs, exp_values)
             return np.real(expectation_value)
-        
+
         else:
             circ_ansatz = qtn.circuit.Circuit
             circ = circ_ansatz.from_openqasm2_str(circuit.to_qasm())
             expectation_value = 0.0
-            for ops, sites, coeffs in zip(operators_list_grouped, sites_list_grouped, coeffs_list_grouped):
-                exp_values = circ.local_expectation(ops, where=sites, backend=self.backend, optimize=self.optimizer)
+            for ops, sites, coeffs in zip(
+                operators_list_grouped, sites_list_grouped, coeffs_list_grouped
+            ):
+                exp_values = circ.local_expectation(
+                    ops, where=sites, backend=self.backend, optimize=self.optimizer
+                )
                 expectation_value += np.dot(coeffs, exp_values)
             return np.real(expectation_value)
 
-    def _qiboobs_to_quimbobs(
-        self, 
-        hamiltonian
-    ):
+    def _qiboobs_to_quimbobs(self, hamiltonian):
         """
         Convert a Qibo SymbolicHamiltonian into a Quimb-compatible decomposition.
 
@@ -247,16 +254,16 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             coeffs_list.append(coeff)
 
         return operators_list, sites_list, coeffs_list
-    
+
     def _group_by_tuples(self, A, B, C):
         """
         Groups the elements of B and C by the unique tuples in A.
-        
+
         Parameters:
             A (list of tuples): key tuples (can contain duplicates)
             B (list): values aligned with A
             C (list): values aligned with A
-        
+
         Returns:
             (A_new, B_new, C_new):
                 A_new: list of unique tuples

From 63266c5ba0a08c1660b32e0677fc6c60aa91ce4a Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Sat, 20 Sep 2025 00:18:32 +0200
Subject: [PATCH 08/33] refactor: added function for converting qibo circuit to
 quimb circuit directly. modified expectation making use of it. added new test
 script.

---
 examples/quimb_intro/test.py |  50 ++++++++++++++
 src/qibotn/backends/quimb.py | 125 ++++++++++++++++++++++++++++++++++-
 2 files changed, 174 insertions(+), 1 deletion(-)
 create mode 100644 examples/quimb_intro/test.py

diff --git a/examples/quimb_intro/test.py b/examples/quimb_intro/test.py
new file mode 100644
index 0000000..a6f1d7e
--- /dev/null
+++ b/examples/quimb_intro/test.py
@@ -0,0 +1,50 @@
+import numpy as np
+import jax
+from qibo.backends import construct_backend
+from qibo import Circuit, gates, hamiltonians
+from qibo.symbols import Z, X, Y
+
+# construct qibotn backend
+quimb_backend = construct_backend(backend="qibotn", platform="quimb")
+
+quimb_backend.setup_backend_specifics(
+    qimb_backend="jax", 
+    optimizer='auto-hq'
+    )
+
+quimb_backend.configure_tn_simulation(
+    max_bond_dimension=10
+)
+
+
+# define Hamiltonian
+form = 0.5 * Z(0) * Z(1) +- 1.5 *  X(0) * Z(2) + Z(3)
+hamiltonian = hamiltonians.SymbolicHamiltonian(form)
+
+
+# define circuit
+def build_circuit(nqubits, nlayers):
+    """Construct a Qibo parametric quantum circuit."""
+    circ = Circuit(nqubits)
+    for _ in range(nlayers):
+        for q in range(nqubits):
+            circ.add(gates.RY(q=q, theta=0.))
+            circ.add(gates.RZ(q=q, theta=0.))
+        [circ.add(gates.CNOT(q%nqubits, (q+1)%nqubits) for q in range(nqubits))]
+    circ.add(gates.M(*range(nqubits)))
+    return circ
+
+nqubits = 4
+circuit = build_circuit(nqubits=nqubits, nlayers=3)
+
+
+def f(params):
+    circuit.set_parameters(params)
+    return quimb_backend.expectation(
+        circuit=circuit,
+        observable=hamiltonian,
+    )
+
+parameters = np.random.uniform(-np.pi, np.pi, size=len(circuit.get_parameters()))
+print(f(parameters))
+print(jax.value_and_grad(f)(parameters))
\ No newline at end of file
diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index e024528..b25e559 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -3,6 +3,8 @@ import warnings
 from collections import Counter, defaultdict
 
 import numpy as np
+import jax
+import jax.numpy as jnp
 import quimb as qu
 import quimb.tensor as qtn
 from qibo.backends import NumpyBackend
@@ -12,6 +14,43 @@ from qibo.result import QuantumState
 from qibotn.backends.abstract import QibotnBackend
 from qibotn.result import TensorNetworkResult
 
+GATE_MAP = {
+        "h": "H",
+        "x": "X",
+        "y": "Y",
+        "z": "Z",
+        "s": "S",
+        "sdg": "SDG",
+        "t": "T",
+        "tdg": "TDG",
+        "sx": "SX",
+        "sxdg": "SXDG",
+        "rx": "RX",
+        "ry": "RY",
+        "rz": "RZ",
+        "u1": "U1",
+        "u2": "U2",
+        "u3": "U3",
+        "cx": "CNOT",
+        "cnot": "CNOT",
+        "cy": "CY",
+        "cz": "CZ",
+        "iswap": "ISWAP",
+        "swap": "SWAP",
+        "ccx": "CCX",
+        "toffoli": "CCX",
+        "ccz": "CCZ",
+        "cswap": "CSWAP",
+        "fredkin": "CSWAP",
+        "crx": "CRX",
+        "cry": "CRY",
+        "crz": "CRZ",
+        "fsim": "FSIM",
+        "rxx": "RXX",
+        "ryy": "RYY",
+        "rzz": "RZZ",
+        "m": None,  # measurement, skip
+    }
 
 class QuimbBackend(QibotnBackend, NumpyBackend):
 
@@ -145,8 +184,52 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             prob_type="default",
             statevector=statevector,
         )
-
+  
     def expectation(self, circuit, observable):
+        """
+        Compute the expectation value of a Qibo-friendly ``observable`` on the Tensor Network constructed from a Qibo ``circuit``.
+        This method takes a Qibo-style symbolic Hamiltonian (e.g., `X(0)*Z(1) + 2.0*Y(2)*Z(0)`)
+        as the observable, converts it into a Quimb observable and computes its expectation
+        value using the provided circuit.
+
+        Args:
+            circuit: A Qibo quantum circuit object on which the expectation value
+                is computed.
+            observable: The observable whose expectation value we want to compute.
+                This must be provided in the symbolic Hamiltonian form supported by Qibo
+                (e.g., `X(0)*Y(1)` or `Z(0)*Z(1) + 1.5*Y(2)`).
+
+        Returns:
+            float: The expectation value (real part).
+        """
+
+        '''Convert Qibo observables to Quimb'''
+        operators_list, sites_list, coeffs_list = self._qiboobs_to_quimbobs(observable)
+
+        '''Convert Qibo circuit to Quimb circuit'''
+        parameters = circuit.get_parameters()
+        quimb_circuit = self._qibo_circuit_to_quimb(
+            circuit, quimb_circuit_type=qtn.Circuit, to_backend=jnp.array, convert_eager=True
+        )
+        quimb_parameters = {
+            key: jnp.asarray(parameters[i]) for i, key in enumerate(quimb_circuit.get_params().keys())
+        }
+        quimb_circuit.set_params(quimb_parameters)
+
+        '''Compute expectation value'''
+        expectation_value = 0.0
+        for ops, sites, coeffs in zip(operators_list, sites_list, coeffs_list):
+            exp_values = quimb_circuit.local_expectation(
+                ops,
+                where=sites,
+                backend=self.backend,
+                optimize=self.optimizer
+            )
+            expectation_value = expectation_value + coeffs * exp_values
+        
+        return jnp.real(expectation_value)
+
+    def expectation_old(self, circuit, observable):
         """Compute the expectation value of a Qibo-friendly ``observable`` on the Tensor Network constructed from a Qibo ``circuit``.
 
         This method takes a Qibo-style symbolic Hamiltonian (e.g., `X(0)*Z(1) + 2.0*Y(2)*Z(0)`)
@@ -191,6 +274,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         else:
             circ_ansatz = qtn.circuit.Circuit
             circ = circ_ansatz.from_openqasm2_str(circuit.to_qasm())
+
             expectation_value = 0.0
             for ops, sites, coeffs in zip(
                 operators_list_grouped, sites_list_grouped, coeffs_list_grouped
@@ -283,3 +367,42 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         C_new = list(grouped_C.values())
 
         return A_new, B_new, C_new
+
+    def _qibo_circuit_to_quimb(self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs):
+        """
+        Convert a Qibo Circuit to a Quimb Circuit.
+
+        Parameters
+        ----------
+        qibo_circ : qibo.models.circuit.Circuit
+            The circuit to convert.
+        quimb_circuit_type : type
+            The Quimb circuit class to use (Circuit, CircuitMPS, etc).
+        circuit_kwargs : dict
+            Extra arguments to pass to the Quimb circuit constructor.
+
+        Returns
+        -------
+        circ : quimb.tensor.circuit.Circuit
+            The converted circuit.
+        """
+        nqubits = qibo_circ.nqubits
+        quimb_gates = []
+
+        for gate in qibo_circ.queue:
+            gname = getattr(gate, "name", None)
+            qname = GATE_MAP.get(gname, None)
+            if qname is None:
+                continue  # skip measurements and unknown gates
+
+            # Handle parametrized gates (Qibo: .parameters, Quimb: expects flat tuple)
+            params = getattr(gate, "parameters", ())
+            qubits = getattr(gate, "qubits", ())
+
+            # Quimb expects (*params, *qubits)
+            gate_spec = (qname,) + tuple(params) + tuple(qubits)
+            quimb_gates.append(gate_spec)
+
+        circ = quimb_circuit_type(nqubits, **circuit_kwargs)
+        circ.apply_gates(quimb_gates)
+        return circ
\ No newline at end of file

From 9853e86deb76971ad5973ad1d1f77153c7e9eda9 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Sat, 20 Sep 2025 15:15:40 +0200
Subject: [PATCH 09/33] fixing grad nan

---
 examples/quimb_intro/test.py |  6 +--
 src/qibotn/backends/quimb.py | 78 +++++++++++++++++++++++++++++++-----
 2 files changed, 70 insertions(+), 14 deletions(-)

diff --git a/examples/quimb_intro/test.py b/examples/quimb_intro/test.py
index a6f1d7e..da499f2 100644
--- a/examples/quimb_intro/test.py
+++ b/examples/quimb_intro/test.py
@@ -30,13 +30,14 @@ def build_circuit(nqubits, nlayers):
         for q in range(nqubits):
             circ.add(gates.RY(q=q, theta=0.))
             circ.add(gates.RZ(q=q, theta=0.))
-        [circ.add(gates.CNOT(q%nqubits, (q+1)%nqubits) for q in range(nqubits))]
+        [circ.add(gates.CZ(q % nqubits, (q + 1) % nqubits)) for q in range(nqubits)]
     circ.add(gates.M(*range(nqubits)))
     return circ
 
 nqubits = 4
 circuit = build_circuit(nqubits=nqubits, nlayers=3)
 
+quimb_circuit = quimb_backend._qibo_circuit_to_quimb(circuit)
 
 def f(params):
     circuit.set_parameters(params)
@@ -46,5 +47,4 @@ def f(params):
     )
 
 parameters = np.random.uniform(-np.pi, np.pi, size=len(circuit.get_parameters()))
-print(f(parameters))
-print(jax.value_and_grad(f)(parameters))
\ No newline at end of file
+print(jax.value_and_grad(f)(parameters))
diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index b25e559..3f09859 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -14,27 +14,35 @@ from qibo.result import QuantumState
 from qibotn.backends.abstract import QibotnBackend
 from qibotn.result import TensorNetworkResult
 
+from qibo.gates.abstract import ParametrizedGate
+
+
 GATE_MAP = {
         "h": "H",
         "x": "X",
         "y": "Y",
         "z": "Z",
         "s": "S",
+
         "sdg": "SDG",
         "t": "T",
         "tdg": "TDG",
         "sx": "SX",
         "sxdg": "SXDG",
+
         "rx": "RX",
         "ry": "RY",
         "rz": "RZ",
+
         "u1": "U1",
         "u2": "U2",
         "u3": "U3",
-        "cx": "CNOT",
+
+        "cx": "CX",
         "cnot": "CNOT",
         "cy": "CY",
         "cz": "CZ",
+
         "iswap": "ISWAP",
         "swap": "SWAP",
         "ccx": "CCX",
@@ -368,6 +376,45 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
 
         return A_new, B_new, C_new
 
+    # def _qibo_circuit_to_quimb(self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs):
+    #     """
+    #     Convert a Qibo Circuit to a Quimb Circuit.
+
+    #     Parameters
+    #     ----------
+    #     qibo_circ : qibo.models.circuit.Circuit
+    #         The circuit to convert.
+    #     quimb_circuit_type : type
+    #         The Quimb circuit class to use (Circuit, CircuitMPS, etc).
+    #     circuit_kwargs : dict
+    #         Extra arguments to pass to the Quimb circuit constructor.
+
+    #     Returns
+    #     -------
+    #     circ : quimb.tensor.circuit.Circuit
+    #         The converted circuit.
+    #     """
+    #     nqubits = qibo_circ.nqubits
+    #     quimb_gates = []
+    #     circ = quimb_circuit_type(nqubits, **circuit_kwargs)
+
+    #     for gate in qibo_circ.queue:
+    #         gname = getattr(gate, "name", None)
+    #         qname = GATE_MAP.get(gname, None)
+    #         if qname is None:
+    #             continue  # skip measurements and unknown gates
+
+    #         # Handle parametrized gates (Qibo: .parameters, Quimb: expects flat tuple)
+    #         params = getattr(gate, "parameters", ())
+    #         qubits = getattr(gate, "qubits", ())
+
+    #         # Quimb expects (*params, *qubits)
+    #         gate_spec = (qname,) + tuple(params) + tuple(qubits)
+    #         quimb_gates.append(gate_spec)
+
+    #     circ.apply_gates(quimb_gates)
+    #     return circ
+
     def _qibo_circuit_to_quimb(self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs):
         """
         Convert a Qibo Circuit to a Quimb Circuit.
@@ -387,7 +434,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             The converted circuit.
         """
         nqubits = qibo_circ.nqubits
-        quimb_gates = []
+        circ = quimb_circuit_type(nqubits, **circuit_kwargs)
 
         for gate in qibo_circ.queue:
             gname = getattr(gate, "name", None)
@@ -395,14 +442,23 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             if qname is None:
                 continue  # skip measurements and unknown gates
 
-            # Handle parametrized gates (Qibo: .parameters, Quimb: expects flat tuple)
             params = getattr(gate, "parameters", ())
             qubits = getattr(gate, "qubits", ())
-
-            # Quimb expects (*params, *qubits)
-            gate_spec = (qname,) + tuple(params) + tuple(qubits)
-            quimb_gates.append(gate_spec)
-
-        circ = quimb_circuit_type(nqubits, **circuit_kwargs)
-        circ.apply_gates(quimb_gates)
-        return circ
\ No newline at end of file
+            
+            # Check if the gate is parametrized
+            is_parametrized = isinstance(gate, ParametrizedGate)
+            
+            if is_parametrized:
+                circ.apply_gate(
+                    qname,
+                    *params,
+                    *qubits,
+                    parametrized= is_parametrized
+                )
+            else:
+                circ.apply_gate(
+                    qname,
+                    *params,
+                    *qubits,
+                                )
+        return circ

From 271a44576dd4837e73efdce7b8597f30cc69abf2 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Sat, 20 Sep 2025 17:00:07 +0200
Subject: [PATCH 10/33] fixing parametrization flag and updating relevant test
 scripts

---
 examples/quimb_intro/quimb_introduction.ipynb | 713 +++++++-----------
 examples/quimb_intro/test.py                  |  14 +-
 src/qibotn/backends/quimb.py                  |  46 +-
 3 files changed, 284 insertions(+), 489 deletions(-)

diff --git a/examples/quimb_intro/quimb_introduction.ipynb b/examples/quimb_intro/quimb_introduction.ipynb
index 6153e90..266b49d 100644
--- a/examples/quimb_intro/quimb_introduction.ipynb
+++ b/examples/quimb_intro/quimb_introduction.ipynb
@@ -19,9 +19,9 @@
    "source": [
     "import time\n",
     "import numpy as np\n",
-    "from scipy import stats\n",
+    "# from scipy import stats\n",
     "\n",
-    "import qibo\n",
+    "# import qibo\n",
     "from qibo import Circuit, gates, hamiltonians\n",
     "from qibo.backends import construct_backend"
    ]
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "id": "b0a1da82",
    "metadata": {},
    "outputs": [],
@@ -53,7 +53,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "64162116-1555-4a68-811c-01593739d622",
    "metadata": {},
    "outputs": [],
@@ -62,7 +62,7 @@
     "quimb_backend = construct_backend(backend=\"qibotn\", platform=\"quimb\")\n",
     "\n",
     "# set number of qubits\n",
-    "nqubits = 25\n",
+    "nqubits = 4\n",
     "\n",
     "# set numpy random seed\n",
     "np.random.seed(42)\n",
@@ -83,7 +83,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 3,
    "id": "4a22a172-f50d-411d-afa3-fa61937c7b3a",
    "metadata": {},
    "outputs": [],
@@ -102,7 +102,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 4,
    "id": "76f23c57-6d08-496b-9a27-52fb63bbfcb1",
    "metadata": {},
    "outputs": [
@@ -110,83 +110,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0 :     ─RY─RZ─o───────────────────────────────────────────────X─RY─RZ─o────── ...\n",
-      "1 :     ─RY─RZ─X─o─────────────────────────────────────────────|─RY─RZ─X─o──── ...\n",
-      "2 :     ─RY─RZ───X─o───────────────────────────────────────────|─RY─RZ───X─o── ...\n",
-      "3 :     ─RY─RZ─────X─o─────────────────────────────────────────|─RY─RZ─────X─o ...\n",
-      "4 :     ─RY─RZ───────X─o───────────────────────────────────────|─RY─RZ───────X ...\n",
-      "5 :     ─RY─RZ─────────X─o─────────────────────────────────────|─RY─RZ──────── ...\n",
-      "6 :     ─RY─RZ───────────X─o───────────────────────────────────|─RY─RZ──────── ...\n",
-      "7 :     ─RY─RZ─────────────X─o─────────────────────────────────|─RY─RZ──────── ...\n",
-      "8 :     ─RY─RZ───────────────X─o───────────────────────────────|─RY─RZ──────── ...\n",
-      "9 :     ─RY─RZ─────────────────X─o─────────────────────────────|─RY─RZ──────── ...\n",
-      "10:     ─RY─RZ───────────────────X─o───────────────────────────|─RY─RZ──────── ...\n",
-      "11:     ─RY─RZ─────────────────────X─o─────────────────────────|─RY─RZ──────── ...\n",
-      "12:     ─RY─RZ───────────────────────X─o───────────────────────|─RY─RZ──────── ...\n",
-      "13:     ─RY─RZ─────────────────────────X─o─────────────────────|─RY─RZ──────── ...\n",
-      "14:     ─RY─RZ───────────────────────────X─o───────────────────|─RY─RZ──────── ...\n",
-      "15:     ─RY─RZ─────────────────────────────X─o─────────────────|─RY─RZ──────── ...\n",
-      "16:     ─RY─RZ───────────────────────────────X─o───────────────|─RY─RZ──────── ...\n",
-      "17:     ─RY─RZ─────────────────────────────────X─o─────────────|─RY─RZ──────── ...\n",
-      "18:     ─RY─RZ───────────────────────────────────X─o───────────|─RY─RZ──────── ...\n",
-      "19:     ─RY─RZ─────────────────────────────────────X─o─────────|─RY─RZ──────── ...\n",
-      "20:     ─RY─RZ───────────────────────────────────────X─o───────|─RY─RZ──────── ...\n",
-      "21:     ─RY─RZ─────────────────────────────────────────X─o─────|─RY─RZ──────── ...\n",
-      "22:     ─RY─RZ───────────────────────────────────────────X─o───|─RY─RZ──────── ...\n",
-      "23:     ─RY─RZ─────────────────────────────────────────────X─o─|─RY─RZ──────── ...\n",
-      "24:     ─RY─RZ───────────────────────────────────────────────X─o─RY─RZ──────── ...\n",
-      "\n",
-      "0 : ... ─────────────────────────────────────────X─RY─RZ─o──────────────────── ...\n",
-      "1 : ... ─────────────────────────────────────────|─RY─RZ─X─o────────────────── ...\n",
-      "2 : ... ─────────────────────────────────────────|─RY─RZ───X─o──────────────── ...\n",
-      "3 : ... ─────────────────────────────────────────|─RY─RZ─────X─o────────────── ...\n",
-      "4 : ... ─o───────────────────────────────────────|─RY─RZ───────X─o──────────── ...\n",
-      "5 : ... ─X─o─────────────────────────────────────|─RY─RZ─────────X─o────────── ...\n",
-      "6 : ... ───X─o───────────────────────────────────|─RY─RZ───────────X─o──────── ...\n",
-      "7 : ... ─────X─o─────────────────────────────────|─RY─RZ─────────────X─o────── ...\n",
-      "8 : ... ───────X─o───────────────────────────────|─RY─RZ───────────────X─o──── ...\n",
-      "9 : ... ─────────X─o─────────────────────────────|─RY─RZ─────────────────X─o── ...\n",
-      "10: ... ───────────X─o───────────────────────────|─RY─RZ───────────────────X─o ...\n",
-      "11: ... ─────────────X─o─────────────────────────|─RY─RZ─────────────────────X ...\n",
-      "12: ... ───────────────X─o───────────────────────|─RY─RZ────────────────────── ...\n",
-      "13: ... ─────────────────X─o─────────────────────|─RY─RZ────────────────────── ...\n",
-      "14: ... ───────────────────X─o───────────────────|─RY─RZ────────────────────── ...\n",
-      "15: ... ─────────────────────X─o─────────────────|─RY─RZ────────────────────── ...\n",
-      "16: ... ───────────────────────X─o───────────────|─RY─RZ────────────────────── ...\n",
-      "17: ... ─────────────────────────X─o─────────────|─RY─RZ────────────────────── ...\n",
-      "18: ... ───────────────────────────X─o───────────|─RY─RZ────────────────────── ...\n",
-      "19: ... ─────────────────────────────X─o─────────|─RY─RZ────────────────────── ...\n",
-      "20: ... ───────────────────────────────X─o───────|─RY─RZ────────────────────── ...\n",
-      "21: ... ─────────────────────────────────X─o─────|─RY─RZ────────────────────── ...\n",
-      "22: ... ───────────────────────────────────X─o───|─RY─RZ────────────────────── ...\n",
-      "23: ... ─────────────────────────────────────X─o─|─RY─RZ────────────────────── ...\n",
-      "24: ... ───────────────────────────────────────X─o─RY─RZ────────────────────── ...\n",
-      "\n",
-      "0 : ... ───────────────────────────X─M─\n",
-      "1 : ... ───────────────────────────|─M─\n",
-      "2 : ... ───────────────────────────|─M─\n",
-      "3 : ... ───────────────────────────|─M─\n",
-      "4 : ... ───────────────────────────|─M─\n",
-      "5 : ... ───────────────────────────|─M─\n",
-      "6 : ... ───────────────────────────|─M─\n",
-      "7 : ... ───────────────────────────|─M─\n",
-      "8 : ... ───────────────────────────|─M─\n",
-      "9 : ... ───────────────────────────|─M─\n",
-      "10: ... ───────────────────────────|─M─\n",
-      "11: ... ─o─────────────────────────|─M─\n",
-      "12: ... ─X─o───────────────────────|─M─\n",
-      "13: ... ───X─o─────────────────────|─M─\n",
-      "14: ... ─────X─o───────────────────|─M─\n",
-      "15: ... ───────X─o─────────────────|─M─\n",
-      "16: ... ─────────X─o───────────────|─M─\n",
-      "17: ... ───────────X─o─────────────|─M─\n",
-      "18: ... ─────────────X─o───────────|─M─\n",
-      "19: ... ───────────────X─o─────────|─M─\n",
-      "20: ... ─────────────────X─o───────|─M─\n",
-      "21: ... ───────────────────X─o─────|─M─\n",
-      "22: ... ─────────────────────X─o───|─M─\n",
-      "23: ... ───────────────────────X─o─|─M─\n",
-      "24: ... ─────────────────────────X─o─M─\n"
+      "0: ─RY─RZ─o─────X─RY─RZ─o─────X─RY─RZ─o─────X─M─\n",
+      "1: ─RY─RZ─X─o───|─RY─RZ─X─o───|─RY─RZ─X─o───|─M─\n",
+      "2: ─RY─RZ───X─o─|─RY─RZ───X─o─|─RY─RZ───X─o─|─M─\n",
+      "3: ─RY─RZ─────X─o─RY─RZ─────X─o─RY─RZ─────X─o─M─\n"
      ]
     }
    ],
@@ -197,7 +124,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 6,
    "id": "07b2c097-cea2-42ec-8f1d-b4bbb5b71d98",
    "metadata": {},
    "outputs": [],
@@ -220,7 +147,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 7,
    "id": "2ee03e94-d794-4a51-9e76-01e8d8a259ba",
    "metadata": {},
    "outputs": [],
@@ -248,235 +175,84 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 8,
    "id": "35a244c3-adba-4b8b-b28c-0ab592b0f7cf",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/mattia/main_env/lib/python3.12/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: creg\n",
+      "  warnings.warn(\n",
+      "/home/mattia/main_env/lib/python3.12/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: measure\n",
+      "  warnings.warn(\n",
+      "/home/mattia/main_env/lib/python3.12/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
+      "  from .autonotebook import tqdm as notebook_tqdm\n"
+     ]
+    },
     {
      "data": {
       "text/plain": [
-       "{'nqubits': 25,\n",
+       "{'nqubits': 4,\n",
        " 'backend': qibotn (quimb),\n",
-       " 'measures': Counter({'0010101100100011101100110': 1,\n",
-       "          '1101010011101101100010011': 1,\n",
-       "          '0100010101110001100001001': 1,\n",
-       "          '1100001000000010101011101': 1,\n",
-       "          '0100101000100110010010000': 1,\n",
-       "          '0100000111111100111001100': 1,\n",
-       "          '0010101100000111100000000': 1,\n",
-       "          '0101111100011000101100111': 1,\n",
-       "          '0111111001101110011000111': 1,\n",
-       "          '1111011100010111101010110': 1,\n",
-       "          '1001000111111111111000000': 1,\n",
-       "          '1110010011010011000010000': 1,\n",
-       "          '1001101011101101100000000': 1,\n",
-       "          '1010101100011110001110111': 1,\n",
-       "          '0111010110011101010101010': 1,\n",
-       "          '1000110100110010010011101': 1,\n",
-       "          '0010010001010110000011100': 1,\n",
-       "          '1110110010010000110100101': 1,\n",
-       "          '1110010110011111101110101': 1,\n",
-       "          '0101001000011111100010111': 1,\n",
-       "          '0111011101111111101101111': 1,\n",
-       "          '0011111111100001011000010': 1,\n",
-       "          '0110001100010001000101011': 1,\n",
-       "          '0100101101000010101101111': 1,\n",
-       "          '0101010010010010000111001': 1,\n",
-       "          '0000000011111101101011110': 1,\n",
-       "          '0000100100100001101011010': 1,\n",
-       "          '1010111100000101010101110': 1,\n",
-       "          '0110011011000001010101100': 1,\n",
-       "          '1111001101101001111111111': 1,\n",
-       "          '0011001011011110000010000': 1,\n",
-       "          '1001100100010000010010000': 1,\n",
-       "          '1011111101100001111110011': 1,\n",
-       "          '0011101011101010010111001': 1,\n",
-       "          '1111100010010010101100110': 1,\n",
-       "          '0101100001011110010100010': 1,\n",
-       "          '0100101110010011000011000': 1,\n",
-       "          '1011001011101011101000101': 1,\n",
-       "          '0000101111101100010100010': 1,\n",
-       "          '1101000010100000011000110': 1,\n",
-       "          '1100110110101111110010001': 1,\n",
-       "          '1100001011010011010111101': 1,\n",
-       "          '1000101011010011111001101': 1,\n",
-       "          '1100001001010101110010100': 1,\n",
-       "          '0110101101110000001100110': 1,\n",
-       "          '0111110111010101101000110': 1,\n",
-       "          '1110010111101010101000101': 1,\n",
-       "          '1000110010011010000110000': 1,\n",
-       "          '1001011101010100010010001': 1,\n",
-       "          '0100110100010001000101000': 1,\n",
-       "          '0000100010100010010100010': 1,\n",
-       "          '1010110110011100011000101': 1,\n",
-       "          '0000110010100001101001010': 1,\n",
-       "          '0100101000111100110010111': 1,\n",
-       "          '1011101011011110000001011': 1,\n",
-       "          '1010011111111101011110110': 1,\n",
-       "          '1100110111100010000011110': 1,\n",
-       "          '0100110100100000101100111': 1,\n",
-       "          '1110111100011110001011101': 1,\n",
-       "          '0011001100110011101000110': 1,\n",
-       "          '1000110000111001101011101': 1,\n",
-       "          '0100101101000010101011111': 1,\n",
-       "          '0101010000000110010101001': 1,\n",
-       "          '0110111101101010010111000': 1,\n",
-       "          '0010010010100010101010101': 1,\n",
-       "          '1100001000101011101100101': 1,\n",
-       "          '1010101000011101101101011': 1,\n",
-       "          '1000010111001110010011110': 1,\n",
-       "          '0000010001110001100000011': 1,\n",
-       "          '0011010000101101111101100': 1,\n",
-       "          '1011010000100011000010000': 1,\n",
-       "          '1110100011001010000110000': 1,\n",
-       "          '1101000111110111001100101': 1,\n",
-       "          '0110001101010001110011010': 1,\n",
-       "          '1001011000100110101010101': 1,\n",
-       "          '0000110010100000000110111': 1,\n",
-       "          '1111001000001000111001000': 1,\n",
-       "          '0011100011100010010100001': 1,\n",
-       "          '0111111110010000001010111': 1,\n",
-       "          '1011100100101101101011110': 1,\n",
-       "          '0111001011100110001000001': 1,\n",
-       "          '0111001000110000111101111': 1,\n",
-       "          '1101111011001110000000000': 1,\n",
-       "          '0010111101011101010010100': 1,\n",
-       "          '1100100010010001111101000': 1,\n",
-       "          '0101011111100010101010100': 1,\n",
-       "          '1110100111011111111000001': 1,\n",
-       "          '1100000010101100001000110': 1,\n",
-       "          '0111011011010001011001011': 1,\n",
-       "          '0111000000100001101010011': 1,\n",
-       "          '1001111100110001111101000': 1,\n",
-       "          '0011010010100101010101100': 1,\n",
-       "          '1010111011011001101100011': 1,\n",
-       "          '1001000100001110000110000': 1,\n",
-       "          '1011011110100101010100101': 1,\n",
-       "          '0101100010011101111111001': 1,\n",
-       "          '0000100000101110000001000': 1,\n",
-       "          '1110010111000010111001000': 1,\n",
-       "          '1011011101101101111011101': 1,\n",
-       "          '0111100010010001111001011': 1}),\n",
-       " 'measured_probabilities': {'0010101100100011101100110': np.float64(1.4287479948554065e-07),\n",
-       "  '1101010011101101100010011': np.float64(6.840535900713192e-07),\n",
-       "  '0100010101110001100001001': np.float64(2.4297656493808975e-08),\n",
-       "  '1100001000000010101011101': np.float64(8.093409548935148e-07),\n",
-       "  '0100101000100110010010000': np.float64(4.2843525768921185e-07),\n",
-       "  '0100000111111100111001100': np.float64(5.4788880664882446e-08),\n",
-       "  '0010101100000111100000000': np.float64(6.350945339007582e-09),\n",
-       "  '0101111100011000101100111': np.float64(1.6189384309546533e-09),\n",
-       "  '0111111001101110011000111': np.float64(4.231070771736262e-07),\n",
-       "  '1111011100010111101010110': np.float64(8.809840523521098e-08),\n",
-       "  '1001000111111111111000000': np.float64(2.2649917694883763e-09),\n",
-       "  '1110010011010011000010000': np.float64(2.9400450442747213e-06),\n",
-       "  '1001101011101101100000000': np.float64(3.564993949972801e-07),\n",
-       "  '1010101100011110001110111': np.float64(2.0353895972901936e-07),\n",
-       "  '0111010110011101010101010': np.float64(9.272342830457222e-08),\n",
-       "  '1000110100110010010011101': np.float64(1.0554195999421195e-07),\n",
-       "  '0010010001010110000011100': np.float64(4.926758473909799e-08),\n",
-       "  '1110110010010000110100101': np.float64(3.6907560113556863e-07),\n",
-       "  '1110010110011111101110101': np.float64(1.0912695706428317e-07),\n",
-       "  '0101001000011111100010111': np.float64(2.3749237133846456e-07),\n",
-       "  '0111011101111111101101111': np.float64(4.4313847930510314e-07),\n",
-       "  '0011111111100001011000010': np.float64(2.879407202649115e-09),\n",
-       "  '0110001100010001000101011': np.float64(2.2970898298927726e-08),\n",
-       "  '0100101101000010101101111': np.float64(1.2403396951734157e-06),\n",
-       "  '0101010010010010000111001': np.float64(3.2580433289301146e-06),\n",
-       "  '0000000011111101101011110': np.float64(7.551781140278402e-07),\n",
-       "  '0000100100100001101011010': np.float64(7.342186380985404e-06),\n",
-       "  '1010111100000101010101110': np.float64(2.0803417549284257e-07),\n",
-       "  '0110011011000001010101100': np.float64(6.536548485677532e-09),\n",
-       "  '1111001101101001111111111': np.float64(6.662093312934175e-08),\n",
-       "  '0011001011011110000010000': np.float64(9.152885414596061e-07),\n",
-       "  '1001100100010000010010000': np.float64(1.1822334160129414e-06),\n",
-       "  '1011111101100001111110011': np.float64(1.2742285932601216e-05),\n",
-       "  '0011101011101010010111001': np.float64(8.001218354241628e-07),\n",
-       "  '1111100010010010101100110': np.float64(9.3255563882172e-07),\n",
-       "  '0101100001011110010100010': np.float64(1.0626891034969866e-06),\n",
-       "  '0100101110010011000011000': np.float64(1.5652631724013031e-07),\n",
-       "  '1011001011101011101000101': np.float64(1.025423997199104e-06),\n",
-       "  '0000101111101100010100010': np.float64(6.003473256257238e-07),\n",
-       "  '1101000010100000011000110': np.float64(1.085658621941692e-06),\n",
-       "  '1100110110101111110010001': np.float64(4.659708973943698e-09),\n",
-       "  '1100001011010011010111101': np.float64(5.295910969809775e-07),\n",
-       "  '1000101011010011111001101': np.float64(3.6779048150728553e-07),\n",
-       "  '1100001001010101110010100': np.float64(4.92126869361337e-09),\n",
-       "  '0110101101110000001100110': np.float64(7.741427610734003e-08),\n",
-       "  '0111110111010101101000110': np.float64(2.399267980010788e-07),\n",
-       "  '1110010111101010101000101': np.float64(5.667518009732859e-07),\n",
-       "  '1000110010011010000110000': np.float64(2.084260073059544e-06),\n",
-       "  '1001011101010100010010001': np.float64(2.6571545078690544e-08),\n",
-       "  '0100110100010001000101000': np.float64(3.079779061777933e-08),\n",
-       "  '0000100010100010010100010': np.float64(6.929792821857359e-06),\n",
-       "  '1010110110011100011000101': np.float64(4.630180771716902e-08),\n",
-       "  '0000110010100001101001010': np.float64(9.116530823953186e-07),\n",
-       "  '0100101000111100110010111': np.float64(1.3249324853060952e-07),\n",
-       "  '1011101011011110000001011': np.float64(1.1907229585114808e-06),\n",
-       "  '1010011111111101011110110': np.float64(4.56149319722231e-09),\n",
-       "  '1100110111100010000011110': np.float64(5.257006816629565e-07),\n",
-       "  '0100110100100000101100111': np.float64(5.776773429581827e-07),\n",
-       "  '1110111100011110001011101': np.float64(1.9990466754187882e-07),\n",
-       "  '0011001100110011101000110': np.float64(4.3593985418091113e-08),\n",
-       "  '1000110000111001101011101': np.float64(3.6389888110895923e-07),\n",
-       "  '0100101101000010101011111': np.float64(7.622087666902094e-07),\n",
-       "  '0101010000000110010101001': np.float64(2.994365575033701e-07),\n",
-       "  '0110111101101010010111000': np.float64(3.147129865281865e-08),\n",
-       "  '0010010010100010101010101': np.float64(3.7955795123562516e-07),\n",
-       "  '1100001000101011101100101': np.float64(2.483089067956661e-07),\n",
-       "  '1010101000011101101101011': np.float64(3.09860035910458e-07),\n",
-       "  '1000010111001110010011110': np.float64(4.718847603022761e-08),\n",
-       "  '0000010001110001100000011': np.float64(1.618347020880399e-08),\n",
-       "  '0011010000101101111101100': np.float64(2.307864975407703e-07),\n",
-       "  '1011010000100011000010000': np.float64(1.604607088007449e-07),\n",
-       "  '1110100011001010000110000': np.float64(5.735844296703352e-07),\n",
-       "  '1101000111110111001100101': np.float64(7.018930935740711e-10),\n",
-       "  '0110001101010001110011010': np.float64(1.426676825693035e-07),\n",
-       "  '1001011000100110101010101': np.float64(1.3658924161666397e-07),\n",
-       "  '0000110010100000000110111': np.float64(7.127088059066376e-07),\n",
-       "  '1111001000001000111001000': np.float64(9.382957208112125e-08),\n",
-       "  '0011100011100010010100001': np.float64(1.5633352068001958e-07),\n",
-       "  '0111111110010000001010111': np.float64(6.24916842986095e-07),\n",
-       "  '1011100100101101101011110': np.float64(5.277053774965453e-08),\n",
-       "  '0111001011100110001000001': np.float64(2.706733332328552e-07),\n",
-       "  '0111001000110000111101111': np.float64(8.740290927759748e-07),\n",
-       "  '1101111011001110000000000': np.float64(1.1390459236761492e-07),\n",
-       "  '0010111101011101010010100': np.float64(2.851294124498577e-06),\n",
-       "  '1100100010010001111101000': np.float64(8.627935077391886e-06),\n",
-       "  '0101011111100010101010100': np.float64(6.937375172146743e-08),\n",
-       "  '1110100111011111111000001': np.float64(2.517698486277455e-07),\n",
-       "  '1100000010101100001000110': np.float64(2.1300563007206324e-07),\n",
-       "  '0111011011010001011001011': np.float64(5.8246768046662493e-08),\n",
-       "  '0111000000100001101010011': np.float64(3.123499806377365e-07),\n",
-       "  '1001111100110001111101000': np.float64(4.777318918055056e-07),\n",
-       "  '0011010010100101010101100': np.float64(5.494449035514909e-07),\n",
-       "  '1010111011011001101100011': np.float64(1.1425290362328705e-06),\n",
-       "  '1001000100001110000110000': np.float64(3.266349767666358e-08),\n",
-       "  '1011011110100101010100101': np.float64(5.947082800379298e-07),\n",
-       "  '0101100010011101111111001': np.float64(3.5373491729489938e-06),\n",
-       "  '0000100000101110000001000': np.float64(3.041450478019988e-07),\n",
-       "  '1110010111000010111001000': np.float64(2.0041305331234744e-07),\n",
-       "  '1011011101101101111011101': np.float64(2.701698118830075e-07),\n",
-       "  '0111100010010001111001011': np.float64(1.3996687152906713e-06)},\n",
+       " 'measures': Counter({'0011': 8,\n",
+       "          '0010': 12,\n",
+       "          '0111': 4,\n",
+       "          '1011': 7,\n",
+       "          '0000': 8,\n",
+       "          '1110': 14,\n",
+       "          '0101': 4,\n",
+       "          '1010': 4,\n",
+       "          '1000': 14,\n",
+       "          '1111': 8,\n",
+       "          '0100': 6,\n",
+       "          '1101': 8,\n",
+       "          '1100': 1,\n",
+       "          '0110': 2}),\n",
+       " 'measured_probabilities': {'1110': np.float64(0.07174919872959985),\n",
+       "  '1000': np.float64(0.11330883548333587),\n",
+       "  '0010': np.float64(0.09466860481989385),\n",
+       "  '0011': np.float64(0.07571277233522114),\n",
+       "  '0000': np.float64(0.08390937969317269),\n",
+       "  '1111': np.float64(0.10184806171791962),\n",
+       "  '1101': np.float64(0.12331159869893256),\n",
+       "  '1011': np.float64(0.053499396925872744),\n",
+       "  '0100': np.float64(0.07142939529687138),\n",
+       "  '0111': np.float64(0.04029185074729259),\n",
+       "  '0101': np.float64(0.05622305772698622),\n",
+       "  '1010': np.float64(0.03872758515126756),\n",
+       "  '0110': np.float64(0.05146064807369214),\n",
+       "  '1100': np.float64(0.013605984872668404)},\n",
        " 'prob_type': 'default',\n",
-       " 'statevector': Array([[-5.8646699e-05-1.0826049e-04j],\n",
-       "        [-1.9374731e-05+8.6432210e-06j],\n",
-       "        [ 7.7656114e-05-3.3436768e-04j],\n",
-       "        ...,\n",
-       "        [ 1.4206149e-05+6.0087572e-05j],\n",
-       "        [ 1.2372108e-04-1.6373204e-05j],\n",
-       "        [ 3.0789568e-05+3.2571501e-05j]], dtype=complex64)}"
+       " 'statevector': Array([[ 0.08809624-0.27594998j],\n",
+       "        [-0.05174781+0.04471217j],\n",
+       "        [ 0.00470147+0.30764672j],\n",
+       "        [-0.27208942+0.0409893j ],\n",
+       "        [ 0.18807822+0.18988408j],\n",
+       "        [ 0.2237706 +0.07842042j],\n",
+       "        [-0.18900308+0.12545314j],\n",
+       "        [ 0.17105256-0.10503749j],\n",
+       "        [ 0.24859734-0.22695419j],\n",
+       "        [-0.0411739 -0.06230037j],\n",
+       "        [ 0.17371392-0.09247189j],\n",
+       "        [-0.22748128+0.0418529j ],\n",
+       "        [ 0.09444095+0.06846087j],\n",
+       "        [-0.21784972-0.2754144j ],\n",
+       "        [-0.17359753+0.20399286j],\n",
+       "        [-0.01729754-0.31866732j]], dtype=complex64)}"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "# Simple execution (defaults)\n",
+    "# # Simple execution (defaults)\n",
     "outcome = quimb_backend.execute_circuit(circuit=circuit, nshots=100, return_array=True)\n",
     "\n",
-    "# Print outcome\n",
+    "# # Print outcome\n",
     "vars(outcome)"
    ]
   },
@@ -492,38 +268,36 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 9,
    "id": "c0443efc-21ef-4ed5-9cf4-785d204a1881",
    "metadata": {},
    "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "[Qibo 0.2.20|ERROR|2025-09-08 17:57:29]: Tensor network simulation cannot be used to reconstruct statevector for >= 20 .\n"
-     ]
-    },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Probabilities:\n",
-      " {'0010101100100011101100110': np.float64(1.4287479948554065e-07), '1101010011101101100010011': np.float64(6.840535900713192e-07), '0100010101110001100001001': np.float64(2.4297656493808975e-08), '1100001000000010101011101': np.float64(8.093409548935148e-07), '0100101000100110010010000': np.float64(4.2843525768921185e-07), '0100000111111100111001100': np.float64(5.4788880664882446e-08), '0010101100000111100000000': np.float64(6.350945339007582e-09), '0101111100011000101100111': np.float64(1.6189384309546533e-09), '0111111001101110011000111': np.float64(4.231070771736262e-07), '1111011100010111101010110': np.float64(8.809840523521098e-08), '1001000111111111111000000': np.float64(2.2649917694883763e-09), '1110010011010011000010000': np.float64(2.9400450442747213e-06), '1001101011101101100000000': np.float64(3.564993949972801e-07), '1010101100011110001110111': np.float64(2.0353895972901936e-07), '0111010110011101010101010': np.float64(9.272342830457222e-08), '1000110100110010010011101': np.float64(1.0554195999421195e-07), '0010010001010110000011100': np.float64(4.926758473909799e-08), '1110110010010000110100101': np.float64(3.6907560113556863e-07), '1110010110011111101110101': np.float64(1.0912695706428317e-07), '0101001000011111100010111': np.float64(2.3749237133846456e-07), '0111011101111111101101111': np.float64(4.4313847930510314e-07), '0011111111100001011000010': np.float64(2.879407202649115e-09), '0110001100010001000101011': np.float64(2.2970898298927726e-08), '0100101101000010101101111': np.float64(1.2403396951734157e-06), '0101010010010010000111001': np.float64(3.2580433289301146e-06), '0000000011111101101011110': np.float64(7.551781140278402e-07), '0000100100100001101011010': np.float64(7.342186380985404e-06), '1010111100000101010101110': np.float64(2.0803417549284257e-07), '0110011011000001010101100': np.float64(6.536548485677532e-09), '1111001101101001111111111': np.float64(6.662093312934175e-08), '0011001011011110000010000': np.float64(9.152885414596061e-07), '1001100100010000010010000': np.float64(1.1822334160129414e-06), '1011111101100001111110011': np.float64(1.2742285932601216e-05), '0011101011101010010111001': np.float64(8.001218354241628e-07), '1111100010010010101100110': np.float64(9.3255563882172e-07), '0101100001011110010100010': np.float64(1.0626891034969866e-06), '0100101110010011000011000': np.float64(1.5652631724013031e-07), '1011001011101011101000101': np.float64(1.025423997199104e-06), '0000101111101100010100010': np.float64(6.003473256257238e-07), '1101000010100000011000110': np.float64(1.085658621941692e-06), '1100110110101111110010001': np.float64(4.659708973943698e-09), '1100001011010011010111101': np.float64(5.295910969809775e-07), '1000101011010011111001101': np.float64(3.6779048150728553e-07), '1100001001010101110010100': np.float64(4.92126869361337e-09), '0110101101110000001100110': np.float64(7.741427610734003e-08), '0111110111010101101000110': np.float64(2.399267980010788e-07), '1110010111101010101000101': np.float64(5.667518009732859e-07), '1000110010011010000110000': np.float64(2.084260073059544e-06), '1001011101010100010010001': np.float64(2.6571545078690544e-08), '0100110100010001000101000': np.float64(3.079779061777933e-08), '0000100010100010010100010': np.float64(6.929792821857359e-06), '1010110110011100011000101': np.float64(4.630180771716902e-08), '0000110010100001101001010': np.float64(9.116530823953186e-07), '0100101000111100110010111': np.float64(1.3249324853060952e-07), '1011101011011110000001011': np.float64(1.1907229585114808e-06), '1010011111111101011110110': np.float64(4.56149319722231e-09), '1100110111100010000011110': np.float64(5.257006816629565e-07), '0100110100100000101100111': np.float64(5.776773429581827e-07), '1110111100011110001011101': np.float64(1.9990466754187882e-07), '0011001100110011101000110': np.float64(4.3593985418091113e-08), '1000110000111001101011101': np.float64(3.6389888110895923e-07), '0100101101000010101011111': np.float64(7.622087666902094e-07), '0101010000000110010101001': np.float64(2.994365575033701e-07), '0110111101101010010111000': np.float64(3.147129865281865e-08), '0010010010100010101010101': np.float64(3.7955795123562516e-07), '1100001000101011101100101': np.float64(2.483089067956661e-07), '1010101000011101101101011': np.float64(3.09860035910458e-07), '1000010111001110010011110': np.float64(4.718847603022761e-08), '0000010001110001100000011': np.float64(1.618347020880399e-08), '0011010000101101111101100': np.float64(2.307864975407703e-07), '1011010000100011000010000': np.float64(1.604607088007449e-07), '1110100011001010000110000': np.float64(5.735844296703352e-07), '1101000111110111001100101': np.float64(7.018930935740711e-10), '0110001101010001110011010': np.float64(1.426676825693035e-07), '1001011000100110101010101': np.float64(1.3658924161666397e-07), '0000110010100000000110111': np.float64(7.127088059066376e-07), '1111001000001000111001000': np.float64(9.382957208112125e-08), '0011100011100010010100001': np.float64(1.5633352068001958e-07), '0111111110010000001010111': np.float64(6.24916842986095e-07), '1011100100101101101011110': np.float64(5.277053774965453e-08), '0111001011100110001000001': np.float64(2.706733332328552e-07), '0111001000110000111101111': np.float64(8.740290927759748e-07), '1101111011001110000000000': np.float64(1.1390459236761492e-07), '0010111101011101010010100': np.float64(2.851294124498577e-06), '1100100010010001111101000': np.float64(8.627935077391886e-06), '0101011111100010101010100': np.float64(6.937375172146743e-08), '1110100111011111111000001': np.float64(2.517698486277455e-07), '1100000010101100001000110': np.float64(2.1300563007206324e-07), '0111011011010001011001011': np.float64(5.8246768046662493e-08), '0111000000100001101010011': np.float64(3.123499806377365e-07), '1001111100110001111101000': np.float64(4.777318918055056e-07), '0011010010100101010101100': np.float64(5.494449035514909e-07), '1010111011011001101100011': np.float64(1.1425290362328705e-06), '1001000100001110000110000': np.float64(3.266349767666358e-08), '1011011110100101010100101': np.float64(5.947082800379298e-07), '0101100010011101111111001': np.float64(3.5373491729489938e-06), '0000100000101110000001000': np.float64(3.041450478019988e-07), '1110010111000010111001000': np.float64(2.0041305331234744e-07), '1011011101101101111011101': np.float64(2.701698118830075e-07), '0111100010010001111001011': np.float64(1.3996687152906713e-06)}\n",
+      " {'1110': np.float64(0.07174919872959985), '1000': np.float64(0.11330883548333587), '0010': np.float64(0.09466860481989385), '0011': np.float64(0.07571277233522114), '0000': np.float64(0.08390937969317269), '1111': np.float64(0.10184806171791962), '1101': np.float64(0.12331159869893256), '1011': np.float64(0.053499396925872744), '0100': np.float64(0.07142939529687138), '0111': np.float64(0.04029185074729259), '0101': np.float64(0.05622305772698622), '1010': np.float64(0.03872758515126756), '0110': np.float64(0.05146064807369214), '1100': np.float64(0.013605984872668404)}\n",
+      "\n",
+      "State:\n",
+      " [[ 0.08809624-0.27594998j]\n",
+      " [-0.05174781+0.04471217j]\n",
+      " [ 0.00470147+0.30764672j]\n",
+      " [-0.27208942+0.0409893j ]\n",
+      " [ 0.18807822+0.18988408j]\n",
+      " [ 0.2237706 +0.07842042j]\n",
+      " [-0.18900308+0.12545314j]\n",
+      " [ 0.17105256-0.10503749j]\n",
+      " [ 0.24859734-0.22695419j]\n",
+      " [-0.0411739 -0.06230037j]\n",
+      " [ 0.17371392-0.09247189j]\n",
+      " [-0.22748128+0.0418529j ]\n",
+      " [ 0.09444095+0.06846087j]\n",
+      " [-0.21784972-0.2754144j ]\n",
+      " [-0.17359753+0.20399286j]\n",
+      " [-0.01729754-0.31866732j]]\n",
       "\n"
      ]
-    },
-    {
-     "ename": "NotImplementedError",
-     "evalue": "Tensor network simulation cannot be used to reconstruct statevector for >= 20 .",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
-      "\u001b[0;32m/tmp/ipykernel_44825/1053899561.py\u001b[0m in \u001b[0;36m<cell line: 0>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"\u001b[0m\u001b[0;34mProbabilities:\\n \u001b[0m\u001b[0;34m{\u001b[0m\u001b[0moutcome\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprobabilities\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\\n\u001b[0m\u001b[0;34m\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"\u001b[0m\u001b[0;34mState:\\n \u001b[0m\u001b[0;34m{\u001b[0m\u001b[0moutcome\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\\n\u001b[0m\u001b[0;34m\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m~/repo/qibotn/src/qibotn/result.py\u001b[0m in \u001b[0;36mstate\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     61\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnqubits\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatevector\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 63\u001b[0;31m         raise_error(\n\u001b[0m\u001b[1;32m     64\u001b[0m             \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     65\u001b[0m             \u001b[0;34mf\"\u001b[0m\u001b[0;34mTensor network simulation cannot be used to reconstruct statevector for >= 20 .\u001b[0m\u001b[0;34m\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m~/main_env/lib/python3.12/site-packages/qibo/config.py\u001b[0m in \u001b[0;36mraise_error\u001b[0;34m(exception, message)\u001b[0m\n\u001b[1;32m     44\u001b[0m     \"\"\"\n\u001b[1;32m     45\u001b[0m     \u001b[0mlog\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0merror\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 46\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mexception\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     47\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     48\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mNotImplementedError\u001b[0m: Tensor network simulation cannot be used to reconstruct statevector for >= 20 ."
-     ]
     }
    ],
    "source": [
@@ -547,7 +321,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 10,
    "id": "37385485-e8a3-4ab0-ad44-bcc4e9da24ca",
    "metadata": {},
    "outputs": [
@@ -555,83 +329,10 @@
      "name": "stdout",
      "output_type": "stream",
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@@ -647,60 +348,53 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 11,
    "id": "ddecc910-7804-4199-8577-a7db38a16db8",
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/latex": [
-       "$\\displaystyle 3.6 X_{0} + 3.6 X_{1} + 3.6 X_{10} + 3.6 X_{11} + 3.6 X_{12} + 3.6 X_{13} + 3.6 X_{14} + 3.6 X_{15} + 3.6 X_{16} + 3.6 X_{17} + 3.6 X_{18} + 3.6 X_{19} + 3.6 X_{2} + 3.6 X_{20} + 3.6 X_{21} + 3.6 X_{22} + 3.6 X_{23} + 3.6 X_{24} + 3.6 X_{3} + 3.6 X_{4} + 3.6 X_{5} + 3.6 X_{6} + 3.6 X_{7} + 3.6 X_{8} + 3.6 X_{9} + 8.4 Z_{0} + 8.4 Z_{1} + 8.4 Z_{10} + 8.4 Z_{11} + 8.4 Z_{12} + 8.4 Z_{13} + 8.4 Z_{14} + 8.4 Z_{15} + 8.4 Z_{16} + 8.4 Z_{17} + 8.4 Z_{18} + 8.4 Z_{19} + 8.4 Z_{2} + 8.4 Z_{20} + 8.4 Z_{21} + 8.4 Z_{22} + 8.4 Z_{23} + 8.4 Z_{24} + 8.4 Z_{3} + 8.4 Z_{4} + 8.4 Z_{5} + 8.4 Z_{6} + 8.4 Z_{7} + 8.4 Z_{8} + 8.4 Z_{9}$"
-      ],
-      "text/plain": [
-       "3.6*X0 + 3.6*X1 + 3.6*X10 + 3.6*X11 + 3.6*X12 + 3.6*X13 + 3.6*X14 + 3.6*X15 + 3.6*X16 + 3.6*X17 + 3.6*X18 + 3.6*X19 + 3.6*X2 + 3.6*X20 + 3.6*X21 + 3.6*X22 + 3.6*X23 + 3.6*X24 + 3.6*X3 + 3.6*X4 + 3.6*X5 + 3.6*X6 + 3.6*X7 + 3.6*X8 + 3.6*X9 + 8.4*Z0 + 8.4*Z1 + 8.4*Z10 + 8.4*Z11 + 8.4*Z12 + 8.4*Z13 + 8.4*Z14 + 8.4*Z15 + 8.4*Z16 + 8.4*Z17 + 8.4*Z18 + 8.4*Z19 + 8.4*Z2 + 8.4*Z20 + 8.4*Z21 + 8.4*Z22 + 8.4*Z23 + 8.4*Z24 + 8.4*Z3 + 8.4*Z4 + 8.4*Z5 + 8.4*Z6 + 8.4*Z7 + 8.4*Z8 + 8.4*Z9"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "from qibo.symbols import Z, X, I\n",
-    "\n",
-    "form = 0\n",
-    "for i in range(nqubits):\n",
-    "    for _ in range(12):\n",
-    "        form += 0.7 * Z(i)\n",
-    "        form += 0.3 * X(i)\n",
-    "\n",
-    "hamiltonian = hamiltonians.SymbolicHamiltonian(form)\n",
-    "\n",
-    "hamiltonian.form\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "id": "163b70a3-814a-4a62-a98a-2ffca933a544",
-   "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/home/mattia/main_env/lib/python3.12/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: creg\n",
-      "  warnings.warn(\n",
-      "/home/mattia/main_env/lib/python3.12/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: measure\n",
-      "  warnings.warn(\n"
+      "[Qibo 0.2.20|INFO|2025-09-20 16:43:42]: Using qibojit (numba) backend on /CPU:0\n"
      ]
     },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle - 1.5 X_{0} Z_{2} + 0.5 Z_{0} Z_{1} + Z_{3}$"
+      ],
+      "text/plain": [
+       "-1.5*X0*Z2 + 0.5*Z0*Z1 + Z3"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from qibo.symbols import Z, X, I\n",
+    "# We can create a symbolic Hamiltonian\n",
+    "form = 0.5 * Z(0) * Z(1) +- 1.5 *  X(0) * Z(2) + Z(3)\n",
+    "hamiltonian = hamiltonians.SymbolicHamiltonian(form)\n",
+    "\n",
+    "#  Let's show it\n",
+    "hamiltonian.form"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "163b70a3-814a-4a62-a98a-2ffca933a544",
+   "metadata": {},
+   "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Expectation value: -0.9053105195111129\n",
-      "Elapsed time: 20.0296 seconds\n"
+      "Expectation value: 0.7143489122390747\n",
+      "Elapsed time: 12.4550 seconds\n"
      ]
     }
    ],
@@ -725,7 +419,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 14,
    "id": "e2d05707",
    "metadata": {},
    "outputs": [
@@ -733,8 +427,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Expectation value: -0.9053096709847108\n",
-      "Elapsed time: 319.1915 seconds\n"
+      "Expectation value: 0.7143570920618565\n",
+      "Elapsed time: 0.5871 seconds\n"
      ]
     }
    ],
@@ -753,6 +447,141 @@
    "source": [
     "They match! 🥳"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d2d119fc",
+   "metadata": {},
+   "source": [
+    "### Derivative of the extimation function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "8df55c5f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: ─RY─RZ─o─────X─RY─RZ─o─────X─RY─RZ─o─────X─M─\n",
+      "1: ─RY─RZ─X─o───|─RY─RZ─X─o───|─RY─RZ─X─o───|─M─\n",
+      "2: ─RY─RZ───X─o─|─RY─RZ───X─o─|─RY─RZ───X─o─|─M─\n",
+      "3: ─RY─RZ─────X─o─RY─RZ─────X─o─RY─RZ─────X─o─M─\n"
+     ]
+    }
+   ],
+   "source": [
+    "# grad of this circuit returning nan for some reason...\n",
+    "\n",
+    "def build_circuit(nqubits, nlayers):\n",
+    "    \"\"\"Construct a parametric quantum circuit.\"\"\"\n",
+    "    circ = Circuit(nqubits)\n",
+    "    for _ in range(nlayers):\n",
+    "        for q in range(nqubits):\n",
+    "            circ.add(gates.RY(q=q, theta=0.))\n",
+    "            circ.add(gates.RZ(q=q, theta=0.))\n",
+    "        [circ.add(gates.CNOT(q%nqubits, (q+1)%nqubits) for q in range(nqubits))]\n",
+    "    circ.add(gates.M(*range(nqubits)))\n",
+    "    return circ\n",
+    "\n",
+    "circuit = build_circuit(nqubits=nqubits, nlayers=3)\n",
+    "circuit.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b02de56b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: ─RY─RZ─RX─o─x─────────RY─RZ─RX─o─x─────────RY─RZ─RX─o─x─────────M─\n",
+      "1: ─RY─RZ─RX─X─x─o─x─────RY─RZ─RX─X─x─o─x─────RY─RZ─RX─X─x─o─x─────M─\n",
+      "2: ─RY─RZ─RX─────X─x─o─x─RY─RZ─RX─────X─x─o─x─RY─RZ─RX─────X─x─o─x─M─\n",
+      "3: ─RY─RZ─RX─────────X─x─RY─RZ─RX─────────X─x─RY─RZ─RX─────────X─x─M─\n"
+     ]
+    }
+   ],
+   "source": [
+    "def build_circuit(nqubits, nlayers):\n",
+    "    circ = Circuit(nqubits)\n",
+    "    for _ in range(nlayers):\n",
+    "        for q in range(nqubits):\n",
+    "            circ.add(gates.RY(q=q, theta=0.))\n",
+    "            circ.add(gates.RZ(q=q, theta=0.))\n",
+    "            circ.add(gates.RX(q=q, theta=0.))\n",
+    "        for q in range(nqubits - 1):\n",
+    "            circ.add(gates.CNOT(q, q + 1))\n",
+    "            circ.add(gates.SWAP(q, q + 1))\n",
+    "    circ.add(gates.M(*range(nqubits)))\n",
+    "    return circ\n",
+    "\n",
+    "circuit = build_circuit(nqubits=nqubits, nlayers=3)\n",
+    "circuit.draw()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "b803250f",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Array(1.4999985, dtype=float32)"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "quimb_backend.expectation(\n",
+    "        circuit=circuit,         \n",
+    "        observable=hamiltonian,\n",
+    "   )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "0943482e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(Array(0.4465402, dtype=float32), Array([-1.5755819e-01,  9.7801067e-02, -1.2350259e-01,  1.3670625e-01,\n",
+      "        3.6954228e-03, -1.7437905e-02,  2.7746204e-01, -1.0357879e-01,\n",
+      "        1.1504190e-01, -4.5175910e-02, -4.8447326e-02,  1.4743687e-01,\n",
+      "       -3.0708680e-01,  2.0652822e-01,  1.9298886e-01,  5.1306009e-02,\n",
+      "       -3.3362946e-01, -7.5548244e-01, -3.0034758e-02, -5.2868712e-01,\n",
+      "        4.8458660e-01, -2.9802322e-08,  8.0767423e-02,  0.0000000e+00],      dtype=float32))\n"
+     ]
+    }
+   ],
+   "source": [
+    "import jax\n",
+    "\n",
+    "def f(params):\n",
+    "    circuit.set_parameters(params)\n",
+    "    return quimb_backend.expectation(\n",
+    "        circuit=circuit,\n",
+    "        observable=hamiltonian,\n",
+    "    )\n",
+    "\n",
+    "parameters = np.random.uniform(-np.pi, np.pi, size=len(circuit.get_parameters()))\n",
+    "print(jax.value_and_grad(f)(parameters))\n"
+   ]
   }
  ],
  "metadata": {
diff --git a/examples/quimb_intro/test.py b/examples/quimb_intro/test.py
index da499f2..2eccd91 100644
--- a/examples/quimb_intro/test.py
+++ b/examples/quimb_intro/test.py
@@ -24,21 +24,23 @@ hamiltonian = hamiltonians.SymbolicHamiltonian(form)
 
 # define circuit
 def build_circuit(nqubits, nlayers):
-    """Construct a Qibo parametric quantum circuit."""
+    """Construct a more complex Qibo parametric quantum circuit without CNOT gates."""
     circ = Circuit(nqubits)
-    for _ in range(nlayers):
+    for layer in range(nlayers):
         for q in range(nqubits):
             circ.add(gates.RY(q=q, theta=0.))
             circ.add(gates.RZ(q=q, theta=0.))
-        [circ.add(gates.CZ(q % nqubits, (q + 1) % nqubits)) for q in range(nqubits)]
+            circ.add(gates.RX(q=q, theta=0.))
+        # Add controlled rotations and SWAPs for entanglement
+        for q in range(nqubits - 1):
+            circ.add(gates.CNOT(q, q + 1))
+            circ.add(gates.SWAP(q, q + 1))
     circ.add(gates.M(*range(nqubits)))
     return circ
 
-nqubits = 4
+nqubits = 6
 circuit = build_circuit(nqubits=nqubits, nlayers=3)
 
-quimb_circuit = quimb_backend._qibo_circuit_to_quimb(circuit)
-
 def f(params):
     circuit.set_parameters(params)
     return quimb_backend.expectation(
diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 3f09859..e4ebd5d 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -376,45 +376,6 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
 
         return A_new, B_new, C_new
 
-    # def _qibo_circuit_to_quimb(self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs):
-    #     """
-    #     Convert a Qibo Circuit to a Quimb Circuit.
-
-    #     Parameters
-    #     ----------
-    #     qibo_circ : qibo.models.circuit.Circuit
-    #         The circuit to convert.
-    #     quimb_circuit_type : type
-    #         The Quimb circuit class to use (Circuit, CircuitMPS, etc).
-    #     circuit_kwargs : dict
-    #         Extra arguments to pass to the Quimb circuit constructor.
-
-    #     Returns
-    #     -------
-    #     circ : quimb.tensor.circuit.Circuit
-    #         The converted circuit.
-    #     """
-    #     nqubits = qibo_circ.nqubits
-    #     quimb_gates = []
-    #     circ = quimb_circuit_type(nqubits, **circuit_kwargs)
-
-    #     for gate in qibo_circ.queue:
-    #         gname = getattr(gate, "name", None)
-    #         qname = GATE_MAP.get(gname, None)
-    #         if qname is None:
-    #             continue  # skip measurements and unknown gates
-
-    #         # Handle parametrized gates (Qibo: .parameters, Quimb: expects flat tuple)
-    #         params = getattr(gate, "parameters", ())
-    #         qubits = getattr(gate, "qubits", ())
-
-    #         # Quimb expects (*params, *qubits)
-    #         gate_spec = (qname,) + tuple(params) + tuple(qubits)
-    #         quimb_gates.append(gate_spec)
-
-    #     circ.apply_gates(quimb_gates)
-    #     return circ
-
     def _qibo_circuit_to_quimb(self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs):
         """
         Convert a Qibo Circuit to a Quimb Circuit.
@@ -446,8 +407,11 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             qubits = getattr(gate, "qubits", ())
             
             # Check if the gate is parametrized
-            is_parametrized = isinstance(gate, ParametrizedGate)
-            
+            is_parametrized = (
+                isinstance(gate, ParametrizedGate)
+                and getattr(gate, "trainable", True)
+            )
+            # import pdb; pdb.set_trace()
             if is_parametrized:
                 circ.apply_gate(
                     qname,

From 386891ee1aaa28a8deb7eeb1875461188d985af7 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Tue, 23 Sep 2025 00:37:11 +0200
Subject: [PATCH 11/33] updaged examples

---
 examples/quimb_intro/quimb_introduction.ipynb | 217 +++++++++---------
 examples/quimb_intro/test.py                  |  52 -----
 2 files changed, 106 insertions(+), 163 deletions(-)
 delete mode 100644 examples/quimb_intro/test.py

diff --git a/examples/quimb_intro/quimb_introduction.ipynb b/examples/quimb_intro/quimb_introduction.ipynb
index 266b49d..73a831b 100644
--- a/examples/quimb_intro/quimb_introduction.ipynb
+++ b/examples/quimb_intro/quimb_introduction.ipynb
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "b0a1da82",
    "metadata": {},
    "outputs": [],
@@ -53,7 +53,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 23,
    "id": "64162116-1555-4a68-811c-01593739d622",
    "metadata": {},
    "outputs": [],
@@ -69,7 +69,7 @@
     "\n",
     "quimb_backend.setup_backend_specifics(\n",
     "    qimb_backend=\"jax\", \n",
-    "    optimizer='auto-hq'\n",
+    "    contractions_optimizer=ctg_opt\n",
     "    )"
    ]
   },
@@ -83,7 +83,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 6,
    "id": "4a22a172-f50d-411d-afa3-fa61937c7b3a",
    "metadata": {},
    "outputs": [],
@@ -102,7 +102,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 7,
    "id": "76f23c57-6d08-496b-9a27-52fb63bbfcb1",
    "metadata": {},
    "outputs": [
@@ -124,7 +124,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 8,
    "id": "07b2c097-cea2-42ec-8f1d-b4bbb5b71d98",
    "metadata": {},
    "outputs": [],
@@ -147,7 +147,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 9,
    "id": "2ee03e94-d794-4a51-9e76-01e8d8a259ba",
    "metadata": {},
    "outputs": [],
@@ -175,7 +175,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 10,
    "id": "35a244c3-adba-4b8b-b28c-0ab592b0f7cf",
    "metadata": {},
    "outputs": [
@@ -196,33 +196,33 @@
       "text/plain": [
        "{'nqubits': 4,\n",
        " 'backend': qibotn (quimb),\n",
-       " 'measures': Counter({'0011': 8,\n",
+       " 'measures': Counter({'1000': 14,\n",
+       "          '1011': 9,\n",
+       "          '0101': 5,\n",
        "          '0010': 12,\n",
-       "          '0111': 4,\n",
-       "          '1011': 7,\n",
        "          '0000': 8,\n",
-       "          '1110': 14,\n",
-       "          '0101': 4,\n",
        "          '1010': 4,\n",
-       "          '1000': 14,\n",
-       "          '1111': 8,\n",
-       "          '0100': 6,\n",
-       "          '1101': 8,\n",
-       "          '1100': 1,\n",
-       "          '0110': 2}),\n",
-       " 'measured_probabilities': {'1110': np.float64(0.07174919872959985),\n",
+       "          '1101': 19,\n",
+       "          '0011': 6,\n",
+       "          '0100': 3,\n",
+       "          '1111': 9,\n",
+       "          '0111': 4,\n",
+       "          '0110': 4,\n",
+       "          '1110': 2,\n",
+       "          '1100': 1}),\n",
+       " 'measured_probabilities': {'1101': np.float64(0.12331159869893256),\n",
        "  '1000': np.float64(0.11330883548333587),\n",
        "  '0010': np.float64(0.09466860481989385),\n",
-       "  '0011': np.float64(0.07571277233522114),\n",
-       "  '0000': np.float64(0.08390937969317269),\n",
-       "  '1111': np.float64(0.10184806171791962),\n",
-       "  '1101': np.float64(0.12331159869893256),\n",
        "  '1011': np.float64(0.053499396925872744),\n",
-       "  '0100': np.float64(0.07142939529687138),\n",
-       "  '0111': np.float64(0.04029185074729259),\n",
+       "  '1111': np.float64(0.10184806171791962),\n",
+       "  '0000': np.float64(0.08390937969317269),\n",
+       "  '0011': np.float64(0.07571277233522114),\n",
        "  '0101': np.float64(0.05622305772698622),\n",
        "  '1010': np.float64(0.03872758515126756),\n",
+       "  '0111': np.float64(0.04029185074729259),\n",
        "  '0110': np.float64(0.05146064807369214),\n",
+       "  '0100': np.float64(0.07142939529687138),\n",
+       "  '1110': np.float64(0.07174919872959985),\n",
        "  '1100': np.float64(0.013605984872668404)},\n",
        " 'prob_type': 'default',\n",
        " 'statevector': Array([[ 0.08809624-0.27594998j],\n",
@@ -243,7 +243,7 @@
        "        [-0.01729754-0.31866732j]], dtype=complex64)}"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -268,7 +268,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 11,
    "id": "c0443efc-21ef-4ed5-9cf4-785d204a1881",
    "metadata": {},
    "outputs": [
@@ -277,7 +277,7 @@
      "output_type": "stream",
      "text": [
       "Probabilities:\n",
-      " {'1110': np.float64(0.07174919872959985), '1000': np.float64(0.11330883548333587), '0010': np.float64(0.09466860481989385), '0011': np.float64(0.07571277233522114), '0000': np.float64(0.08390937969317269), '1111': np.float64(0.10184806171791962), '1101': np.float64(0.12331159869893256), '1011': np.float64(0.053499396925872744), '0100': np.float64(0.07142939529687138), '0111': np.float64(0.04029185074729259), '0101': np.float64(0.05622305772698622), '1010': np.float64(0.03872758515126756), '0110': np.float64(0.05146064807369214), '1100': np.float64(0.013605984872668404)}\n",
+      " {'1101': np.float64(0.12331159869893256), '1000': np.float64(0.11330883548333587), '0010': np.float64(0.09466860481989385), '1011': np.float64(0.053499396925872744), '1111': np.float64(0.10184806171791962), '0000': np.float64(0.08390937969317269), '0011': np.float64(0.07571277233522114), '0101': np.float64(0.05622305772698622), '1010': np.float64(0.03872758515126756), '0111': np.float64(0.04029185074729259), '0110': np.float64(0.05146064807369214), '0100': np.float64(0.07142939529687138), '1110': np.float64(0.07174919872959985), '1100': np.float64(0.013605984872668404)}\n",
       "\n",
       "State:\n",
       " [[ 0.08809624-0.27594998j]\n",
@@ -321,7 +321,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 12,
    "id": "37385485-e8a3-4ab0-ad44-bcc4e9da24ca",
    "metadata": {},
    "outputs": [
@@ -348,17 +348,61 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
-   "id": "ddecc910-7804-4199-8577-a7db38a16db8",
+   "execution_count": 20,
+   "id": "9712783d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# define Hamiltonian\n",
+    "operators = [\"zz\", \"xz\", \"z\"]\n",
+    "qubits = [\"01\", \"02\", \"3\"]\n",
+    "coefficients = [\"0.5\", \"-1.5\", \"1\"]\n",
+    "hamiltonian = (operators, qubits, coefficients)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "163b70a3-814a-4a62-a98a-2ffca933a544",
    "metadata": {},
    "outputs": [
     {
-     "name": "stderr",
+     "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[Qibo 0.2.20|INFO|2025-09-20 16:43:42]: Using qibojit (numba) backend on /CPU:0\n"
+      "Expectation value: 0.7143570184707642\n",
+      "Elapsed time: 0.1498 seconds\n"
      ]
-    },
+    }
+   ],
+   "source": [
+    "start = time.time()\n",
+    "expval = quimb_backend.expectation(\n",
+    "        circuit=circuit,\n",
+    "        operators_list=hamiltonian[0],\n",
+    "        sites_list=hamiltonian[1],\n",
+    "        coeffs_list=hamiltonian[2]\n",
+    "    )\n",
+    "\n",
+    "elapsed = time.time() - start\n",
+    "print(f\"Expectation value: {expval}\")\n",
+    "print(f\"Elapsed time: {elapsed:.4f} seconds\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "90663e28",
+   "metadata": {},
+   "source": [
+    "Try with Qibo (which is by default using the Qibojit backend)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "c8760074",
+   "metadata": {},
+   "outputs": [
     {
      "data": {
       "text/latex": [
@@ -368,7 +412,7 @@
        "-1.5*X0*Z2 + 0.5*Z0*Z1 + Z3"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -385,41 +429,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
-   "id": "163b70a3-814a-4a62-a98a-2ffca933a544",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Expectation value: 0.7143489122390747\n",
-      "Elapsed time: 12.4550 seconds\n"
-     ]
-    }
-   ],
-   "source": [
-    "start = time.time()\n",
-    "expval = quimb_backend.expectation(\n",
-    "    circuit=circuit,\n",
-    "    observable=hamiltonian,\n",
-    ")\n",
-    "elapsed = time.time() - start\n",
-    "print(f\"Expectation value: {expval}\")\n",
-    "print(f\"Elapsed time: {elapsed:.4f} seconds\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "90663e28",
-   "metadata": {},
-   "source": [
-    "Try with Qibo (which is by default using the Qibojit backend)\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 19,
    "id": "e2d05707",
    "metadata": {},
    "outputs": [
@@ -428,7 +438,7 @@
      "output_type": "stream",
      "text": [
       "Expectation value: 0.7143570920618565\n",
-      "Elapsed time: 0.5871 seconds\n"
+      "Elapsed time: 0.5597 seconds\n"
      ]
     }
    ],
@@ -458,7 +468,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": null,
    "id": "8df55c5f",
    "metadata": {},
    "outputs": [
@@ -474,9 +484,7 @@
     }
    ],
    "source": [
-    "# grad of this circuit returning nan for some reason...\n",
-    "\n",
-    "def build_circuit(nqubits, nlayers):\n",
+    "def build_circuit_A(nqubits, nlayers):\n",
     "    \"\"\"Construct a parametric quantum circuit.\"\"\"\n",
     "    circ = Circuit(nqubits)\n",
     "    for _ in range(nlayers):\n",
@@ -509,7 +517,7 @@
     }
    ],
    "source": [
-    "def build_circuit(nqubits, nlayers):\n",
+    "def build_circuit_B(nqubits, nlayers):\n",
     "    circ = Circuit(nqubits)\n",
     "    for _ in range(nlayers):\n",
     "        for q in range(nqubits):\n",
@@ -528,31 +536,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
-   "id": "b803250f",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Array(1.4999985, dtype=float32)"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "quimb_backend.expectation(\n",
-    "        circuit=circuit,         \n",
-    "        observable=hamiltonian,\n",
-    "   )"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": null,
    "id": "0943482e",
    "metadata": {},
    "outputs": [
@@ -560,27 +544,38 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "(Array(0.4465402, dtype=float32), Array([-1.5755819e-01,  9.7801067e-02, -1.2350259e-01,  1.3670625e-01,\n",
-      "        3.6954228e-03, -1.7437905e-02,  2.7746204e-01, -1.0357879e-01,\n",
-      "        1.1504190e-01, -4.5175910e-02, -4.8447326e-02,  1.4743687e-01,\n",
-      "       -3.0708680e-01,  2.0652822e-01,  1.9298886e-01,  5.1306009e-02,\n",
-      "       -3.3362946e-01, -7.5548244e-01, -3.0034758e-02, -5.2868712e-01,\n",
-      "        4.8458660e-01, -2.9802322e-08,  8.0767423e-02,  0.0000000e+00],      dtype=float32))\n"
+      "[ 2.57090405e-02 -2.24703997e-02 -2.82387018e-01 -1.02654770e-01\n",
+      "  1.03672206e-01  1.03572123e-01 -9.93297935e-01  3.26367974e-01\n",
+      " -8.58561993e-01 -3.14284384e-01 -1.22645356e-01 -2.13570029e-01\n",
+      " -4.55642402e-01  1.11669600e-02 -2.92290837e-01 -1.91316485e-01\n",
+      "  2.78813928e-01  8.80600572e-01  5.07975101e-01 -1.97107181e-01\n",
+      " -4.69740361e-01 -8.50831568e-02  4.45045829e-01  3.42172906e-02\n",
+      " -8.43066633e-01  1.86891228e-01  4.52477366e-01  7.36747682e-03\n",
+      " -6.28291368e-01 -9.38566178e-02  5.43581992e-02  3.57441790e-02\n",
+      "  5.15162945e-04  2.55566716e-01 -3.20922613e-01  4.96513635e-01]\n",
+      "Elapsed time: 11.3724 seconds\n"
      ]
     }
    ],
    "source": [
     "import jax\n",
+    "import time\n",
     "\n",
-    "def f(params):\n",
+    "def f(circuit, hamiltonian, params):\n",
     "    circuit.set_parameters(params)\n",
     "    return quimb_backend.expectation(\n",
     "        circuit=circuit,\n",
-    "        observable=hamiltonian,\n",
+    "        operators_list=hamiltonian[0],\n",
+    "        sites_list=hamiltonian[1],\n",
+    "        coeffs_list=hamiltonian[2]\n",
     "    )\n",
     "\n",
     "parameters = np.random.uniform(-np.pi, np.pi, size=len(circuit.get_parameters()))\n",
-    "print(jax.value_and_grad(f)(parameters))\n"
+    "start = time.time()\n",
+    "grad = jax.grad(f, argnums=2)(circuit, hamiltonian, parameters)\n",
+    "elapsed = time.time() - start\n",
+    "print(grad)\n",
+    "print(f\"Elapsed time: {elapsed:.4f} seconds\")"
    ]
   }
  ],
diff --git a/examples/quimb_intro/test.py b/examples/quimb_intro/test.py
deleted file mode 100644
index 2eccd91..0000000
--- a/examples/quimb_intro/test.py
+++ /dev/null
@@ -1,52 +0,0 @@
-import numpy as np
-import jax
-from qibo.backends import construct_backend
-from qibo import Circuit, gates, hamiltonians
-from qibo.symbols import Z, X, Y
-
-# construct qibotn backend
-quimb_backend = construct_backend(backend="qibotn", platform="quimb")
-
-quimb_backend.setup_backend_specifics(
-    qimb_backend="jax", 
-    optimizer='auto-hq'
-    )
-
-quimb_backend.configure_tn_simulation(
-    max_bond_dimension=10
-)
-
-
-# define Hamiltonian
-form = 0.5 * Z(0) * Z(1) +- 1.5 *  X(0) * Z(2) + Z(3)
-hamiltonian = hamiltonians.SymbolicHamiltonian(form)
-
-
-# define circuit
-def build_circuit(nqubits, nlayers):
-    """Construct a more complex Qibo parametric quantum circuit without CNOT gates."""
-    circ = Circuit(nqubits)
-    for layer in range(nlayers):
-        for q in range(nqubits):
-            circ.add(gates.RY(q=q, theta=0.))
-            circ.add(gates.RZ(q=q, theta=0.))
-            circ.add(gates.RX(q=q, theta=0.))
-        # Add controlled rotations and SWAPs for entanglement
-        for q in range(nqubits - 1):
-            circ.add(gates.CNOT(q, q + 1))
-            circ.add(gates.SWAP(q, q + 1))
-    circ.add(gates.M(*range(nqubits)))
-    return circ
-
-nqubits = 6
-circuit = build_circuit(nqubits=nqubits, nlayers=3)
-
-def f(params):
-    circuit.set_parameters(params)
-    return quimb_backend.expectation(
-        circuit=circuit,
-        observable=hamiltonian,
-    )
-
-parameters = np.random.uniform(-np.pi, np.pi, size=len(circuit.get_parameters()))
-print(jax.value_and_grad(f)(parameters))

From ec07b8ea86b749f7fe3eda40dadb3cf9dde01a95 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Tue, 23 Sep 2025 00:41:19 +0200
Subject: [PATCH 12/33] refactored execute. The observable is now passed as
 lists of operators, coefficients and qubits. Implemented functions for
 handling conversion from Pauli string to quimb operator and coefficients.
 Fixed: error in parameters handing in expectation. Fixed GATE_MAP to match
 the common observables

---
 src/qibotn/backends/quimb.py | 340 +++++++++++++----------------------
 1 file changed, 121 insertions(+), 219 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index e4ebd5d..53bcc6b 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -1,21 +1,17 @@
-import re
-import warnings
-from collections import Counter, defaultdict
+from collections import Counter
 
 import numpy as np
-import jax
-import jax.numpy as jnp
-import quimb as qu
-import quimb.tensor as qtn
+
+from qibo.models import Circuit
 from qibo.backends import NumpyBackend
 from qibo.config import raise_error
-from qibo.result import QuantumState
-
 from qibotn.backends.abstract import QibotnBackend
 from qibotn.result import TensorNetworkResult
-
 from qibo.gates.abstract import ParametrizedGate
 
+import quimb as qu
+import quimb.tensor as qtn
+
 
 GATE_MAP = {
         "h": "H",
@@ -23,20 +19,13 @@ GATE_MAP = {
         "y": "Y",
         "z": "Z",
         "s": "S",
-
-        "sdg": "SDG",
         "t": "T",
-        "tdg": "TDG",
-        "sx": "SX",
-        "sxdg": "SXDG",
 
         "rx": "RX",
         "ry": "RY",
         "rz": "RZ",
 
-        "u1": "U1",
-        "u2": "U2",
-        "u3": "U3",
+        "u3": "U3", # TODO: check
 
         "cx": "CX",
         "cnot": "CNOT",
@@ -45,19 +34,18 @@ GATE_MAP = {
 
         "iswap": "ISWAP",
         "swap": "SWAP",
+
         "ccx": "CCX",
-        "toffoli": "CCX",
+        "ccy": "CCY",
         "ccz": "CCZ",
+
+        "toffoli": "TOFFOLI",
         "cswap": "CSWAP",
-        "fredkin": "CSWAP",
-        "crx": "CRX",
-        "cry": "CRY",
-        "crz": "CRZ",
-        "fsim": "FSIM",
-        "rxx": "RXX",
-        "ryy": "RYY",
-        "rzz": "RZZ",
-        "m": None,  # measurement, skip
+        "fredkin": "FREDKIN",
+
+        "fsim": "fsim",
+
+        "m": "measure"
     }
 
 class QuimbBackend(QibotnBackend, NumpyBackend):
@@ -73,7 +61,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
 
     def configure_tn_simulation(
         self,
-        ansatz: str = "any",
+        ansatz: str = None,
         max_bond_dimension: int = 10,
         n_most_frequent_states: int = 100,
     ):
@@ -82,9 +70,9 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
 
         Args:
             ansatz : str, optional
-                The tensor network ansatz to use. Currently, only "MPS" or "any" is supported. In the second case
-                the generic Circuit Quimb class is used.
-            max_bond_dimension : int, optional
+                The tensor network ansatz to use. Default is `None` and, in this case, a
+                generic Circuit Quimb class is used.            
+                max_bond_dimension : int, optional
                 The maximum bond dimension for the MPS ansatz. Default is 10.
 
         Notes:
@@ -95,20 +83,32 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         self.max_bond_dimension = max_bond_dimension
         self.n_most_frequent_states = n_most_frequent_states
 
-    def setup_backend_specifics(self, qimb_backend="numpy", optimizer="auto-hq"):
+    def setup_backend_specifics(self, qimb_backend="numpy", contractions_optimizer="auto-hq"):
         """Setup backend specifics.
         Args:
             qimb_backend: str
                 The backend to use for the quimb tensor network simulation.
-            optimizer: str, optional
-                The optimizer to use for the quimb tensor network simulation.
+            contractions_optimizer: str, optional
+                The contractions_optimizer to use for the quimb tensor network simulation.
         """
+        if qimb_backend == "jax":
+            import jax.numpy as jnp
+            self.np = jnp
+        elif qimb_backend == "numpy":
+            import numpy as np
+            self.np = np
+        elif qimb_backend == "torch":
+            import torch
+            self.np = torch
+        else:
+            raise_error(ValueError, f"Unsupported quimb backend: {qimb_backend}")
+
         self.backend = qimb_backend
-        self.optimizer = optimizer
+        self.contractions_optimizer = contractions_optimizer
 
     def execute_circuit(
         self,
-        circuit,
+        circuit: Circuit,
         initial_state=None,
         nshots=None,
         return_array=False,
@@ -180,7 +180,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             measured_probabilities = None
 
         statevector = (
-            circ_quimb.to_dense(backend=self.backend, optimize=self.optimizer)
+            circ_quimb.to_dense(backend=self.backend, optimize=self.contractions_optimizer)
             if return_array
             else None
         )
@@ -192,193 +192,53 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             prob_type="default",
             statevector=statevector,
         )
-  
-    def expectation(self, circuit, observable):
+
+    def expectation(self, circuit: Circuit, operators_list: list[str], sites_list: list[str], coeffs_list: list[str]):
         """
-        Compute the expectation value of a Qibo-friendly ``observable`` on the Tensor Network constructed from a Qibo ``circuit``.
-        This method takes a Qibo-style symbolic Hamiltonian (e.g., `X(0)*Z(1) + 2.0*Y(2)*Z(0)`)
-        as the observable, converts it into a Quimb observable and computes its expectation
-        value using the provided circuit.
-
-        Args:
-            circuit: A Qibo quantum circuit object on which the expectation value
-                is computed.
-            observable: The observable whose expectation value we want to compute.
-                This must be provided in the symbolic Hamiltonian form supported by Qibo
-                (e.g., `X(0)*Y(1)` or `Z(0)*Z(1) + 1.5*Y(2)`).
-
-        Returns:
-            float: The expectation value (real part).
+        Compute the expectation value of a symbolic Hamiltonian on a quantum circuit using tensor network contraction.
+        This method takes a Qibo circuit, converts it to a Quimb tensor network circuit, and evaluates the expectation value
+        of a Hamiltonian specified by three lists of strings: operators, sites, and coefficients.
+        The expectation value is computed by summing the contributions from each term in the Hamiltonian, where each term's
+        expectation is calculated using Quimb's `local_expectation` function.
+        
+        Parameters
+        ----------
+        circuit : qibo.models.Circuit
+            The quantum circuit to evaluate, provided as a Qibo circuit object.
+        operators_list : list of str
+            List of operator strings representing the symbolic Hamiltonian terms.
+        sites_list : list of str
+            List of strings, each specifying the qubits (sites) the corresponding operator acts on.
+        coeffs_list : list of str
+            List of strings representing the coefficients for each Hamiltonian term.
+        Returns
+        -------
+        float
+            The real part of the expectation value of the Hamiltonian on the given circuit state.
         """
-
-        '''Convert Qibo observables to Quimb'''
-        operators_list, sites_list, coeffs_list = self._qiboobs_to_quimbobs(observable)
-
-        '''Convert Qibo circuit to Quimb circuit'''
-        parameters = circuit.get_parameters()
-        quimb_circuit = self._qibo_circuit_to_quimb(
-            circuit, quimb_circuit_type=qtn.Circuit, to_backend=jnp.array, convert_eager=True
-        )
-        quimb_parameters = {
-            key: jnp.asarray(parameters[i]) for i, key in enumerate(quimb_circuit.get_params().keys())
-        }
-        quimb_circuit.set_params(quimb_parameters)
-
-        '''Compute expectation value'''
+        quimb_circuit = self._qibo_circuit_to_quimb(circuit, quimb_circuit_type=qtn.Circuit)
+            
         expectation_value = 0.0
-        for ops, sites, coeffs in zip(operators_list, sites_list, coeffs_list):
+        for opstr, sitesstr, coeffstr in zip(operators_list, sites_list, coeffs_list):
+            
+            ops = self._string_to_quimb_operator(opstr)
+            coeff = self._parse_coefficient(coeffstr)
+            sites = tuple(int(q) for q in sitesstr)
+            
             exp_values = quimb_circuit.local_expectation(
                 ops,
                 where=sites,
                 backend=self.backend,
-                optimize=self.optimizer
+                optimize=self.contractions_optimizer
             )
-            expectation_value = expectation_value + coeffs * exp_values
+
+            expectation_value = expectation_value + coeff * exp_values
         
-        return jnp.real(expectation_value)
-
-    def expectation_old(self, circuit, observable):
-        """Compute the expectation value of a Qibo-friendly ``observable`` on the Tensor Network constructed from a Qibo ``circuit``.
-
-        This method takes a Qibo-style symbolic Hamiltonian (e.g., `X(0)*Z(1) + 2.0*Y(2)*Z(0)`)
-        as the observable, converts it into a Quimb observable and computes its expectation
-        value using the provided circuit. In case of multiple terms on the same group of qubits, they can be computed in a single contraction.
-        A grouping procedure is applied to optimize the number of contractions performed.
-
-        Args:
-            circuit: A Qibo quantum circuit object on which the expectation value
-                is computed.
-            observable: The observable whose expectation value we want to compute.
-                This must be provided in the symbolic Hamiltonian form supported by Qibo
-                (e.g., `X(0)*Y(1)` or `Z(0)*Z(1) + 1.5*Y(2)`).
-
-        Returns:
-            float: The expectation value (real part).
-        """
-
-        # Map the Qibo observable to Quimb operators and group local operators on the same sites
-        # for computing them in a single contraction. This does not work with CircuitMPS for some now
-        # for Quimb 1.11.1
-        operators_list, sites_list, coeffs_list = self._qiboobs_to_quimbobs(observable)
-        sites_list_grouped, operators_list_grouped, coeffs_list_grouped = (
-            self._group_by_tuples(sites_list, operators_list, coeffs_list)
-        )
-
-        if self.ansatz == "MPS":
-            if len(sites_list) - len(sites_list_grouped) > 10:
-                warnings.warn(
-                    "More than 10 local operators on the same sites are not being grouped as this is not compatible with CircuitMPS. Expected value computation can be more efficient without an MPS ansatz."
-                )
-            circ_ansatz = qtn.circuit.CircuitMPS
-            circ = circ_ansatz.from_openqasm2_str(circuit.to_qasm())
-            expectation_value = 0.0
-            for ops, sites, coeffs in zip(operators_list, sites_list, coeffs_list):
-                exp_values = circ.local_expectation(
-                    ops, where=sites, backend=self.backend, optimize=self.optimizer
-                )
-                expectation_value += np.dot(coeffs, exp_values)
-            return np.real(expectation_value)
-
-        else:
-            circ_ansatz = qtn.circuit.Circuit
-            circ = circ_ansatz.from_openqasm2_str(circuit.to_qasm())
-
-            expectation_value = 0.0
-            for ops, sites, coeffs in zip(
-                operators_list_grouped, sites_list_grouped, coeffs_list_grouped
-            ):
-                exp_values = circ.local_expectation(
-                    ops, where=sites, backend=self.backend, optimize=self.optimizer
-                )
-                expectation_value += np.dot(coeffs, exp_values)
-            return np.real(expectation_value)
-
-    def _qiboobs_to_quimbobs(self, hamiltonian):
-        """
-        Convert a Qibo SymbolicHamiltonian into a Quimb-compatible decomposition.
-
-        Returns three lists:
-        - operators_list: Quimb operators (tensor products of Pauli matrices).
-        - sites_list: tuples of qubit indices the operators act on.
-        - coeffs_list: coefficients for each term.
-        """
-
-        factor_pattern = re.compile(r"([^\d]+)(\d+)")
-
-        operators_list = []
-        sites_list = []
-        coeffs_list = []
-
-        for term in hamiltonian.terms:
-            coeff = term.coefficient
-            term_ops = []
-            term_sites = []
-
-            for factor in term.factors:
-                match = factor_pattern.match(str(factor))
-                if not match:
-                    raise ValueError(
-                        f"Factor '{str(factor)}' does not match the expected format."
-                    )
-
-                operator_name = match.group(1)
-                qubit_index = int(match.group(2))
-
-                # Build the single-qubit operator
-                if operator_name not in {"X", "Y", "Z", "I"}:
-                    raise ValueError(f"Unsupported operator {operator_name}")
-                op = qu.pauli(operator_name)
-
-                term_ops.append(op)
-                term_sites.append(qubit_index)
-
-            # Build the tensor product if more than one factor
-            if term_ops:
-                full_op = term_ops[0]
-                for op in term_ops[1:]:
-                    full_op = full_op & op
-            else:
-                # Identity term (just coefficient)
-                full_op = qu.eye(2)
-
-            operators_list.append(full_op)
-            sites_list.append(tuple(term_sites))
-            coeffs_list.append(coeff)
-
-        return operators_list, sites_list, coeffs_list
-
-    def _group_by_tuples(self, A, B, C):
-        """
-        Groups the elements of B and C by the unique tuples in A.
-
-        Parameters:
-            A (list of tuples): key tuples (can contain duplicates)
-            B (list): values aligned with A
-            C (list): values aligned with A
-
-        Returns:
-            (A_new, B_new, C_new):
-                A_new: list of unique tuples
-                B_new: list of lists of grouped values from B
-                C_new: list of lists of grouped values from C
-        """
-
-        grouped_B = defaultdict(list)
-        grouped_C = defaultdict(list)
-
-        for a, b, c in zip(A, B, C):
-            grouped_B[a].append(b)
-            grouped_C[a].append(c)
-
-        A_new = list(grouped_B.keys())
-        B_new = list(grouped_B.values())
-        C_new = list(grouped_C.values())
-
-        return A_new, B_new, C_new
+        return np.real(expectation_value)
 
     def _qibo_circuit_to_quimb(self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs):
         """
-        Convert a Qibo Circuit to a Quimb Circuit.
+        Convert a Qibo Circuit to a Quimb Circuit. Measurement gates are ignored. If are given gates not supported by Quimb, an error is raised.
 
         Parameters
         ----------
@@ -400,29 +260,71 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         for gate in qibo_circ.queue:
             gname = getattr(gate, "name", None)
             qname = GATE_MAP.get(gname, None)
+            if qname == "measure":
+                continue
             if qname is None:
-                continue  # skip measurements and unknown gates
+                raise_error(ValueError, f"Gate {gname} not supported in Quimb backend.")
 
             params = getattr(gate, "parameters", ())
             qubits = getattr(gate, "qubits", ())
             
-            # Check if the gate is parametrized
             is_parametrized = (
                 isinstance(gate, ParametrizedGate)
                 and getattr(gate, "trainable", True)
-            )
-            # import pdb; pdb.set_trace()
+                )
             if is_parametrized:
                 circ.apply_gate(
                     qname,
                     *params,
                     *qubits,
-                    parametrized= is_parametrized
+                    parametrized=is_parametrized
                 )
             else:
                 circ.apply_gate(
                     qname,
                     *params,
                     *qubits,
-                                )
+                )
         return circ
+
+    def _parse_coefficient(self, s):
+        """Parse a coefficient from string to float, int, or complex.
+        Args:
+            s: str
+                The string representation of the coefficient.
+        Returns:
+            The coefficient as float, int, or complex.
+        """ 
+        try:
+            return float(s)
+        except ValueError:
+            pass
+        if s == "j":
+            return 1j
+        elif s == "-j":
+            return -1j
+        else:
+            try:
+                return complex(s)
+            except ValueError:
+                raise ValueError(f"Cannot parse coefficient: {s}")
+
+    def _string_to_quimb_operator(self, op_str):
+        """
+        Convert a Pauli string (e.g. 'xzy') to a Quimb operator using '&' chaining.
+
+        Parameters
+        ----------
+        op_str : str
+            A string like 'xzy', where each character is one of 'x', 'y', 'z', 'i'.
+
+        Returns
+        -------
+        qu_op : quimb.Qarray
+            The corresponding Quimb operator.
+        """
+        op_str = op_str.lower()
+        op = qu.pauli(op_str[0])
+        for c in op_str[1:]:
+            op = op & qu.pauli(c)
+        return op

From 82fcffb1adc2b0b18fa3c5c1eeab9d4b2242e26d Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Tue, 23 Sep 2025 01:42:20 +0200
Subject: [PATCH 13/33] update notebook

---
 examples/quimb_intro/quimb_introduction.ipynb | 318 +++++++-----------
 1 file changed, 129 insertions(+), 189 deletions(-)

diff --git a/examples/quimb_intro/quimb_introduction.ipynb b/examples/quimb_intro/quimb_introduction.ipynb
index 73a831b..70fdf45 100644
--- a/examples/quimb_intro/quimb_introduction.ipynb
+++ b/examples/quimb_intro/quimb_introduction.ipynb
@@ -53,7 +53,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 3,
    "id": "64162116-1555-4a68-811c-01593739d622",
    "metadata": {},
    "outputs": [],
@@ -67,10 +67,7 @@
     "# set numpy random seed\n",
     "np.random.seed(42)\n",
     "\n",
-    "quimb_backend.setup_backend_specifics(\n",
-    "    qimb_backend=\"jax\", \n",
-    "    contractions_optimizer=ctg_opt\n",
-    "    )"
+    "quimb_backend.setup_backend_specifics(qimb_backend=\"jax\")"
    ]
   },
   {
@@ -83,7 +80,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "id": "4a22a172-f50d-411d-afa3-fa61937c7b3a",
    "metadata": {},
    "outputs": [],
@@ -102,7 +99,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "id": "76f23c57-6d08-496b-9a27-52fb63bbfcb1",
    "metadata": {},
    "outputs": [
@@ -124,7 +121,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 6,
    "id": "07b2c097-cea2-42ec-8f1d-b4bbb5b71d98",
    "metadata": {},
    "outputs": [],
@@ -147,7 +144,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 7,
    "id": "2ee03e94-d794-4a51-9e76-01e8d8a259ba",
    "metadata": {},
    "outputs": [],
@@ -175,7 +172,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 8,
    "id": "35a244c3-adba-4b8b-b28c-0ab592b0f7cf",
    "metadata": {},
    "outputs": [
@@ -196,34 +193,32 @@
       "text/plain": [
        "{'nqubits': 4,\n",
        " 'backend': qibotn (quimb),\n",
-       " 'measures': Counter({'1000': 14,\n",
-       "          '1011': 9,\n",
-       "          '0101': 5,\n",
-       "          '0010': 12,\n",
+       " 'measures': Counter({'1010': 9,\n",
+       "          '0100': 8,\n",
+       "          '1101': 15,\n",
+       "          '1011': 4,\n",
+       "          '1111': 12,\n",
+       "          '1000': 13,\n",
        "          '0000': 8,\n",
-       "          '1010': 4,\n",
-       "          '1101': 19,\n",
+       "          '0010': 6,\n",
        "          '0011': 6,\n",
-       "          '0100': 3,\n",
-       "          '1111': 9,\n",
-       "          '0111': 4,\n",
-       "          '0110': 4,\n",
-       "          '1110': 2,\n",
-       "          '1100': 1}),\n",
+       "          '0101': 8,\n",
+       "          '1110': 5,\n",
+       "          '0110': 5,\n",
+       "          '0111': 1}),\n",
        " 'measured_probabilities': {'1101': np.float64(0.12331159869893256),\n",
        "  '1000': np.float64(0.11330883548333587),\n",
-       "  '0010': np.float64(0.09466860481989385),\n",
-       "  '1011': np.float64(0.053499396925872744),\n",
        "  '1111': np.float64(0.10184806171791962),\n",
-       "  '0000': np.float64(0.08390937969317269),\n",
-       "  '0011': np.float64(0.07571277233522114),\n",
-       "  '0101': np.float64(0.05622305772698622),\n",
        "  '1010': np.float64(0.03872758515126756),\n",
-       "  '0111': np.float64(0.04029185074729259),\n",
-       "  '0110': np.float64(0.05146064807369214),\n",
        "  '0100': np.float64(0.07142939529687138),\n",
+       "  '0000': np.float64(0.08390937969317269),\n",
+       "  '0101': np.float64(0.05622305772698622),\n",
+       "  '0010': np.float64(0.09466860481989385),\n",
+       "  '0011': np.float64(0.07571277233522114),\n",
        "  '1110': np.float64(0.07174919872959985),\n",
-       "  '1100': np.float64(0.013605984872668404)},\n",
+       "  '0110': np.float64(0.05146064807369214),\n",
+       "  '1011': np.float64(0.053499396925872744),\n",
+       "  '0111': np.float64(0.04029185074729259)},\n",
        " 'prob_type': 'default',\n",
        " 'statevector': Array([[ 0.08809624-0.27594998j],\n",
        "        [-0.05174781+0.04471217j],\n",
@@ -243,7 +238,7 @@
        "        [-0.01729754-0.31866732j]], dtype=complex64)}"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -268,7 +263,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 9,
    "id": "c0443efc-21ef-4ed5-9cf4-785d204a1881",
    "metadata": {},
    "outputs": [
@@ -277,7 +272,7 @@
      "output_type": "stream",
      "text": [
       "Probabilities:\n",
-      " {'1101': np.float64(0.12331159869893256), '1000': np.float64(0.11330883548333587), '0010': np.float64(0.09466860481989385), '1011': np.float64(0.053499396925872744), '1111': np.float64(0.10184806171791962), '0000': np.float64(0.08390937969317269), '0011': np.float64(0.07571277233522114), '0101': np.float64(0.05622305772698622), '1010': np.float64(0.03872758515126756), '0111': np.float64(0.04029185074729259), '0110': np.float64(0.05146064807369214), '0100': np.float64(0.07142939529687138), '1110': np.float64(0.07174919872959985), '1100': np.float64(0.013605984872668404)}\n",
+      " {'1101': np.float64(0.12331159869893256), '1000': np.float64(0.11330883548333587), '1111': np.float64(0.10184806171791962), '1010': np.float64(0.03872758515126756), '0100': np.float64(0.07142939529687138), '0000': np.float64(0.08390937969317269), '0101': np.float64(0.05622305772698622), '0010': np.float64(0.09466860481989385), '0011': np.float64(0.07571277233522114), '1110': np.float64(0.07174919872959985), '0110': np.float64(0.05146064807369214), '1011': np.float64(0.053499396925872744), '0111': np.float64(0.04029185074729259)}\n",
       "\n",
       "State:\n",
       " [[ 0.08809624-0.27594998j]\n",
@@ -307,7 +302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd84f1f3-7aa5-4ad1-ae09-81e0aff75b5b",
+   "id": "9531f9d6",
    "metadata": {},
    "source": [
     "### Compute expectation values\n",
@@ -321,57 +316,99 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
-   "id": "37385485-e8a3-4ab0-ad44-bcc4e9da24ca",
+   "execution_count": 10,
+   "id": "647f2073",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ─RY─RZ─o─────X─RY─RZ─o─────X─RY─RZ─o─────X─M─\n",
-      "1: ─RY─RZ─X─o───|─RY─RZ─X─o───|─RY─RZ─X─o───|─M─\n",
-      "2: ─RY─RZ───X─o─|─RY─RZ───X─o─|─RY─RZ───X─o─|─M─\n",
-      "3: ─RY─RZ─────X─o─RY─RZ─────X─o─RY─RZ─────X─o─M─\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "# We are going to compute the expval of an Hamiltonian\n",
-    "# On the state prepared by the following circuit\n",
-    "circuit.draw()\n",
+    "import numpy as np\n",
+    "import jax\n",
+    "from qibo.backends import construct_backend\n",
+    "from qibo import Circuit, gates"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "74c63a41",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# construct qibotn backend\n",
+    "quimb_backend = construct_backend(backend=\"qibotn\", platform=\"quimb\")\n",
     "\n",
-    "circuit.set_parameters(\n",
-    "    np.random.randn(len(circuit.get_parameters()))\n",
+    "quimb_backend.setup_backend_specifics(\n",
+    "    qimb_backend    =\"jax\", \n",
+    "    contractions_optimizer='auto-hq'\n",
+    "    )\n",
+    "\n",
+    "quimb_backend.configure_tn_simulation(\n",
+    "    max_bond_dimension=10\n",
     ")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
-   "id": "9712783d",
+   "execution_count": 19,
+   "id": "b2a0decb",
    "metadata": {},
    "outputs": [],
    "source": [
     "# define Hamiltonian\n",
-    "operators = [\"zz\", \"xz\", \"z\"]\n",
-    "qubits = [\"01\", \"02\", \"3\"]\n",
-    "coefficients = [\"0.5\", \"-1.5\", \"1\"]\n",
+    "operators = [\"xzy\", \"yxzy\", \"zy\"]\n",
+    "qubits = [\"011\", \"0112\", \"01\"]\n",
+    "coefficients = [\"1\", \"2\", \"j\"]\n",
     "hamiltonian = (operators, qubits, coefficients)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
-   "id": "163b70a3-814a-4a62-a98a-2ffca933a544",
+   "execution_count": 18,
+   "id": "bd734be8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# define circuit\n",
+    "def build_circuit(nqubits, nlayers):\n",
+    "    circ = Circuit(nqubits)\n",
+    "    for layer in range(nlayers):\n",
+    "        for q in range(nqubits):\n",
+    "            circ.add(gates.RY(q=q, theta=0.))\n",
+    "            circ.add(gates.RZ(q=q, theta=0.))\n",
+    "            circ.add(gates.RX(q=q, theta=0.))\n",
+    "        for q in range(nqubits - 1):\n",
+    "            circ.add(gates.CNOT(q, q + 1))\n",
+    "            circ.add(gates.SWAP(q, q + 1))\n",
+    "    circ.add(gates.M(*range(nqubits)))\n",
+    "    return circ\n",
+    "\n",
+    "def build_circuit_problematic(nqubits, nlayers):\n",
+    "    circ = Circuit(nqubits)\n",
+    "    for _ in range(nlayers):\n",
+    "        for q in range(nqubits):\n",
+    "            circ.add(gates.RY(q=q, theta=0.))\n",
+    "            circ.add(gates.RZ(q=q, theta=0.))\n",
+    "        [circ.add(gates.CNOT(q%nqubits, (q+1)%nqubits) for q in range(nqubits))]\n",
+    "    circ.add(gates.M(*range(nqubits)))\n",
+    "    return circ\n",
+    "\n",
+    "\n",
+    "nqubits = 4\n",
+    "circuit = build_circuit(nqubits=nqubits, nlayers=3)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "fe63ff24",
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Expectation value: 0.7143570184707642\n",
-      "Elapsed time: 0.1498 seconds\n"
+      "Expectation value: 0.0\n",
+      "Elapsed time: 0.1071 seconds\n"
      ]
     }
    ],
@@ -391,7 +428,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90663e28",
+   "id": "d976a849",
    "metadata": {},
    "source": [
     "Try with Qibo (which is by default using the Qibojit backend)\n"
@@ -399,52 +436,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
-   "id": "c8760074",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/latex": [
-       "$\\displaystyle - 1.5 X_{0} Z_{2} + 0.5 Z_{0} Z_{1} + Z_{3}$"
-      ],
-      "text/plain": [
-       "-1.5*X0*Z2 + 0.5*Z0*Z1 + Z3"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "from qibo.symbols import Z, X, I\n",
-    "# We can create a symbolic Hamiltonian\n",
-    "form = 0.5 * Z(0) * Z(1) +- 1.5 *  X(0) * Z(2) + Z(3)\n",
-    "hamiltonian = hamiltonians.SymbolicHamiltonian(form)\n",
-    "\n",
-    "#  Let's show it\n",
-    "hamiltonian.form"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "id": "e2d05707",
+   "execution_count": 22,
+   "id": "fb1436c8",
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Expectation value: 0.7143570920618565\n",
-      "Elapsed time: 0.5597 seconds\n"
+      "Expectation value: 1.5\n",
+      "Elapsed time: 0.0501 seconds\n"
      ]
     }
    ],
    "source": [
+    "from qibo.symbols import Z, X, I\n",
+    "# We can create a symbolic Hamiltonian\n",
+    "form = 0.5 * Z(0) * Z(1) +- 1.5 *  X(0) * Z(2) + Z(3)\n",
+    "sym_hamiltonian = hamiltonians.SymbolicHamiltonian(form)\n",
+    "\n",
+    "#  Let's show it\n",
+    "sym_hamiltonian.form\n",
+    "\n",
+    "# Compute expectation value\n",
     "start = time.time()\n",
-    "result = hamiltonian.expectation(circuit().state())\n",
+    "result = sym_hamiltonian.expectation(circuit().state())\n",
     "elapsed = time.time() - start\n",
     "print(f\"Expectation value: {result}\")\n",
     "print(f\"Elapsed time: {elapsed:.4f} seconds\")"
@@ -452,7 +468,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94df291c-9ddc-4b2e-8442-5fca00784bd8",
+   "id": "77bef077",
    "metadata": {},
    "source": [
     "They match! 🥳"
@@ -460,107 +476,35 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2d119fc",
+   "id": "50130ae6",
    "metadata": {},
    "source": [
-    "### Derivative of the extimation function"
+    "We can also compute gradient of expectation function"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "id": "8df55c5f",
+   "execution_count": 23,
+   "id": "6a3b26e4",
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0: ─RY─RZ─o─────X─RY─RZ─o─────X─RY─RZ─o─────X─M─\n",
-      "1: ─RY─RZ─X─o───|─RY─RZ─X─o───|─RY─RZ─X─o───|─M─\n",
-      "2: ─RY─RZ───X─o─|─RY─RZ───X─o─|─RY─RZ───X─o─|─M─\n",
-      "3: ─RY─RZ─────X─o─RY─RZ─────X─o─RY─RZ─────X─o─M─\n"
+      "[ 8.19939339e-10 -3.14190913e-08 -2.99498648e-09 -1.03641796e-07\n",
+      "  8.48652704e-10  1.00297093e-07 -6.75429277e-08 -9.78565140e-09\n",
+      " -5.11915417e-08  1.29225235e-08 -7.44280655e-08 -3.49115048e-08\n",
+      " -4.98508879e-09  6.80729357e-08 -3.29755920e-08  4.20008526e-08\n",
+      " -2.89742630e-08  1.18602941e-07 -2.88252178e-08  5.57985391e-09\n",
+      " -3.17434115e-08 -1.03342952e-08  1.34079716e-08 -7.05437886e-09\n",
+      " -4.34059650e-08 -2.18019203e-08 -5.36932561e-08 -6.38544009e-08\n",
+      "  5.85312279e-08  8.45709067e-08 -1.12777876e-09 -6.41545981e-08\n",
+      "  7.25317406e-08  4.10035668e-08 -1.29046382e-08  6.07501676e-08]\n"
      ]
     }
    ],
    "source": [
-    "def build_circuit_A(nqubits, nlayers):\n",
-    "    \"\"\"Construct a parametric quantum circuit.\"\"\"\n",
-    "    circ = Circuit(nqubits)\n",
-    "    for _ in range(nlayers):\n",
-    "        for q in range(nqubits):\n",
-    "            circ.add(gates.RY(q=q, theta=0.))\n",
-    "            circ.add(gates.RZ(q=q, theta=0.))\n",
-    "        [circ.add(gates.CNOT(q%nqubits, (q+1)%nqubits) for q in range(nqubits))]\n",
-    "    circ.add(gates.M(*range(nqubits)))\n",
-    "    return circ\n",
-    "\n",
-    "circuit = build_circuit(nqubits=nqubits, nlayers=3)\n",
-    "circuit.draw()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "b02de56b",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ─RY─RZ─RX─o─x─────────RY─RZ─RX─o─x─────────RY─RZ─RX─o─x─────────M─\n",
-      "1: ─RY─RZ─RX─X─x─o─x─────RY─RZ─RX─X─x─o─x─────RY─RZ─RX─X─x─o─x─────M─\n",
-      "2: ─RY─RZ─RX─────X─x─o─x─RY─RZ─RX─────X─x─o─x─RY─RZ─RX─────X─x─o─x─M─\n",
-      "3: ─RY─RZ─RX─────────X─x─RY─RZ─RX─────────X─x─RY─RZ─RX─────────X─x─M─\n"
-     ]
-    }
-   ],
-   "source": [
-    "def build_circuit_B(nqubits, nlayers):\n",
-    "    circ = Circuit(nqubits)\n",
-    "    for _ in range(nlayers):\n",
-    "        for q in range(nqubits):\n",
-    "            circ.add(gates.RY(q=q, theta=0.))\n",
-    "            circ.add(gates.RZ(q=q, theta=0.))\n",
-    "            circ.add(gates.RX(q=q, theta=0.))\n",
-    "        for q in range(nqubits - 1):\n",
-    "            circ.add(gates.CNOT(q, q + 1))\n",
-    "            circ.add(gates.SWAP(q, q + 1))\n",
-    "    circ.add(gates.M(*range(nqubits)))\n",
-    "    return circ\n",
-    "\n",
-    "circuit = build_circuit(nqubits=nqubits, nlayers=3)\n",
-    "circuit.draw()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "0943482e",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 2.57090405e-02 -2.24703997e-02 -2.82387018e-01 -1.02654770e-01\n",
-      "  1.03672206e-01  1.03572123e-01 -9.93297935e-01  3.26367974e-01\n",
-      " -8.58561993e-01 -3.14284384e-01 -1.22645356e-01 -2.13570029e-01\n",
-      " -4.55642402e-01  1.11669600e-02 -2.92290837e-01 -1.91316485e-01\n",
-      "  2.78813928e-01  8.80600572e-01  5.07975101e-01 -1.97107181e-01\n",
-      " -4.69740361e-01 -8.50831568e-02  4.45045829e-01  3.42172906e-02\n",
-      " -8.43066633e-01  1.86891228e-01  4.52477366e-01  7.36747682e-03\n",
-      " -6.28291368e-01 -9.38566178e-02  5.43581992e-02  3.57441790e-02\n",
-      "  5.15162945e-04  2.55566716e-01 -3.20922613e-01  4.96513635e-01]\n",
-      "Elapsed time: 11.3724 seconds\n"
-     ]
-    }
-   ],
-   "source": [
-    "import jax\n",
-    "import time\n",
-    "\n",
     "def f(circuit, hamiltonian, params):\n",
     "    circuit.set_parameters(params)\n",
     "    return quimb_backend.expectation(\n",
@@ -571,11 +515,7 @@
     "    )\n",
     "\n",
     "parameters = np.random.uniform(-np.pi, np.pi, size=len(circuit.get_parameters()))\n",
-    "start = time.time()\n",
-    "grad = jax.grad(f, argnums=2)(circuit, hamiltonian, parameters)\n",
-    "elapsed = time.time() - start\n",
-    "print(grad)\n",
-    "print(f\"Elapsed time: {elapsed:.4f} seconds\")"
+    "print(jax.grad(f, argnums=2)(circuit, hamiltonian, parameters))\n"
    ]
   }
  ],

From 12020911912f4ce5ef280be1bb3499f454eb3467 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Tue, 23 Sep 2025 01:44:44 +0200
Subject: [PATCH 14/33] fixed issue with measure gates name and expectation
 function type hint

---
 src/qibotn/backends/quimb.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 53bcc6b..8a11bb9 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -45,7 +45,7 @@ GATE_MAP = {
 
         "fsim": "fsim",
 
-        "m": "measure"
+        "measure": "measure"
     }
 
 class QuimbBackend(QibotnBackend, NumpyBackend):
@@ -193,7 +193,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             statevector=statevector,
         )
 
-    def expectation(self, circuit: Circuit, operators_list: list[str], sites_list: list[str], coeffs_list: list[str]):
+    def expectation(self, circuit, operators_list, sites_list, coeffs_list):
         """
         Compute the expectation value of a symbolic Hamiltonian on a quantum circuit using tensor network contraction.
         This method takes a Qibo circuit, converts it to a Quimb tensor network circuit, and evaluates the expectation value

From 2b5fca800cf6d40590e4dd31304f5b9bf134c49d Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Tue, 23 Sep 2025 16:27:29 +0200
Subject: [PATCH 15/33] fix: some small corrections

---
 poetry.lock                  | 1609 ++++++++++++++++++----------------
 pyproject.toml               |    2 +-
 src/qibotn/backends/quimb.py |  168 ++--
 3 files changed, 913 insertions(+), 866 deletions(-)

diff --git a/poetry.lock b/poetry.lock
index 3b25b7e..1bb918b 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,4 +1,4 @@
-# This file is automatically @generated by Poetry 2.1.3 and should not be changed by hand.
+# This file is automatically @generated by Poetry 2.1.2 and should not be changed by hand.
 
 [[package]]
 name = "alabaster"
@@ -14,14 +14,14 @@ files = [
 
 [[package]]
 name = "alembic"
-version = "1.16.4"
+version = "1.16.5"
 description = "A database migration tool for SQLAlchemy."
 optional = false
 python-versions = ">=3.9"
 groups = ["main"]
 files = [
-    {file = "alembic-1.16.4-py3-none-any.whl", hash = "sha256:b05e51e8e82efc1abd14ba2af6392897e145930c3e0a2faf2b0da2f7f7fd660d"},
-    {file = "alembic-1.16.4.tar.gz", hash = "sha256:efab6ada0dd0fae2c92060800e0bf5c1dc26af15a10e02fb4babff164b4725e2"},
+    {file = "alembic-1.16.5-py3-none-any.whl", hash = "sha256:e845dfe090c5ffa7b92593ae6687c5cb1a101e91fa53868497dbd79847f9dbe3"},
+    {file = "alembic-1.16.5.tar.gz", hash = "sha256:a88bb7f6e513bd4301ecf4c7f2206fe93f9913f9b48dac3b78babde2d6fe765e"},
 ]
 
 [package.dependencies]
@@ -71,14 +71,14 @@ files = [
 
 [[package]]
 name = "autoray"
-version = "0.7.2"
+version = "0.8.0"
 description = "Abstract your array operations."
 optional = false
 python-versions = ">=3.9"
 groups = ["main"]
 files = [
-    {file = "autoray-0.7.2-py3-none-any.whl", hash = "sha256:f692f0f21a6f187ce877f3cc810f035d601ccd713beac02974811650bb60f580"},
-    {file = "autoray-0.7.2.tar.gz", hash = "sha256:7f8f375af12deea65736b65305b86eff2e11ebaf8c58d3e599752681772ff0d7"},
+    {file = "autoray-0.8.0-py3-none-any.whl", hash = "sha256:fda5e20b072d41818ccdf26c251dfde4c49595e7c323b141dc2640e52f5889c9"},
+    {file = "autoray-0.8.0.tar.gz", hash = "sha256:5d0d71da03cb02d5bc590a1af64e0ba58589352d628843a0ecbcfe90040dc520"},
 ]
 
 [package.extras]
@@ -114,14 +114,14 @@ files = [
 
 [[package]]
 name = "beautifulsoup4"
-version = "4.13.4"
+version = "4.13.5"
 description = "Screen-scraping library"
 optional = false
 python-versions = ">=3.7.0"
 groups = ["docs"]
 files = [
-    {file = "beautifulsoup4-4.13.4-py3-none-any.whl", hash = "sha256:9bbbb14bfde9d79f38b8cd5f8c7c85f4b8f2523190ebed90e950a8dea4cb1c4b"},
-    {file = "beautifulsoup4-4.13.4.tar.gz", hash = "sha256:dbb3c4e1ceae6aefebdaf2423247260cd062430a410e38c66f2baa50a8437195"},
+    {file = "beautifulsoup4-4.13.5-py3-none-any.whl", hash = "sha256:642085eaa22233aceadff9c69651bc51e8bf3f874fb6d7104ece2beb24b47c4a"},
+    {file = "beautifulsoup4-4.13.5.tar.gz", hash = "sha256:5e70131382930e7c3de33450a2f54a63d5e4b19386eab43a5b34d594268f3695"},
 ]
 
 [package.dependencies]
@@ -137,116 +137,103 @@ lxml = ["lxml"]
 
 [[package]]
 name = "certifi"
-version = "2025.7.14"
+version = "2025.8.3"
 description = "Python package for providing Mozilla's CA Bundle."
 optional = false
 python-versions = ">=3.7"
 groups = ["docs"]
 files = [
-    {file = "certifi-2025.7.14-py3-none-any.whl", hash = "sha256:6b31f564a415d79ee77df69d757bb49a5bb53bd9f756cbbe24394ffd6fc1f4b2"},
-    {file = "certifi-2025.7.14.tar.gz", hash = "sha256:8ea99dbdfaaf2ba2f9bac77b9249ef62ec5218e7c2b2e903378ed5fccf765995"},
+    {file = "certifi-2025.8.3-py3-none-any.whl", hash = "sha256:f6c12493cfb1b06ba2ff328595af9350c65d6644968e5d3a2ffd78699af217a5"},
+    {file = "certifi-2025.8.3.tar.gz", hash = "sha256:e564105f78ded564e3ae7c923924435e1daa7463faeab5bb932bc53ffae63407"},
 ]
 
 [[package]]
 name = "charset-normalizer"
-version = "3.4.2"
+version = "3.4.3"
 description = "The Real First Universal Charset Detector. Open, modern and actively maintained alternative to Chardet."
 optional = false
 python-versions = ">=3.7"
 groups = ["docs"]
 files = [
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 [[package]]
@@ -413,100 +400,116 @@ test = ["altair", "baytune", "chocolate", "cmaes", "dask", "distributed", "kahyp
 
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 [package.extras]
 docs = ["Sphinx", "furo"]
-test = ["objgraph", "psutil"]
+test = ["objgraph", "psutil", "setuptools"]
 
 [[package]]
 name = "h5py"
@@ -1209,104 +1228,125 @@ i18n = ["Babel (>=2.7)"]
 
 [[package]]
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 [package.dependencies]
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 ]
 
 [[package]]
@@ -1689,14 +1769,14 @@ tests = ["pytest (>=6.0)", "pyyaml"]
 
 [[package]]
 name = "optuna"
-version = "4.4.0"
+version = "4.5.0"
 description = "A hyperparameter optimization framework"
 optional = false
 python-versions = ">=3.8"
 groups = ["main"]
 files = [
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+    {file = "optuna-4.5.0.tar.gz", hash = "sha256:264844da16dad744dea295057d8bc218646129c47567d52c35a201d9f99942ba"},
 ]
 
 [package.dependencies]
@@ -1710,10 +1790,10 @@ tqdm = "*"
 
 [package.extras]
 benchmark = ["asv (>=0.5.0)", "cma", "virtualenv"]
-checking = ["black", "blackdoc", "flake8", "isort", "mypy", "mypy_boto3_s3", "types-PyYAML", "types-redis", "types-setuptools", "types-tqdm", "typing_extensions (>=3.10.0.0)"]
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-test = ["coverage", "fakeredis[lua]", "grpcio", "kaleido (<0.4)", "moto", "protobuf (>=5.28.1)", "pytest", "scipy (>=1.9.2)", "torch ; python_version <= \"3.12\""]
+checking = ["black", "blackdoc", "flake8", "isort", "mypy", "mypy_boto3_s3", "scipy-stubs ; python_version >= \"3.10\"", "types-PyYAML", "types-redis", "types-setuptools", "types-tqdm", "typing_extensions (>=3.10.0.0)"]
+document = ["ase", "cmaes (>=0.12.0)", "fvcore", "kaleido (<0.4)", "lightgbm", "matplotlib (!=3.6.0)", "pandas", "pillow", "plotly (>=4.9.0)", "scikit-learn", "sphinx", "sphinx-copybutton", "sphinx-gallery", "sphinx-notfound-page", "sphinx_rtd_theme (>=1.2.0)", "torch", "torchvision"]
+optional = ["boto3", "cmaes (>=0.12.0)", "google-cloud-storage", "grpcio", "matplotlib (!=3.6.0)", "pandas", "plotly (>=4.9.0)", "protobuf (>=5.28.1)", "redis", "scikit-learn (>=0.24.2)", "scipy", "torch"]
+test = ["coverage", "fakeredis[lua]", "grpcio", "kaleido (<0.4)", "moto", "protobuf (>=5.28.1)", "pytest", "pytest-xdist", "scipy (>=1.9.2)", "torch"]
 
 [[package]]
 name = "packaging"
@@ -1729,36 +1809,20 @@ files = [
 
 [[package]]
 name = "parso"
-version = "0.8.4"
+version = "0.8.5"
 description = "A Python Parser"
 optional = false
 python-versions = ">=3.6"
 groups = ["dev"]
 files = [
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 ]
 
 [package.extras]
 qa = ["flake8 (==5.0.4)", "mypy (==0.971)", "types-setuptools (==67.2.0.1)"]
 testing = ["docopt", "pytest"]
 
-[[package]]
-name = "pbr"
-version = "6.1.1"
-description = "Python Build Reasonableness"
-optional = true
-python-versions = ">=2.6"
-groups = ["main"]
-markers = "extra == \"qmatchatea\""
-files = [
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-]
-
-[package.dependencies]
-setuptools = "*"
-
 [[package]]
 name = "pexpect"
 version = "4.9.0"
@@ -1914,14 +1978,14 @@ xmp = ["defusedxml"]
 
 [[package]]
 name = "platformdirs"
-version = "4.3.8"
+version = "4.4.0"
 description = "A small Python package for determining appropriate platform-specific dirs, e.g. a `user data dir`."
 optional = false
 python-versions = ">=3.9"
 groups = ["analysis"]
 files = [
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+    {file = "platformdirs-4.4.0-py3-none-any.whl", hash = "sha256:abd01743f24e5287cd7a5db3752faf1a2d65353f38ec26d98e25a6db65958c85"},
+    {file = "platformdirs-4.4.0.tar.gz", hash = "sha256:ca753cf4d81dc309bc67b0ea38fd15dc97bc30ce419a7f58d13eb3bf14c4febf"},
 ]
 
 [package.extras]
@@ -1947,14 +2011,14 @@ testing = ["coverage", "pytest", "pytest-benchmark"]
 
 [[package]]
 name = "prompt-toolkit"
-version = "3.0.51"
+version = "3.0.52"
 description = "Library for building powerful interactive command lines in Python"
 optional = false
 python-versions = ">=3.8"
 groups = ["dev"]
 files = [
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+    {file = "prompt_toolkit-3.0.52-py3-none-any.whl", hash = "sha256:9aac639a3bbd33284347de5ad8d68ecc044b91a762dc39b7c21095fcd6a19955"},
+    {file = "prompt_toolkit-3.0.52.tar.gz", hash = "sha256:28cde192929c8e7321de85de1ddbe736f1375148b02f2e17edd840042b1be855"},
 ]
 
 [package.dependencies]
@@ -1962,27 +2026,26 @@ wcwidth = "*"
 
 [[package]]
 name = "psutil"
-version = "7.0.0"
-description = "Cross-platform lib for process and system monitoring in Python.  NOTE: the syntax of this script MUST be kept compatible with Python 2.7."
+version = "7.1.0"
+description = "Cross-platform lib for process and system monitoring."
 optional = false
 python-versions = ">=3.6"
 groups = ["main"]
 files = [
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+    {file = "psutil-7.1.0.tar.gz", hash = "sha256:655708b3c069387c8b77b072fc429a57d0e214221d01c0a772df7dfedcb3bcd2"},
 ]
 
 [package.extras]
-dev = ["abi3audit", "black (==24.10.0)", "check-manifest", "coverage", "packaging", "pylint", "pyperf", "pypinfo", "pytest", "pytest-cov", "pytest-xdist", "requests", "rstcheck", "ruff", "setuptools", "sphinx", "sphinx_rtd_theme", "toml-sort", "twine", "virtualenv", "vulture", "wheel"]
-test = ["pytest", "pytest-xdist", "setuptools"]
+dev = ["abi3audit", "black", "check-manifest", "coverage", "packaging", "pylint", "pyperf", "pypinfo", "pyreadline ; os_name == \"nt\"", "pytest", "pytest-cov", "pytest-instafail", "pytest-subtests", "pytest-xdist", "pywin32 ; os_name == \"nt\" and platform_python_implementation != \"PyPy\"", "requests", "rstcheck", "ruff", "setuptools", "sphinx", "sphinx_rtd_theme", "toml-sort", "twine", "virtualenv", "vulture", "wheel", "wheel ; os_name == \"nt\" and platform_python_implementation != \"PyPy\"", "wmi ; os_name == \"nt\" and platform_python_implementation != \"PyPy\""]
+test = ["pytest", "pytest-instafail", "pytest-subtests", "pytest-xdist", "pywin32 ; os_name == \"nt\" and platform_python_implementation != \"PyPy\"", "setuptools", "wheel ; os_name == \"nt\" and platform_python_implementation != \"PyPy\"", "wmi ; os_name == \"nt\" and platform_python_implementation != \"PyPy\""]
 
 [[package]]
 name = "ptyprocess"
@@ -2050,14 +2113,14 @@ windows-terminal = ["colorama (>=0.4.6)"]
 
 [[package]]
 name = "pylint"
-version = "3.3.7"
+version = "3.3.8"
 description = "python code static checker"
 optional = false
 python-versions = ">=3.9.0"
 groups = ["analysis"]
 files = [
-    {file = "pylint-3.3.7-py3-none-any.whl", hash = "sha256:43860aafefce92fca4cf6b61fe199cdc5ae54ea28f9bf4cd49de267b5195803d"},
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+    {file = "pylint-3.3.8-py3-none-any.whl", hash = "sha256:7ef94aa692a600e82fabdd17102b73fc226758218c97473c7ad67bd4cb905d83"},
+    {file = "pylint-3.3.8.tar.gz", hash = "sha256:26698de19941363037e2937d3db9ed94fb3303fdadf7d98847875345a8bb6b05"},
 ]
 
 [package.dependencies]
@@ -2078,14 +2141,14 @@ testutils = ["gitpython (>3)"]
 
 [[package]]
 name = "pyparsing"
-version = "3.2.3"
-description = "pyparsing module - Classes and methods to define and execute parsing grammars"
+version = "3.2.5"
+description = "pyparsing - Classes and methods to define and execute parsing grammars"
 optional = false
 python-versions = ">=3.9"
 groups = ["main"]
 files = [
-    {file = "pyparsing-3.2.3-py3-none-any.whl", hash = "sha256:a749938e02d6fd0b59b356ca504a24982314bb090c383e3cf201c95ef7e2bfcf"},
-    {file = "pyparsing-3.2.3.tar.gz", hash = "sha256:b9c13f1ab8b3b542f72e28f634bad4de758ab3ce4546e4301970ad6fa77c38be"},
+    {file = "pyparsing-3.2.5-py3-none-any.whl", hash = "sha256:e38a4f02064cf41fe6593d328d0512495ad1f3d8a91c4f73fc401b3079a59a5e"},
+    {file = "pyparsing-3.2.5.tar.gz", hash = "sha256:2df8d5b7b2802ef88e8d016a2eb9c7aeaa923529cd251ed0fe4608275d4105b6"},
 ]
 
 [package.extras]
@@ -2093,14 +2156,14 @@ diagrams = ["jinja2", "railroad-diagrams"]
 
 [[package]]
 name = "pytest"
-version = "8.4.1"
+version = "8.4.2"
 description = "pytest: simple powerful testing with Python"
 optional = false
 python-versions = ">=3.9"
 groups = ["tests"]
 files = [
-    {file = "pytest-8.4.1-py3-none-any.whl", hash = "sha256:539c70ba6fcead8e78eebbf1115e8b589e7565830d7d006a8723f19ac8a0afb7"},
-    {file = "pytest-8.4.1.tar.gz", hash = "sha256:7c67fd69174877359ed9371ec3af8a3d2b04741818c51e5e99cc1742251fa93c"},
+    {file = "pytest-8.4.2-py3-none-any.whl", hash = "sha256:872f880de3fc3a5bdc88a11b39c9710c3497a547cfa9320bc3c5e62fbf272e79"},
+    {file = "pytest-8.4.2.tar.gz", hash = "sha256:86c0d0b93306b961d58d62a4db4879f27fe25513d4b969df351abdddb3c30e01"},
 ]
 
 [package.dependencies]
@@ -2230,49 +2293,54 @@ files = [
 
 [[package]]
 name = "qibo"
-version = "0.2.20"
+version = "0.2.21"
 description = "A framework for quantum computing with hardware acceleration."
 optional = false
-python-versions = "<3.14,>=3.10"
+python-versions = ">=3.10,<3.14"
 groups = ["main"]
-files = [
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-]
+files = []
+develop = false
 
 [package.dependencies]
-cma = ">=3.4.0,<4.0.0"
-joblib = ">=1.4.2,<2.0.0"
-networkx = ">=3.2.1,<4.0.0"
-numpy = ">=2.0.0,<3.0.0"
-openqasm3 = {version = ">=1.0.1,<2.0.0", extras = ["parser"]}
-optuna = ">=4.2.1,<5.0.0"
-scipy = ">=1.15.2,<2.0.0"
-sympy = ">=1.13.1,<2.0.0"
-tabulate = ">=0.9.0,<0.10.0"
+cma = "^3.4.0"
+joblib = "^1.4.2"
+networkx = "^3.2.1"
+numpy = "^2.0.0"
+openqasm3 = {version = "^1.0.1", extras = ["parser"]}
+optuna = "^4.2.1"
+scipy = "^1.15.2"
+sympy = "^1.13.1"
+tabulate = "^0.9.0"
 
 [package.extras]
+qinfo = []
 qulacs = ["qulacs (>=0.6.4,<0.7.0) ; python_version < \"3.13\""]
 
+[package.source]
+type = "git"
+url = "https://github.com/qiboteam/qibo"
+reference = "expectation"
+resolved_reference = "41b52af8faba1974c776a074fc0aba3461aeb6fe"
+
 [[package]]
 name = "qiskit"
-version = "1.4.3"
+version = "1.4.4"
 description = "An open-source SDK for working with quantum computers at the level of extended quantum circuits, operators, and primitives."
 optional = true
 python-versions = ">=3.9"
 groups = ["main"]
 markers = "extra == \"qmatchatea\""
 files = [
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-    {file = "qiskit-1.4.3.tar.gz", hash = "sha256:e4e311190c159578f253d219dc860241ccb71955ca08725bb092c74cf7fbdac5"},
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+    {file = "qiskit-1.4.4-cp39-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:496c7f6a324b9ee60e2f59503ad25559fec7ec771a74b5e233b6512f01b019f8"},
+    {file = "qiskit-1.4.4-cp39-abi3-win32.whl", hash = "sha256:4e839612835422d0c285b1879bca547fcf875000f347377ceb1463aa2324c5e1"},
+    {file = "qiskit-1.4.4-cp39-abi3-win_amd64.whl", hash = "sha256:52c1f04345c6093305f1f4fe9d22a69ee86aa79b6b2beca7e0c89d3694d8b104"},
+    {file = "qiskit-1.4.4.tar.gz", hash = "sha256:96251c94b14175455809016c08c013dfb615020289e2920a9878fddf35bdda86"},
 ]
 
 [package.dependencies]
@@ -2361,14 +2429,14 @@ scipy = "*"
 
 [[package]]
 name = "quimb"
-version = "1.11.1"
+version = "1.11.2"
 description = "Quantum information and many-body library."
 optional = false
 python-versions = ">=3.9"
 groups = ["main"]
 files = [
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-    {file = "quimb-1.11.1.tar.gz", hash = "sha256:8f3ff7630c4a2b50781d068bfe55dfbb58cf694886707ce95c245a21e7126ee8"},
+    {file = "quimb-1.11.2-py3-none-any.whl", hash = "sha256:5c8a66311f54f3894e39f23d83cef4537cc6d41011779733ca303f3e5f09c7b8"},
+    {file = "quimb-1.11.2.tar.gz", hash = "sha256:12546651f714e4ff3adb53dc7b620b4c4eb3fd8d8aafad0f92ac4cc04f03440c"},
 ]
 
 [package.dependencies]
@@ -2391,14 +2459,14 @@ tests = ["coverage", "pytest", "pytest-cov"]
 
 [[package]]
 name = "requests"
-version = "2.32.4"
+version = "2.32.5"
 description = "Python HTTP for Humans."
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
 groups = ["docs"]
 files = [
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-    {file = "requests-2.32.4.tar.gz", hash = "sha256:27d0316682c8a29834d3264820024b62a36942083d52caf2f14c0591336d3422"},
+    {file = "requests-2.32.5-py3-none-any.whl", hash = "sha256:2462f94637a34fd532264295e186976db0f5d453d1cdd31473c85a6a161affb6"},
+    {file = "requests-2.32.5.tar.gz", hash = "sha256:dbba0bac56e100853db0ea71b82b4dfd5fe2bf6d3754a8893c3af500cec7d7cf"},
 ]
 
 [package.dependencies]
@@ -2413,24 +2481,25 @@ use-chardet-on-py3 = ["chardet (>=3.0.2,<6)"]
 
 [[package]]
 name = "rustworkx"
-version = "0.16.0"
-description = "A python graph library implemented in Rust"
+version = "0.17.1"
+description = "A High-Performance Graph Library for Python"
 optional = true
 python-versions = ">=3.9"
 groups = ["main"]
 markers = "extra == \"qmatchatea\""
 files = [
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+    {file = "rustworkx-0.17.1-cp39-abi3-musllinux_1_2_x86_64.whl", hash = "sha256:48784a673cf8d04f3cd246fa6b53fd1ccc4d83304503463bd561c153517bccc1"},
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 ]
 
 [package.dependencies]
@@ -2443,67 +2512,73 @@ mpl = ["matplotlib (>=3.0)"]
 
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 [[package]]
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 description = "Easily download, build, install, upgrade, and uninstall Python packages"
 optional = false
 python-versions = ">=3.9"
-groups = ["main", "dev"]
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 description = "A modern CSS selector implementation for Beautiful Soup."
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+    {file = "sqlalchemy-2.0.43.tar.gz", hash = "sha256:788bfcef6787a7764169cfe9859fe425bf44559619e1d9f56f5bddf2ebf6f417"},
 ]
 
 [package.dependencies]
@@ -2878,20 +2952,17 @@ sqlcipher = ["sqlcipher3_binary"]
 
 [[package]]
 name = "stevedore"
-version = "5.4.1"
+version = "5.5.0"
 description = "Manage dynamic plugins for Python applications"
 optional = true
 python-versions = ">=3.9"
 groups = ["main"]
 markers = "extra == \"qmatchatea\""
 files = [
-    {file = "stevedore-5.4.1-py3-none-any.whl", hash = "sha256:d10a31c7b86cba16c1f6e8d15416955fc797052351a56af15e608ad20811fcfe"},
-    {file = "stevedore-5.4.1.tar.gz", hash = "sha256:3135b5ae50fe12816ef291baff420acb727fcd356106e3e9cbfa9e5985cd6f4b"},
+    {file = "stevedore-5.5.0-py3-none-any.whl", hash = "sha256:18363d4d268181e8e8452e71a38cd77630f345b2ef6b4a8d5614dac5ee0d18cf"},
+    {file = "stevedore-5.5.0.tar.gz", hash = "sha256:d31496a4f4df9825e1a1e4f1f74d19abb0154aff311c3b376fcc89dae8fccd73"},
 ]
 
-[package.dependencies]
-pbr = ">=2.0.0"
-
 [[package]]
 name = "symengine"
 version = "0.13.0"
@@ -3042,14 +3113,14 @@ test = ["argcomplete (>=3.0.3)", "mypy (>=1.7.0)", "pre-commit", "pytest (>=7.0,
 
 [[package]]
 name = "typing-extensions"
-version = "4.14.1"
+version = "4.15.0"
 description = "Backported and Experimental Type Hints for Python 3.9+"
 optional = false
 python-versions = ">=3.9"
 groups = ["main", "docs"]
 files = [
-    {file = "typing_extensions-4.14.1-py3-none-any.whl", hash = "sha256:d1e1e3b58374dc93031d6eda2420a48ea44a36c2b4766a4fdeb3710755731d76"},
-    {file = "typing_extensions-4.14.1.tar.gz", hash = "sha256:38b39f4aeeab64884ce9f74c94263ef78f3c22467c8724005483154c26648d36"},
+    {file = "typing_extensions-4.15.0-py3-none-any.whl", hash = "sha256:f0fa19c6845758ab08074a0cfa8b7aecb71c999ca73d62883bc25cc018c4e548"},
+    {file = "typing_extensions-4.15.0.tar.gz", hash = "sha256:0cea48d173cc12fa28ecabc3b837ea3cf6f38c6d1136f85cbaaf598984861466"},
 ]
 
 [[package]]
@@ -3072,14 +3143,14 @@ zstd = ["zstandard (>=0.18.0)"]
 
 [[package]]
 name = "wcwidth"
-version = "0.2.13"
+version = "0.2.14"
 description = "Measures the displayed width of unicode strings in a terminal"
 optional = false
-python-versions = "*"
+python-versions = ">=3.6"
 groups = ["dev"]
 files = [
-    {file = "wcwidth-0.2.13-py2.py3-none-any.whl", hash = "sha256:3da69048e4540d84af32131829ff948f1e022c1c6bdb8d6102117aac784f6859"},
-    {file = "wcwidth-0.2.13.tar.gz", hash = "sha256:72ea0c06399eb286d978fdedb6923a9eb47e1c486ce63e9b4e64fc18303972b5"},
+    {file = "wcwidth-0.2.14-py2.py3-none-any.whl", hash = "sha256:a7bb560c8aee30f9957e5f9895805edd20602f2d7f720186dfd906e82b4982e1"},
+    {file = "wcwidth-0.2.14.tar.gz", hash = "sha256:4d478375d31bc5395a3c55c40ccdf3354688364cd61c4f6adacaa9215d0b3605"},
 ]
 
 [extras]
@@ -3089,4 +3160,4 @@ qmatchatea = ["qiskit", "qmatchatea", "qtealeaves"]
 [metadata]
 lock-version = "2.1"
 python-versions = ">=3.11,<3.14"
-content-hash = "fa9982c6a663449880e90e3a0d7ec5782283d27a324d9b41c42d4616ded66048"
+content-hash = "1a588cc02000984b68fc1342301a1e2873b804a82e1b9ba3639ed3a01e637d4b"
diff --git a/pyproject.toml b/pyproject.toml
index efb39ca..a311eff 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -21,7 +21,7 @@ packages = [{ include = "qibotn", from = "src" }]
 
 [tool.poetry.dependencies]
 python = ">=3.11,<3.14"
-qibo = "^0.2.17"
+qibo = { git="https://github.com/qiboteam/qibo", branch="expectation"}
 quimb = { version = "^1.10.0", extras = ["tensor"] }
 cupy-cuda11x = { version = "^13.1.0", optional = true }
 cuquantum-python-cu11 = { version = "^24.1.0", optional = true }
diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 8a11bb9..6e4629b 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -1,63 +1,55 @@
 from collections import Counter
 
 import numpy as np
-
-from qibo.models import Circuit
-from qibo.backends import NumpyBackend
-from qibo.config import raise_error
-from qibotn.backends.abstract import QibotnBackend
-from qibotn.result import TensorNetworkResult
-from qibo.gates.abstract import ParametrizedGate
-
 import quimb as qu
 import quimb.tensor as qtn
+from qibo.backends import NumpyBackend
+from qibo.config import raise_error
+from qibo.gates.abstract import ParametrizedGate
+from qibo.models import Circuit
 
+from qibotn.backends.abstract import QibotnBackend
+from qibotn.result import TensorNetworkResult
 
 GATE_MAP = {
-        "h": "H",
-        "x": "X",
-        "y": "Y",
-        "z": "Z",
-        "s": "S",
-        "t": "T",
+    "h": "H",
+    "x": "X",
+    "y": "Y",
+    "z": "Z",
+    "s": "S",
+    "t": "T",
+    "rx": "RX",
+    "ry": "RY",
+    "rz": "RZ",
+    "u3": "U3",  # TODO: check
+    "cx": "CX",
+    "cnot": "CNOT",
+    "cy": "CY",
+    "cz": "CZ",
+    "iswap": "ISWAP",
+    "swap": "SWAP",
+    "ccx": "CCX",
+    "ccy": "CCY",
+    "ccz": "CCZ",
+    "toffoli": "TOFFOLI",
+    "cswap": "CSWAP",
+    "fredkin": "FREDKIN",
+    "fsim": "fsim",
+    "measure": "measure",
+}
 
-        "rx": "RX",
-        "ry": "RY",
-        "rz": "RZ",
-
-        "u3": "U3", # TODO: check
-
-        "cx": "CX",
-        "cnot": "CNOT",
-        "cy": "CY",
-        "cz": "CZ",
-
-        "iswap": "ISWAP",
-        "swap": "SWAP",
-
-        "ccx": "CCX",
-        "ccy": "CCY",
-        "ccz": "CCZ",
-
-        "toffoli": "TOFFOLI",
-        "cswap": "CSWAP",
-        "fredkin": "FREDKIN",
-
-        "fsim": "fsim",
-
-        "measure": "measure"
-    }
 
 class QuimbBackend(QibotnBackend, NumpyBackend):
 
-    def __init__(self):
+    def __init__(self, engine="numpy"):
         super().__init__()
 
         self.name = "qibotn"
         self.platform = "quimb"
+        self.engine = engine
 
         self.configure_tn_simulation()
-        self.setup_backend_specifics()
+        self.setup_backend_specifics(quimb_backend=engine)
 
     def configure_tn_simulation(
         self,
@@ -71,7 +63,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         Args:
             ansatz : str, optional
                 The tensor network ansatz to use. Default is `None` and, in this case, a
-                generic Circuit Quimb class is used.            
+                generic Circuit Quimb class is used.
                 max_bond_dimension : int, optional
                 The maximum bond dimension for the MPS ansatz. Default is 10.
 
@@ -83,7 +75,9 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         self.max_bond_dimension = max_bond_dimension
         self.n_most_frequent_states = n_most_frequent_states
 
-    def setup_backend_specifics(self, qimb_backend="numpy", contractions_optimizer="auto-hq"):
+    def setup_backend_specifics(
+        self, quimb_backend="numpy", contractions_optimizer="auto-hq"
+    ):
         """Setup backend specifics.
         Args:
             qimb_backend: str
@@ -91,19 +85,22 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             contractions_optimizer: str, optional
                 The contractions_optimizer to use for the quimb tensor network simulation.
         """
-        if qimb_backend == "jax":
+        if quimb_backend == "jax":
             import jax.numpy as jnp
+
             self.np = jnp
-        elif qimb_backend == "numpy":
+        elif quimb_backend == "numpy":
             import numpy as np
+
             self.np = np
-        elif qimb_backend == "torch":
+        elif quimb_backend == "torch":
             import torch
+
             self.np = torch
         else:
-            raise_error(ValueError, f"Unsupported quimb backend: {qimb_backend}")
+            raise_error(ValueError, f"Unsupported quimb backend: {quimb_backend}")
 
-        self.backend = qimb_backend
+        self.backend = quimb_backend
         self.contractions_optimizer = contractions_optimizer
 
     def execute_circuit(
@@ -180,7 +177,9 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             measured_probabilities = None
 
         statevector = (
-            circ_quimb.to_dense(backend=self.backend, optimize=self.contractions_optimizer)
+            circ_quimb.to_dense(
+                backend=self.backend, optimize=self.contractions_optimizer
+            )
             if return_array
             else None
         )
@@ -193,14 +192,16 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             statevector=statevector,
         )
 
-    def expectation(self, circuit, operators_list, sites_list, coeffs_list):
+    def expectation_observable_symbolic_from_state(
+        self, circuit, operators_list, sites_list, coeffs_list, nqubits
+    ):
         """
         Compute the expectation value of a symbolic Hamiltonian on a quantum circuit using tensor network contraction.
         This method takes a Qibo circuit, converts it to a Quimb tensor network circuit, and evaluates the expectation value
         of a Hamiltonian specified by three lists of strings: operators, sites, and coefficients.
         The expectation value is computed by summing the contributions from each term in the Hamiltonian, where each term's
         expectation is calculated using Quimb's `local_expectation` function.
-        
+
         Parameters
         ----------
         circuit : qibo.models.Circuit
@@ -216,27 +217,30 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         float
             The real part of the expectation value of the Hamiltonian on the given circuit state.
         """
-        quimb_circuit = self._qibo_circuit_to_quimb(circuit, quimb_circuit_type=qtn.Circuit)
-            
+        quimb_circuit = self._qibo_circuit_to_quimb(
+            circuit, quimb_circuit_type=qtn.Circuit
+        )
+
         expectation_value = 0.0
-        for opstr, sitesstr, coeffstr in zip(operators_list, sites_list, coeffs_list):
-            
+        for opstr, sites, coeff in zip(operators_list, sites_list, coeffs_list):
+
             ops = self._string_to_quimb_operator(opstr)
-            coeff = self._parse_coefficient(coeffstr)
-            sites = tuple(int(q) for q in sitesstr)
-            
+            coeff = coeff.real
+
             exp_values = quimb_circuit.local_expectation(
                 ops,
                 where=sites,
                 backend=self.backend,
-                optimize=self.contractions_optimizer
+                optimize=self.contractions_optimizer,
             )
 
             expectation_value = expectation_value + coeff * exp_values
-        
-        return np.real(expectation_value)
 
-    def _qibo_circuit_to_quimb(self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs):
+        return self.np.real(expectation_value)
+
+    def _qibo_circuit_to_quimb(
+        self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs
+    ):
         """
         Convert a Qibo Circuit to a Quimb Circuit. Measurement gates are ignored. If are given gates not supported by Quimb, an error is raised.
 
@@ -267,18 +271,12 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
 
             params = getattr(gate, "parameters", ())
             qubits = getattr(gate, "qubits", ())
-            
-            is_parametrized = (
-                isinstance(gate, ParametrizedGate)
-                and getattr(gate, "trainable", True)
-                )
+
+            is_parametrized = isinstance(gate, ParametrizedGate) and getattr(
+                gate, "trainable", True
+            )
             if is_parametrized:
-                circ.apply_gate(
-                    qname,
-                    *params,
-                    *qubits,
-                    parametrized=is_parametrized
-                )
+                circ.apply_gate(qname, *params, *qubits, parametrized=is_parametrized)
             else:
                 circ.apply_gate(
                     qname,
@@ -287,28 +285,6 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
                 )
         return circ
 
-    def _parse_coefficient(self, s):
-        """Parse a coefficient from string to float, int, or complex.
-        Args:
-            s: str
-                The string representation of the coefficient.
-        Returns:
-            The coefficient as float, int, or complex.
-        """ 
-        try:
-            return float(s)
-        except ValueError:
-            pass
-        if s == "j":
-            return 1j
-        elif s == "-j":
-            return -1j
-        else:
-            try:
-                return complex(s)
-            except ValueError:
-                raise ValueError(f"Cannot parse coefficient: {s}")
-
     def _string_to_quimb_operator(self, op_str):
         """
         Convert a Pauli string (e.g. 'xzy') to a Quimb operator using '&' chaining.

From ab10b13d9b7e4691c7b4d58a88c555e61d57ccc7 Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Tue, 23 Sep 2025 17:57:00 +0200
Subject: [PATCH 16/33] feat: dynamically inheriting with quimb

---
 src/qibotn/backends/__init__.py |  5 +++--
 src/qibotn/backends/quimb.py    | 37 ++++++++++++++++++++++++++++++---
 2 files changed, 37 insertions(+), 5 deletions(-)

diff --git a/src/qibotn/backends/__init__.py b/src/qibotn/backends/__init__.py
index 416a384..4a5dbdd 100644
--- a/src/qibotn/backends/__init__.py
+++ b/src/qibotn/backends/__init__.py
@@ -13,7 +13,7 @@ class MetaBackend:
     """Meta-backend class which takes care of loading the qibotn backends."""
 
     @staticmethod
-    def load(platform: str, runcard: dict = None) -> QibotnBackend:
+    def load(platform: str, runcard: dict = None, **kwargs) -> QibotnBackend:
         """Loads the backend.
 
         Args:
@@ -26,7 +26,8 @@ class MetaBackend:
         if platform == "cutensornet":  # pragma: no cover
             return CuTensorNet(runcard)
         elif platform == "quimb":  # pragma: no cover
-            return QuimbBackend()
+            quimb_backend = kwargs.get("quimb_backend", "numpy")
+            return QuimbBackend(quimb_backend)
         elif platform == "qmatchatea":  # pragma: no cover
             from qibotn.backends.qmatchatea import QMatchaTeaBackend
 
diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 6e4629b..658ca7e 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -39,10 +39,12 @@ GATE_MAP = {
 }
 
 
-class QuimbBackend(QibotnBackend, NumpyBackend):
+# class QuimbBackend(QibotnBackend, NumpyBackend):
+if not __name__ == "__main__":
 
     def __init__(self, engine="numpy"):
-        super().__init__()
+        # uper().__init__()
+        super(self.__class__, self).__init__()
 
         self.name = "qibotn"
         self.platform = "quimb"
@@ -85,6 +87,7 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             contractions_optimizer: str, optional
                 The contractions_optimizer to use for the quimb tensor network simulation.
         """
+        # this is not really working because it does not change the inheritance
         if quimb_backend == "jax":
             import jax.numpy as jnp
 
@@ -142,7 +145,6 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
             - If `initial_state` is provided, it must be compatible with the MPS ansatz.
             - The `nshots` parameter enables sampling from the circuit's output distribution. If not specified, the full statevector is computed.
         """
-
         if initial_state is not None and self.ansatz == "MPS":
             initial_state = qtn.tensor_1d.MatrixProductState.from_dense(
                 initial_state, 2
@@ -304,3 +306,32 @@ class QuimbBackend(QibotnBackend, NumpyBackend):
         for c in op_str[1:]:
             op = op & qu.pauli(c)
         return op
+
+
+def QuimbBackend(quimb_backend: str = "numpy") -> QibotnBackend:
+    bases = (QibotnBackend,)
+    methods = {
+        "__init__": __init__,
+        "configure_tn_simulation": configure_tn_simulation,
+        "setup_backend_specifics": setup_backend_specifics,
+        "execute_circuit": execute_circuit,
+        "expectation_observable_symbolic_from_state": expectation_observable_symbolic_from_state,
+        "_qibo_circuit_to_quimb": _qibo_circuit_to_quimb,
+        "_string_to_quimb_operator": _string_to_quimb_operator,
+    }
+    if quimb_backend == "numpy":
+        from qibo.backends import NumpyBackend
+
+        bases += (NumpyBackend,)
+    elif quimb_backend == "torch":
+        from qiboml.backends import PyTorchBackend
+
+        bases += (PyTorchBackend,)
+    elif quimb_backend == "jax":
+        from qiboml.backends import JaxBackend
+
+        bases += (JaxBackend,)
+    else:
+        raise_error(ValueError, f"Unsupported quimb backend: {quimb_backend}")
+
+    return type("QuimbBackend", bases, methods)(quimb_backend)

From 715d100136c3a1bbe1bb39fe2c4183091cb49e91 Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Tue, 23 Sep 2025 18:07:50 +0200
Subject: [PATCH 17/33] fix: removed comments

---
 src/qibotn/backends/quimb.py | 2 --
 1 file changed, 2 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 658ca7e..d948bf9 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -39,11 +39,9 @@ GATE_MAP = {
 }
 
 
-# class QuimbBackend(QibotnBackend, NumpyBackend):
 if not __name__ == "__main__":
 
     def __init__(self, engine="numpy"):
-        # uper().__init__()
         super(self.__class__, self).__init__()
 
         self.name = "qibotn"

From 014f47967ffc68067cde80d9c1fe7ee31ce49041 Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Wed, 24 Sep 2025 13:23:51 +0200
Subject: [PATCH 18/33] fix: changed arg names

---
 src/qibotn/backends/__init__.py |  7 +++++--
 src/qibotn/backends/quimb.py    | 15 ++++++++++-----
 2 files changed, 15 insertions(+), 7 deletions(-)

diff --git a/src/qibotn/backends/__init__.py b/src/qibotn/backends/__init__.py
index 4a5dbdd..9cc1fe7 100644
--- a/src/qibotn/backends/__init__.py
+++ b/src/qibotn/backends/__init__.py
@@ -4,7 +4,7 @@ from qibo.config import raise_error
 
 from qibotn.backends.abstract import QibotnBackend
 from qibotn.backends.cutensornet import CuTensorNet  # pylint: disable=E0401
-from qibotn.backends.quimb import QuimbBackend  # pylint: disable=E0401
+from qibotn.backends.quimb import QuimbBackend
 
 PLATFORMS = ("cutensornet", "qutensornet", "qmatchatea")
 
@@ -27,7 +27,10 @@ class MetaBackend:
             return CuTensorNet(runcard)
         elif platform == "quimb":  # pragma: no cover
             quimb_backend = kwargs.get("quimb_backend", "numpy")
-            return QuimbBackend(quimb_backend)
+            contraction_optimizer = kwargs.get("quimb_backend", "auto-hq")
+            return QuimbBackend(
+                quimb_backend=quimb_backend, contraction_optimizer=contraction_optimizer
+            )
         elif platform == "qmatchatea":  # pragma: no cover
             from qibotn.backends.qmatchatea import QMatchaTeaBackend
 
diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index d948bf9..6efaad7 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -41,15 +41,17 @@ GATE_MAP = {
 
 if not __name__ == "__main__":
 
-    def __init__(self, engine="numpy"):
+    def __init__(self, quimb_backend="numpy", contraction_optimizer="auto-hq"):
         super(self.__class__, self).__init__()
 
         self.name = "qibotn"
         self.platform = "quimb"
-        self.engine = engine
+        self.backend = quimb_backend
 
         self.configure_tn_simulation()
-        self.setup_backend_specifics(quimb_backend=engine)
+        self.setup_backend_specifics(
+            quimb_backend=quimb_backend, contractions_optimizer=contraction_optimizer
+        )
 
     def configure_tn_simulation(
         self,
@@ -300,13 +302,16 @@ if not __name__ == "__main__":
             The corresponding Quimb operator.
         """
         op_str = op_str.lower()
+        # breakpoint()
         op = qu.pauli(op_str[0])
         for c in op_str[1:]:
             op = op & qu.pauli(c)
         return op
 
 
-def QuimbBackend(quimb_backend: str = "numpy") -> QibotnBackend:
+def QuimbBackend(
+    quimb_backend: str = "numpy", contraction_optimizer="auto-hq"
+) -> QibotnBackend:
     bases = (QibotnBackend,)
     methods = {
         "__init__": __init__,
@@ -332,4 +337,4 @@ def QuimbBackend(quimb_backend: str = "numpy") -> QibotnBackend:
     else:
         raise_error(ValueError, f"Unsupported quimb backend: {quimb_backend}")
 
-    return type("QuimbBackend", bases, methods)(quimb_backend)
+    return type("QuimbBackend", bases, methods)(quimb_backend, contraction_optimizer)

From 7de00e2c029824471103eeb6ac1eef509afc8b9d Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Wed, 24 Sep 2025 17:24:42 +0200
Subject: [PATCH 19/33] fix: setting simplify sequence = R

---
 src/qibotn/backends/quimb.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 6efaad7..fdba29c 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -234,6 +234,7 @@ if not __name__ == "__main__":
                 where=sites,
                 backend=self.backend,
                 optimize=self.contractions_optimizer,
+                simplify_sequence="R",
             )
 
             expectation_value = expectation_value + coeff * exp_values

From f8439a5b92a55d639ea696f272d467365e8ab1f6 Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Mon, 29 Sep 2025 16:48:32 +0200
Subject: [PATCH 20/33] fix: backend/__init__ in MetaBackend
 contraction_optimizer variable set with the corresponding keyword

---
 src/qibotn/backends/__init__.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/qibotn/backends/__init__.py b/src/qibotn/backends/__init__.py
index 9cc1fe7..4ec932c 100644
--- a/src/qibotn/backends/__init__.py
+++ b/src/qibotn/backends/__init__.py
@@ -27,7 +27,7 @@ class MetaBackend:
             return CuTensorNet(runcard)
         elif platform == "quimb":  # pragma: no cover
             quimb_backend = kwargs.get("quimb_backend", "numpy")
-            contraction_optimizer = kwargs.get("quimb_backend", "auto-hq")
+            contraction_optimizer = kwargs.get("contraction_optimizer", "auto-hq")
             return QuimbBackend(
                 quimb_backend=quimb_backend, contraction_optimizer=contraction_optimizer
             )

From a6d064c8f0e37e60c35e8fe69efabb7053333f04 Mon Sep 17 00:00:00 2001
From: MatteoRobbiati <robbiati.matteo@gmail.com>
Date: Tue, 30 Sep 2025 16:45:39 +0200
Subject: [PATCH 21/33] feat: setting bd when instantiating a quimb circuit

---
 src/qibotn/backends/quimb.py | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index fdba29c..3e55f0f 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -1,4 +1,5 @@
 from collections import Counter
+from typing import Optional
 
 import numpy as np
 import quimb as qu
@@ -220,7 +221,9 @@ if not __name__ == "__main__":
             The real part of the expectation value of the Hamiltonian on the given circuit state.
         """
         quimb_circuit = self._qibo_circuit_to_quimb(
-            circuit, quimb_circuit_type=qtn.Circuit
+            circuit, 
+            quimb_circuit_type=qtn.Circuit, 
+            gate_opts={"max_bond": self.max_bond_dimension},
         )
 
         expectation_value = 0.0

From c2b11ce1e681bfa0783de4a20145a29d57f2fac0 Mon Sep 17 00:00:00 2001
From: MatteoRobbiati <robbiati.matteo@gmail.com>
Date: Tue, 30 Sep 2025 16:47:26 +0200
Subject: [PATCH 22/33] refactor: rm unused imports

---
 src/qibotn/backends/quimb.py | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 3e55f0f..9bd2ea1 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -1,10 +1,7 @@
 from collections import Counter
-from typing import Optional
 
-import numpy as np
 import quimb as qu
 import quimb.tensor as qtn
-from qibo.backends import NumpyBackend
 from qibo.config import raise_error
 from qibo.gates.abstract import ParametrizedGate
 from qibo.models import Circuit

From 3c3c5c0f5a3f42ce085043956349e438dfeaf65d Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Tue, 30 Sep 2025 18:10:49 +0200
Subject: [PATCH 23/33] in expectation function, building the circuti type
 depending on the value set by user

---
 src/qibotn/backends/quimb.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 9bd2ea1..98c560b 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -219,7 +219,7 @@ if not __name__ == "__main__":
         """
         quimb_circuit = self._qibo_circuit_to_quimb(
             circuit, 
-            quimb_circuit_type=qtn.Circuit, 
+            quimb_circuit_type=qtn.CircuitMPS if self.ansatz == "MPS" else qtn.Circuit, 
             gate_opts={"max_bond": self.max_bond_dimension},
         )
 

From 9328028edeb20a7e67ccbb0318ca4cacf00e0ace Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Wed, 1 Oct 2025 16:24:45 +0200
Subject: [PATCH 24/33] fix: minor adjustments

---
 src/qibotn/backends/quimb.py | 30 +++++++++++++++++++++---------
 1 file changed, 21 insertions(+), 9 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 98c560b..756d994 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -1,4 +1,5 @@
 from collections import Counter
+from typing import Optional
 
 import quimb as qu
 import quimb.tensor as qtn
@@ -46,6 +47,11 @@ if not __name__ == "__main__":
         self.platform = "quimb"
         self.backend = quimb_backend
 
+        self.ansatz = None
+        self.max_bond_dimension = None
+        self.cutoff = None
+        self.n_most_frequent_states = None
+
         self.configure_tn_simulation()
         self.setup_backend_specifics(
             quimb_backend=quimb_backend, contractions_optimizer=contraction_optimizer
@@ -53,8 +59,9 @@ if not __name__ == "__main__":
 
     def configure_tn_simulation(
         self,
-        ansatz: str = None,
-        max_bond_dimension: int = 10,
+        ansatz: str = "mps",
+        max_bond_dimension: Optional[int] = None,
+        cutoff: Optional[float] = 1e-10,
         n_most_frequent_states: int = 100,
     ):
         """
@@ -73,8 +80,15 @@ if not __name__ == "__main__":
         """
         self.ansatz = ansatz
         self.max_bond_dimension = max_bond_dimension
+        self.cutoff = cutoff
         self.n_most_frequent_states = n_most_frequent_states
 
+    @property
+    def circuit_ansatz(self):
+        if self.ansatz == "mps":
+            return qtn.CircuitMPS
+        return qtn.Circuit
+
     def setup_backend_specifics(
         self, quimb_backend="numpy", contractions_optimizer="auto-hq"
     ):
@@ -152,10 +166,7 @@ if not __name__ == "__main__":
                 ValueError, "Initial state not None supported only for MPS ansatz."
             )
 
-        circ_ansatz = (
-            qtn.circuit.CircuitMPS if self.ansatz == "MPS" else qtn.circuit.Circuit
-        )
-        circ_quimb = circ_ansatz.from_openqasm2_str(
+        circ_quimb = self.circuit_ansatz.from_openqasm2_str(
             circuit.to_qasm(), psi0=initial_state
         )
 
@@ -218,9 +229,9 @@ if not __name__ == "__main__":
             The real part of the expectation value of the Hamiltonian on the given circuit state.
         """
         quimb_circuit = self._qibo_circuit_to_quimb(
-            circuit, 
-            quimb_circuit_type=qtn.CircuitMPS if self.ansatz == "MPS" else qtn.Circuit, 
-            gate_opts={"max_bond": self.max_bond_dimension},
+            circuit,
+            quimb_circuit_type=self.circuit_ansatz,
+            gate_opts={"max_bond": self.max_bond_dimension, "cutoff": self.cutoff},
         )
 
         expectation_value = 0.0
@@ -322,6 +333,7 @@ def QuimbBackend(
         "expectation_observable_symbolic_from_state": expectation_observable_symbolic_from_state,
         "_qibo_circuit_to_quimb": _qibo_circuit_to_quimb,
         "_string_to_quimb_operator": _string_to_quimb_operator,
+        "circuit_ansatz": circuit_ansatz,
     }
     if quimb_backend == "numpy":
         from qibo.backends import NumpyBackend

From 06079169ecc98f1b175534da01a2b4eee11db0ea Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Wed, 1 Oct 2025 16:26:48 +0200
Subject: [PATCH 25/33] fix: removed commented breakpoint

---
 src/qibotn/backends/quimb.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 756d994..331c6f7 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -314,7 +314,6 @@ if not __name__ == "__main__":
             The corresponding Quimb operator.
         """
         op_str = op_str.lower()
-        # breakpoint()
         op = qu.pauli(op_str[0])
         for c in op_str[1:]:
             op = op & qu.pauli(c)

From 2787d45b415a0ee4828347b1be303cbbab81829f Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Wed, 1 Oct 2025 17:48:05 +0200
Subject: [PATCH 26/33] fix: renamed cutoff

---
 src/qibotn/backends/quimb.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 331c6f7..667d4fe 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -49,7 +49,7 @@ if not __name__ == "__main__":
 
         self.ansatz = None
         self.max_bond_dimension = None
-        self.cutoff = None
+        self.svd_cutoff = None
         self.n_most_frequent_states = None
 
         self.configure_tn_simulation()
@@ -61,7 +61,7 @@ if not __name__ == "__main__":
         self,
         ansatz: str = "mps",
         max_bond_dimension: Optional[int] = None,
-        cutoff: Optional[float] = 1e-10,
+        svd_cutoff: Optional[float] = 1e-10,
         n_most_frequent_states: int = 100,
     ):
         """
@@ -80,7 +80,7 @@ if not __name__ == "__main__":
         """
         self.ansatz = ansatz
         self.max_bond_dimension = max_bond_dimension
-        self.cutoff = cutoff
+        self.svd_cutoff = svd_cutoff
         self.n_most_frequent_states = n_most_frequent_states
 
     @property
@@ -231,7 +231,7 @@ if not __name__ == "__main__":
         quimb_circuit = self._qibo_circuit_to_quimb(
             circuit,
             quimb_circuit_type=self.circuit_ansatz,
-            gate_opts={"max_bond": self.max_bond_dimension, "cutoff": self.cutoff},
+            gate_opts={"max_bond": self.max_bond_dimension, "cutoff": self.svd_cutoff},
         )
 
         expectation_value = 0.0

From 29ab783cce77e7958686f131731f6e9b7379b08d Mon Sep 17 00:00:00 2001
From: Mattia Robbiano <mattiarobbiano@gmail.com>
Date: Mon, 20 Oct 2025 18:13:51 +0300
Subject: [PATCH 27/33] chore: updated function name

---
 src/qibotn/backends/quimb.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 667d4fe..020951b 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -203,7 +203,7 @@ if not __name__ == "__main__":
             statevector=statevector,
         )
 
-    def expectation_observable_symbolic_from_state(
+    def expectation_observable_symbolic(
         self, circuit, operators_list, sites_list, coeffs_list, nqubits
     ):
         """

From 3be4ffcbfeb4458e1ddca444d1354164fddf13b1 Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Mon, 20 Oct 2025 17:41:49 +0200
Subject: [PATCH 28/33] build: lock update

---
 data/in/backend.json                |   10 +
 data/in/checkpoints.json            |    5 +
 data/in/convergence_parameters.json |    6 +
 data/in/io_info.json                |    5 +
 data/out/temp.pklmps                |  Bin 0 -> 1423 bytes
 poetry.lock                         | 1458 ++++++++++++++-------------
 6 files changed, 802 insertions(+), 682 deletions(-)
 create mode 100644 data/in/backend.json
 create mode 100644 data/in/checkpoints.json
 create mode 100644 data/in/convergence_parameters.json
 create mode 100644 data/in/io_info.json
 create mode 100644 data/out/temp.pklmps

diff --git a/data/in/backend.json b/data/in/backend.json
new file mode 100644
index 0000000..466a7f0
--- /dev/null
+++ b/data/in/backend.json
@@ -0,0 +1,10 @@
+{
+    "device": "cpu",
+    "precision": "Z",
+    "num_procs": 1,
+    "ansatz": "MPS",
+    "mpi_approach": "SR",
+    "mpi_command": [
+        "mpiexec"
+    ]
+}
diff --git a/data/in/checkpoints.json b/data/in/checkpoints.json
new file mode 100644
index 0000000..6d367ed
--- /dev/null
+++ b/data/in/checkpoints.json
@@ -0,0 +1,5 @@
+{
+    "checkpoint_PATH": "data/checkpoints/",
+    "checkpoint_frequency": -1,
+    "initial_line": 1
+}
diff --git a/data/in/convergence_parameters.json b/data/in/convergence_parameters.json
new file mode 100644
index 0000000..ebdcb22
--- /dev/null
+++ b/data/in/convergence_parameters.json
@@ -0,0 +1,6 @@
+{
+    "max_bond_dimension": 10,
+    "cut_ratio": 1e-09,
+    "trunc_tracking_mode": "C",
+    "svd_ctrl": "A"
+}
diff --git a/data/in/io_info.json b/data/in/io_info.json
new file mode 100644
index 0000000..e82eccb
--- /dev/null
+++ b/data/in/io_info.json
@@ -0,0 +1,5 @@
+{
+    "inPATH": "data/in/",
+    "outPATH": "data/out/",
+    "initial_state": "Vacuum"
+}
diff --git a/data/out/temp.pklmps b/data/out/temp.pklmps
new file mode 100644
index 0000000000000000000000000000000000000000..1776bd61adcf2466d92be56d4d886b64cafb6ce6
GIT binary patch
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literal 0
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diff --git a/poetry.lock b/poetry.lock
index 41fb100..4da7ea1 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -14,14 +14,14 @@ files = [
 
 [[package]]
 name = "alembic"
-version = "1.16.5"
+version = "1.17.0"
 description = "A database migration tool for SQLAlchemy."
 optional = false
-python-versions = ">=3.9"
+python-versions = ">=3.10"
 groups = ["main"]
 files = [
-    {file = "alembic-1.16.5-py3-none-any.whl", hash = "sha256:e845dfe090c5ffa7b92593ae6687c5cb1a101e91fa53868497dbd79847f9dbe3"},
-    {file = "alembic-1.16.5.tar.gz", hash = "sha256:a88bb7f6e513bd4301ecf4c7f2206fe93f9913f9b48dac3b78babde2d6fe765e"},
+    {file = "alembic-1.17.0-py3-none-any.whl", hash = "sha256:80523bc437d41b35c5db7e525ad9d908f79de65c27d6a5a5eab6df348a352d99"},
+    {file = "alembic-1.17.0.tar.gz", hash = "sha256:4652a0b3e19616b57d652b82bfa5e38bf5dbea0813eed971612671cb9e90c0fe"},
 ]
 
 [package.dependencies]
@@ -128,103 +128,137 @@ lxml = ["lxml"]
 
 [[package]]
 name = "certifi"
-version = "2025.8.3"
+version = "2025.10.5"
 description = "Python package for providing Mozilla's CA Bundle."
 optional = false
 python-versions = ">=3.7"
 groups = ["docs"]
 files = [
-    {file = "certifi-2025.8.3-py3-none-any.whl", hash = "sha256:f6c12493cfb1b06ba2ff328595af9350c65d6644968e5d3a2ffd78699af217a5"},
-    {file = "certifi-2025.8.3.tar.gz", hash = "sha256:e564105f78ded564e3ae7c923924435e1daa7463faeab5bb932bc53ffae63407"},
+    {file = "certifi-2025.10.5-py3-none-any.whl", hash = "sha256:0f212c2744a9bb6de0c56639a6f68afe01ecd92d91f14ae897c4fe7bbeeef0de"},
+    {file = "certifi-2025.10.5.tar.gz", hash = "sha256:47c09d31ccf2acf0be3f701ea53595ee7e0b8fa08801c6624be771df09ae7b43"},
 ]
 
 [[package]]
 name = "charset-normalizer"
-version = "3.4.3"
+version = "3.4.4"
 description = "The Real First Universal Charset Detector. Open, modern and actively maintained alternative to Chardet."
 optional = false
 python-versions = ">=3.7"
 groups = ["docs"]
 files = [
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 [[package]]
@@ -261,14 +295,14 @@ markers = {main = "sys_platform == \"win32\" or platform_system == \"Windows\"",
 
 [[package]]
 name = "colorlog"
-version = "6.9.0"
+version = "6.10.1"
 description = "Add colours to the output of Python's logging module."
 optional = false
 python-versions = ">=3.6"
 groups = ["main"]
 files = [
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 [package.dependencies]
@@ -391,116 +425,104 @@ test = ["altair", "baytune", "chocolate", "cmaes", "dask", "distributed", "kahyp
 
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 name = "coverage"
-version = "7.10.7"
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 [package.extras]
@@ -644,119 +666,193 @@ tests = ["pytest", "pytest-cov", "pytest-xdist"]
 
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 name = "decorator"
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 [package.dependencies]
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 [package.extras]
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 [package.dependencies]
@@ -1591,7 +1701,7 @@ kiwisolver = ">=1.3.1"
 numpy = ">=1.23"
 packaging = ">=20.0"
 pillow = ">=8"
-pyparsing = ">=2.3.1"
+pyparsing = ">=3"
 python-dateutil = ">=2.7"
 
 [package.extras]
@@ -1700,86 +1810,86 @@ numpy = ">=1.22,<2.4"
 
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-typing = ["typing-extensions ; python_version < \"3.10\""]
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-type = ["mypy (>=1.14.1)"]
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+type = ["mypy (>=1.18.2)"]
 
 [[package]]
 name = "pluggy"
@@ -2049,25 +2143,25 @@ wcwidth = "*"
 
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 [[package]]
@@ -2151,14 +2245,14 @@ windows-terminal = ["colorama (>=0.4.6)"]
 
 [[package]]
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+version = "3.3.9"
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 [package.dependencies]
@@ -2235,21 +2329,21 @@ testing = ["fields", "hunter", "process-tests", "pytest-xdist", "six", "virtuale
 
 [[package]]
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+testing = ["covdefaults (>=2.3)", "coverage (>=7.10.7)", "pytest-mock (>=3.15.1)"]
 
 [[package]]
 name = "python-dateutil"
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 type = "git"
 url = "https://github.com/qiboteam/qibo"
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-resolved_reference = "41b52af8faba1974c776a074fc0aba3461aeb6fe"
+resolved_reference = "a4771911b7ac2b9a911bf63ed60eadbfc1ff5b7a"
 
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 python-versions = ">=3.9"
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+    {file = "sqlalchemy-2.0.44.tar.gz", hash = "sha256:0ae7454e1ab1d780aee69fd2aae7d6b8670a581d8847f2d1e0f7ddfbf47e5a22"},
 ]
 
 [package.dependencies]
-greenlet = {version = ">=1", markers = "python_version < \"3.14\" and (platform_machine == \"aarch64\" or platform_machine == \"ppc64le\" or platform_machine == \"x86_64\" or platform_machine == \"amd64\" or platform_machine == \"AMD64\" or platform_machine == \"win32\" or platform_machine == \"WIN32\")"}
+greenlet = {version = ">=1", markers = "platform_machine == \"aarch64\" or platform_machine == \"ppc64le\" or platform_machine == \"x86_64\" or platform_machine == \"amd64\" or platform_machine == \"AMD64\" or platform_machine == \"win32\" or platform_machine == \"WIN32\""}
 typing-extensions = ">=4.6.0"
 
 [package.extras]
@@ -3120,14 +3214,14 @@ files = [
 
 [[package]]
 name = "toolz"
-version = "1.0.0"
+version = "1.1.0"
 description = "List processing tools and functional utilities"
 optional = false
-python-versions = ">=3.8"
+python-versions = ">=3.9"
 groups = ["main"]
 files = [
-    {file = "toolz-1.0.0-py3-none-any.whl", hash = "sha256:292c8f1c4e7516bf9086f8850935c799a874039c8bcf959d47b600e4c44a6236"},
-    {file = "toolz-1.0.0.tar.gz", hash = "sha256:2c86e3d9a04798ac556793bced838816296a2f085017664e4995cb40a1047a02"},
+    {file = "toolz-1.1.0-py3-none-any.whl", hash = "sha256:15ccc861ac51c53696de0a5d6d4607f99c210739caf987b5d2054f3efed429d8"},
+    {file = "toolz-1.1.0.tar.gz", hash = "sha256:27a5c770d068c110d9ed9323f24f1543e83b2f300a687b7891c1a6d56b697b5b"},
 ]
 
 [[package]]

From 451470f1cb9f58370d9711e9cce269bdf1567e01 Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Mon, 20 Oct 2025 17:42:25 +0200
Subject: [PATCH 29/33] fix: removed data

---
 data/in/backend.json                |  10 ----------
 data/in/checkpoints.json            |   5 -----
 data/in/convergence_parameters.json |   6 ------
 data/in/io_info.json                |   5 -----
 data/out/temp.pklmps                | Bin 1423 -> 0 bytes
 5 files changed, 26 deletions(-)
 delete mode 100644 data/in/backend.json
 delete mode 100644 data/in/checkpoints.json
 delete mode 100644 data/in/convergence_parameters.json
 delete mode 100644 data/in/io_info.json
 delete mode 100644 data/out/temp.pklmps

diff --git a/data/in/backend.json b/data/in/backend.json
deleted file mode 100644
index 466a7f0..0000000
--- a/data/in/backend.json
+++ /dev/null
@@ -1,10 +0,0 @@
-{
-    "device": "cpu",
-    "precision": "Z",
-    "num_procs": 1,
-    "ansatz": "MPS",
-    "mpi_approach": "SR",
-    "mpi_command": [
-        "mpiexec"
-    ]
-}
diff --git a/data/in/checkpoints.json b/data/in/checkpoints.json
deleted file mode 100644
index 6d367ed..0000000
--- a/data/in/checkpoints.json
+++ /dev/null
@@ -1,5 +0,0 @@
-{
-    "checkpoint_PATH": "data/checkpoints/",
-    "checkpoint_frequency": -1,
-    "initial_line": 1
-}
diff --git a/data/in/convergence_parameters.json b/data/in/convergence_parameters.json
deleted file mode 100644
index ebdcb22..0000000
--- a/data/in/convergence_parameters.json
+++ /dev/null
@@ -1,6 +0,0 @@
-{
-    "max_bond_dimension": 10,
-    "cut_ratio": 1e-09,
-    "trunc_tracking_mode": "C",
-    "svd_ctrl": "A"
-}
diff --git a/data/in/io_info.json b/data/in/io_info.json
deleted file mode 100644
index e82eccb..0000000
--- a/data/in/io_info.json
+++ /dev/null
@@ -1,5 +0,0 @@
-{
-    "inPATH": "data/in/",
-    "outPATH": "data/out/",
-    "initial_state": "Vacuum"
-}
diff --git a/data/out/temp.pklmps b/data/out/temp.pklmps
deleted file mode 100644
index 1776bd61adcf2466d92be56d4d886b64cafb6ce6..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

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From b9fe8618484194d192f89be312e38855510e4e30 Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Mon, 20 Oct 2025 18:26:08 +0200
Subject: [PATCH 30/33] fix: small fix

---
 src/qibotn/backends/quimb.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 020951b..276b4b9 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -329,7 +329,7 @@ def QuimbBackend(
         "configure_tn_simulation": configure_tn_simulation,
         "setup_backend_specifics": setup_backend_specifics,
         "execute_circuit": execute_circuit,
-        "expectation_observable_symbolic_from_state": expectation_observable_symbolic_from_state,
+        "expectation_observable_symbolic": expectation_observable_symbolic,
         "_qibo_circuit_to_quimb": _qibo_circuit_to_quimb,
         "_string_to_quimb_operator": _string_to_quimb_operator,
         "circuit_ansatz": circuit_ansatz,

From 7ea8dc861b13178ba8218ebe4c6a6ede03d76408 Mon Sep 17 00:00:00 2001
From: BrunoLiegiBastonLiegi <andreapapaluca@gmail.com>
Date: Mon, 27 Oct 2025 16:25:38 +0100
Subject: [PATCH 31/33] feat: changed backend generation mechanism + updated
 tutorial

---
 examples/quimb_intro/quimb_introduction.ipynb | 216 ++++---
 src/qibotn/backends/__init__.py               |   5 +-
 src/qibotn/backends/quimb.py                  | 580 +++++++++---------
 3 files changed, 419 insertions(+), 382 deletions(-)

diff --git a/examples/quimb_intro/quimb_introduction.ipynb b/examples/quimb_intro/quimb_introduction.ipynb
index 70fdf45..1e043ac 100644
--- a/examples/quimb_intro/quimb_introduction.ipynb
+++ b/examples/quimb_intro/quimb_introduction.ipynb
@@ -67,7 +67,7 @@
     "# set numpy random seed\n",
     "np.random.seed(42)\n",
     "\n",
-    "quimb_backend.setup_backend_specifics(qimb_backend=\"jax\")"
+    "quimb_backend.setup_backend_specifics(quimb_backend=\"jax\")"
    ]
   },
   {
@@ -180,12 +180,10 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/home/mattia/main_env/lib/python3.12/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: creg\n",
+      "/home/andrea/python_envs/3.11/lib/python3.11/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: creg\n",
       "  warnings.warn(\n",
-      "/home/mattia/main_env/lib/python3.12/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: measure\n",
-      "  warnings.warn(\n",
-      "/home/mattia/main_env/lib/python3.12/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
-      "  from .autonotebook import tqdm as notebook_tqdm\n"
+      "/home/andrea/python_envs/3.11/lib/python3.11/site-packages/quimb/tensor/circuit.py:215: SyntaxWarning: Unsupported operation ignored: measure\n",
+      "  warnings.warn(\n"
      ]
     },
     {
@@ -193,49 +191,53 @@
       "text/plain": [
        "{'nqubits': 4,\n",
        " 'backend': qibotn (quimb),\n",
-       " 'measures': Counter({'1010': 9,\n",
-       "          '0100': 8,\n",
-       "          '1101': 15,\n",
-       "          '1011': 4,\n",
-       "          '1111': 12,\n",
-       "          '1000': 13,\n",
+       " 'measures': Counter({'1101': 14,\n",
+       "          '1000': 12,\n",
+       "          '0010': 11,\n",
+       "          '0011': 11,\n",
+       "          '0110': 9,\n",
        "          '0000': 8,\n",
-       "          '0010': 6,\n",
-       "          '0011': 6,\n",
-       "          '0101': 8,\n",
-       "          '1110': 5,\n",
-       "          '0110': 5,\n",
-       "          '0111': 1}),\n",
-       " 'measured_probabilities': {'1101': np.float64(0.12331159869893256),\n",
-       "  '1000': np.float64(0.11330883548333587),\n",
-       "  '1111': np.float64(0.10184806171791962),\n",
-       "  '1010': np.float64(0.03872758515126756),\n",
-       "  '0100': np.float64(0.07142939529687138),\n",
-       "  '0000': np.float64(0.08390937969317269),\n",
-       "  '0101': np.float64(0.05622305772698622),\n",
-       "  '0010': np.float64(0.09466860481989385),\n",
-       "  '0011': np.float64(0.07571277233522114),\n",
-       "  '1110': np.float64(0.07174919872959985),\n",
-       "  '0110': np.float64(0.05146064807369214),\n",
-       "  '1011': np.float64(0.053499396925872744),\n",
-       "  '0111': np.float64(0.04029185074729259)},\n",
+       "          '1010': 7,\n",
+       "          '1110': 6,\n",
+       "          '0100': 5,\n",
+       "          '1111': 5,\n",
+       "          '1011': 5,\n",
+       "          '0101': 4,\n",
+       "          '0111': 1,\n",
+       "          '0001': 1,\n",
+       "          '1100': 1}),\n",
+       " 'measured_probabilities': {'1101': np.float64(0.12331159869893284),\n",
+       "  '1000': np.float64(0.11330883548333684),\n",
+       "  '0010': np.float64(0.0946686048198943),\n",
+       "  '0011': np.float64(0.07571277233522157),\n",
+       "  '0110': np.float64(0.051460648073692314),\n",
+       "  '0000': np.float64(0.08390937969317334),\n",
+       "  '1010': np.float64(0.03872758515126775),\n",
+       "  '1110': np.float64(0.07174919872960006),\n",
+       "  '0100': np.float64(0.07142939529687146),\n",
+       "  '1111': np.float64(0.10184806171791994),\n",
+       "  '1011': np.float64(0.053499396925872716),\n",
+       "  '0101': np.float64(0.05622305772698606),\n",
+       "  '0111': np.float64(0.040291850747292815),\n",
+       "  '0001': np.float64(0.004677011195208322),\n",
+       "  '1100': np.float64(0.013605984872668443)},\n",
        " 'prob_type': 'default',\n",
-       " 'statevector': Array([[ 0.08809624-0.27594998j],\n",
-       "        [-0.05174781+0.04471217j],\n",
-       "        [ 0.00470147+0.30764672j],\n",
-       "        [-0.27208942+0.0409893j ],\n",
-       "        [ 0.18807822+0.18988408j],\n",
-       "        [ 0.2237706 +0.07842042j],\n",
-       "        [-0.18900308+0.12545314j],\n",
-       "        [ 0.17105256-0.10503749j],\n",
-       "        [ 0.24859734-0.22695419j],\n",
-       "        [-0.0411739 -0.06230037j],\n",
-       "        [ 0.17371392-0.09247189j],\n",
-       "        [-0.22748128+0.0418529j ],\n",
-       "        [ 0.09444095+0.06846087j],\n",
-       "        [-0.21784972-0.2754144j ],\n",
-       "        [-0.17359753+0.20399286j],\n",
-       "        [-0.01729754-0.31866732j]], dtype=complex64)}"
+       " 'statevector': Array([[ 0.08809626-0.27595j   ],\n",
+       "        [-0.05174781+0.04471214j],\n",
+       "        [ 0.00470146+0.30764672j],\n",
+       "        [-0.27208942+0.04098931j],\n",
+       "        [ 0.18807825+0.1898841j ],\n",
+       "        [ 0.22377063+0.07842041j],\n",
+       "        [-0.18900302+0.12545316j],\n",
+       "        [ 0.17105258-0.10503745j],\n",
+       "        [ 0.24859732-0.22695422j],\n",
+       "        [-0.04117391-0.0623003j ],\n",
+       "        [ 0.17371394-0.09247189j],\n",
+       "        [-0.22748126+0.04185291j],\n",
+       "        [ 0.09444097+0.06846087j],\n",
+       "        [-0.21784975-0.2754144j ],\n",
+       "        [-0.17359754+0.20399287j],\n",
+       "        [-0.01729751-0.31866732j]], dtype=complex64)}"
       ]
      },
      "execution_count": 8,
@@ -272,25 +274,25 @@
      "output_type": "stream",
      "text": [
       "Probabilities:\n",
-      " {'1101': np.float64(0.12331159869893256), '1000': np.float64(0.11330883548333587), '1111': np.float64(0.10184806171791962), '1010': np.float64(0.03872758515126756), '0100': np.float64(0.07142939529687138), '0000': np.float64(0.08390937969317269), '0101': np.float64(0.05622305772698622), '0010': np.float64(0.09466860481989385), '0011': np.float64(0.07571277233522114), '1110': np.float64(0.07174919872959985), '0110': np.float64(0.05146064807369214), '1011': np.float64(0.053499396925872744), '0111': np.float64(0.04029185074729259)}\n",
+      " {'1101': np.float64(0.12331159869893284), '1000': np.float64(0.11330883548333684), '0010': np.float64(0.0946686048198943), '0011': np.float64(0.07571277233522157), '0110': np.float64(0.051460648073692314), '0000': np.float64(0.08390937969317334), '1010': np.float64(0.03872758515126775), '1110': np.float64(0.07174919872960006), '0100': np.float64(0.07142939529687146), '1111': np.float64(0.10184806171791994), '1011': np.float64(0.053499396925872716), '0101': np.float64(0.05622305772698606), '0111': np.float64(0.040291850747292815), '0001': np.float64(0.004677011195208322), '1100': np.float64(0.013605984872668443)}\n",
       "\n",
       "State:\n",
-      " [[ 0.08809624-0.27594998j]\n",
-      " [-0.05174781+0.04471217j]\n",
-      " [ 0.00470147+0.30764672j]\n",
-      " [-0.27208942+0.0409893j ]\n",
-      " [ 0.18807822+0.18988408j]\n",
-      " [ 0.2237706 +0.07842042j]\n",
-      " [-0.18900308+0.12545314j]\n",
-      " [ 0.17105256-0.10503749j]\n",
-      " [ 0.24859734-0.22695419j]\n",
-      " [-0.0411739 -0.06230037j]\n",
-      " [ 0.17371392-0.09247189j]\n",
-      " [-0.22748128+0.0418529j ]\n",
-      " [ 0.09444095+0.06846087j]\n",
-      " [-0.21784972-0.2754144j ]\n",
-      " [-0.17359753+0.20399286j]\n",
-      " [-0.01729754-0.31866732j]]\n",
+      " [[ 0.08809626-0.27595j   ]\n",
+      " [-0.05174781+0.04471214j]\n",
+      " [ 0.00470146+0.30764672j]\n",
+      " [-0.27208942+0.04098931j]\n",
+      " [ 0.18807825+0.1898841j ]\n",
+      " [ 0.22377063+0.07842041j]\n",
+      " [-0.18900302+0.12545316j]\n",
+      " [ 0.17105258-0.10503745j]\n",
+      " [ 0.24859732-0.22695422j]\n",
+      " [-0.04117391-0.0623003j ]\n",
+      " [ 0.17371394-0.09247189j]\n",
+      " [-0.22748126+0.04185291j]\n",
+      " [ 0.09444097+0.06846087j]\n",
+      " [-0.21784975-0.2754144j ]\n",
+      " [-0.17359754+0.20399287j]\n",
+      " [-0.01729751-0.31866732j]]\n",
       "\n"
      ]
     }
@@ -338,7 +340,7 @@
     "quimb_backend = construct_backend(backend=\"qibotn\", platform=\"quimb\")\n",
     "\n",
     "quimb_backend.setup_backend_specifics(\n",
-    "    qimb_backend    =\"jax\", \n",
+    "    quimb_backend    =\"jax\", \n",
     "    contractions_optimizer='auto-hq'\n",
     "    )\n",
     "\n",
@@ -349,21 +351,21 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 18,
    "id": "b2a0decb",
    "metadata": {},
    "outputs": [],
    "source": [
+    "from qibo.symbols import X, Z, Y\n",
+    "from qibo.hamiltonians import XXZ\n",
+    "\n",
     "# define Hamiltonian\n",
-    "operators = [\"xzy\", \"yxzy\", \"zy\"]\n",
-    "qubits = [\"011\", \"0112\", \"01\"]\n",
-    "coefficients = [\"1\", \"2\", \"j\"]\n",
-    "hamiltonian = (operators, qubits, coefficients)"
+    "hamiltonian = XXZ(4, dense=False, backend=quimb_backend)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "id": "bd734be8",
    "metadata": {},
    "outputs": [],
@@ -407,19 +409,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Expectation value: 0.0\n",
-      "Elapsed time: 0.1071 seconds\n"
+      "Expectation value: 2.0\n",
+      "Elapsed time: 0.0268 seconds\n"
      ]
     }
    ],
    "source": [
     "start = time.time()\n",
-    "expval = quimb_backend.expectation(\n",
-    "        circuit=circuit,\n",
-    "        operators_list=hamiltonian[0],\n",
-    "        sites_list=hamiltonian[1],\n",
-    "        coeffs_list=hamiltonian[2]\n",
-    "    )\n",
+    "expval = hamiltonian.expectation(circuit)\n",
     "\n",
     "elapsed = time.time() - start\n",
     "print(f\"Expectation value: {expval}\")\n",
@@ -436,24 +433,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 21,
    "id": "fb1436c8",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "[Qibo 0.2.21|INFO|2025-10-27 16:24:00]: Using numpy backend on /CPU:0\n",
+      "WARNING:root:Calculation of expectation values starting from the state is deprecated, use the ``expectation_from_state`` method if you really need it, or simply pass the circuit you want to calculate the expectation value from.\n"
+     ]
+    },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Expectation value: 1.5\n",
-      "Elapsed time: 0.0501 seconds\n"
+      "Expectation value: 2.0\n",
+      "Elapsed time: 0.0360 seconds\n"
      ]
     }
    ],
    "source": [
-    "from qibo.symbols import Z, X, I\n",
-    "# We can create a symbolic Hamiltonian\n",
-    "form = 0.5 * Z(0) * Z(1) +- 1.5 *  X(0) * Z(2) + Z(3)\n",
-    "sym_hamiltonian = hamiltonians.SymbolicHamiltonian(form)\n",
+    "sym_hamiltonian = XXZ(4, dense=False, backend=None)\n",
     "\n",
     "#  Let's show it\n",
     "sym_hamiltonian.form\n",
@@ -488,40 +490,52 @@
    "id": "6a3b26e4",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/andrea/python_envs/3.11/lib/python3.11/site-packages/quimb/tensor/circuit.py:4927: UserWarning: Unsupported options for computing local_expectation with an MPS circuit supplied, ignoring: R, None, None, jax, None\n",
+      "  warnings.warn(\n",
+      "/home/andrea/python_envs/3.11/lib/python3.11/site-packages/quimb/tensor/circuit.py:4927: UserWarning: Unsupported options for computing local_expectation with an MPS circuit supplied, ignoring: R, None, None, jax, None\n",
+      "  warnings.warn(\n"
+     ]
+    },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 8.19939339e-10 -3.14190913e-08 -2.99498648e-09 -1.03641796e-07\n",
-      "  8.48652704e-10  1.00297093e-07 -6.75429277e-08 -9.78565140e-09\n",
-      " -5.11915417e-08  1.29225235e-08 -7.44280655e-08 -3.49115048e-08\n",
-      " -4.98508879e-09  6.80729357e-08 -3.29755920e-08  4.20008526e-08\n",
-      " -2.89742630e-08  1.18602941e-07 -2.88252178e-08  5.57985391e-09\n",
-      " -3.17434115e-08 -1.03342952e-08  1.34079716e-08 -7.05437886e-09\n",
-      " -4.34059650e-08 -2.18019203e-08 -5.36932561e-08 -6.38544009e-08\n",
-      "  5.85312279e-08  8.45709067e-08 -1.12777876e-09 -6.41545981e-08\n",
-      "  7.25317406e-08  4.10035668e-08 -1.29046382e-08  6.07501676e-08]\n"
+      "[-0.24630009  0.8370421  -0.11103702 -0.12855841  0.41325414 -0.0628037\n",
+      "  0.51638705  0.794163   -0.27972788 -1.0718998   0.02731732  1.0153619\n",
+      " -0.34494495  1.5744264   0.26920277 -0.36333832  0.12331417  0.5196531\n",
+      "  1.1294655   0.29257926 -0.18237355  0.8914014  -0.9471657   0.3492473\n",
+      " -0.3477673   0.24325958  0.04818404 -0.87983793  0.47196424  0.36605012\n",
+      "  1.005       0.65054715 -0.94860053  0.14459445  0.36571163 -0.2550101 ]\n"
      ]
     }
    ],
    "source": [
     "def f(circuit, hamiltonian, params):\n",
     "    circuit.set_parameters(params)\n",
-    "    return quimb_backend.expectation(\n",
+    "    return hamiltonian.expectation(\n",
     "        circuit=circuit,\n",
-    "        operators_list=hamiltonian[0],\n",
-    "        sites_list=hamiltonian[1],\n",
-    "        coeffs_list=hamiltonian[2]\n",
     "    )\n",
     "\n",
     "parameters = np.random.uniform(-np.pi, np.pi, size=len(circuit.get_parameters()))\n",
     "print(jax.grad(f, argnums=2)(circuit, hamiltonian, parameters))\n"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "aeafa5a6-2afa-429c-a101-effa84bac1d2",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "main_env",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -535,7 +549,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.3"
+   "version": "3.11.12"
   }
  },
  "nbformat": 4,
diff --git a/src/qibotn/backends/__init__.py b/src/qibotn/backends/__init__.py
index 4ec932c..b9d10a1 100644
--- a/src/qibotn/backends/__init__.py
+++ b/src/qibotn/backends/__init__.py
@@ -4,7 +4,6 @@ from qibo.config import raise_error
 
 from qibotn.backends.abstract import QibotnBackend
 from qibotn.backends.cutensornet import CuTensorNet  # pylint: disable=E0401
-from qibotn.backends.quimb import QuimbBackend
 
 PLATFORMS = ("cutensornet", "qutensornet", "qmatchatea")
 
@@ -26,9 +25,11 @@ class MetaBackend:
         if platform == "cutensornet":  # pragma: no cover
             return CuTensorNet(runcard)
         elif platform == "quimb":  # pragma: no cover
+            import qibotn.backends.quimb as qmb
+
             quimb_backend = kwargs.get("quimb_backend", "numpy")
             contraction_optimizer = kwargs.get("contraction_optimizer", "auto-hq")
-            return QuimbBackend(
+            return qmb.BACKENDS[quimb_backend](
                 quimb_backend=quimb_backend, contraction_optimizer=contraction_optimizer
             )
         elif platform == "qmatchatea":  # pragma: no cover
diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 276b4b9..d72361f 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -38,302 +38,306 @@ GATE_MAP = {
 }
 
 
-if not __name__ == "__main__":
+def __init__(self, quimb_backend="numpy", contraction_optimizer="auto-hq"):
+    super(self.__class__, self).__init__()
 
-    def __init__(self, quimb_backend="numpy", contraction_optimizer="auto-hq"):
-        super(self.__class__, self).__init__()
+    self.name = "qibotn"
+    self.platform = "quimb"
+    self.backend = quimb_backend
 
-        self.name = "qibotn"
-        self.platform = "quimb"
-        self.backend = quimb_backend
+    self.ansatz = None
+    self.max_bond_dimension = None
+    self.svd_cutoff = None
+    self.n_most_frequent_states = None
 
-        self.ansatz = None
-        self.max_bond_dimension = None
-        self.svd_cutoff = None
-        self.n_most_frequent_states = None
+    self.configure_tn_simulation()
+    self.setup_backend_specifics(
+        quimb_backend=quimb_backend, contractions_optimizer=contraction_optimizer
+    )
 
-        self.configure_tn_simulation()
-        self.setup_backend_specifics(
-            quimb_backend=quimb_backend, contractions_optimizer=contraction_optimizer
+
+def configure_tn_simulation(
+    self,
+    ansatz: str = "mps",
+    max_bond_dimension: Optional[int] = None,
+    svd_cutoff: Optional[float] = 1e-10,
+    n_most_frequent_states: int = 100,
+):
+    """
+    Configure tensor network simulation.
+
+    Args:
+        ansatz : str, optional
+            The tensor network ansatz to use. Default is `None` and, in this case, a
+            generic Circuit Quimb class is used.
+            max_bond_dimension : int, optional
+            The maximum bond dimension for the MPS ansatz. Default is 10.
+
+    Notes:
+        - The ansatz determines the tensor network structure used for simulation. Currently, only "MPS" is supported.
+        - The `max_bond_dimension` parameter controls the maximum allowed bond dimension for the MPS ansatz.
+    """
+    self.ansatz = ansatz
+    self.max_bond_dimension = max_bond_dimension
+    self.svd_cutoff = svd_cutoff
+    self.n_most_frequent_states = n_most_frequent_states
+
+
+@property
+def circuit_ansatz(self):
+    if self.ansatz == "mps":
+        return qtn.CircuitMPS
+    return qtn.Circuit
+
+
+def setup_backend_specifics(
+    self, quimb_backend="numpy", contractions_optimizer="auto-hq"
+):
+    """Setup backend specifics.
+    Args:
+        quimb_backend: str
+            The backend to use for the quimb tensor network simulation.
+        contractions_optimizer: str, optional
+            The contractions_optimizer to use for the quimb tensor network simulation.
+    """
+    # this is not really working because it does not change the inheritance
+    if quimb_backend == "jax":
+        import jax.numpy as jnp
+
+        self.np = jnp
+    elif quimb_backend == "numpy":
+        import numpy as np
+
+        self.np = np
+    elif quimb_backend == "torch":
+        import torch
+
+        self.np = torch
+    else:
+        raise_error(ValueError, f"Unsupported quimb backend: {quimb_backend}")
+
+    self.backend = quimb_backend
+    self.contractions_optimizer = contractions_optimizer
+
+
+def execute_circuit(
+    self,
+    circuit: Circuit,
+    initial_state=None,
+    nshots=None,
+    return_array=False,
+):
+    """
+    Execute a quantum circuit using the specified tensor network ansatz and initial state.
+
+    Args:
+        circuit : QuantumCircuit
+            The quantum circuit to be executed.
+        initial_state : array-like, optional
+            The initial state of the quantum system. Only supported for Matrix Product States (MPS) ansatz.
+        nshots : int, optional
+            The number of shots for sampling the circuit. If None, no sampling is performed, and the full statevector is used.
+        return_array : bool, optional
+            If True, returns the statevector as a dense array. Default is False.
+
+    Returns:
+        TensorNetworkResult
+            An object containing the results of the circuit execution, including:
+            - nqubits: Number of qubits in the circuit.
+            - backend: The backend used for execution.
+            - measures: The measurement frequencies if nshots is specified, otherwise None.
+            - measured_probabilities: A dictionary of computational basis states and their probabilities.
+            - prob_type: The type of probability computation used (currently "default").
+            - statevector: The final statevector as a dense array if return_array is True, otherwise None.
+
+    Raises:
+        ValueError
+            If an initial state is provided but the ansatz is not "MPS".
+
+    Notes:
+        - The ansatz determines the tensor network structure used for simulation. Currently, only "MPS" is supported.
+        - If `initial_state` is provided, it must be compatible with the MPS ansatz.
+        - The `nshots` parameter enables sampling from the circuit's output distribution. If not specified, the full statevector is computed.
+    """
+    if initial_state is not None and self.ansatz == "MPS":
+        initial_state = qtn.tensor_1d.MatrixProductState.from_dense(
+            initial_state, 2
+        )  # 2 is the physical dimension
+    elif initial_state is not None:
+        raise_error(ValueError, "Initial state not None supported only for MPS ansatz.")
+
+    circ_quimb = self.circuit_ansatz.from_openqasm2_str(
+        circuit.to_qasm(), psi0=initial_state
+    )
+
+    if nshots:
+        frequencies = Counter(circ_quimb.sample(nshots))
+        main_frequencies = {
+            state: count
+            for state, count in frequencies.most_common(self.n_most_frequent_states)
+        }
+        computational_states = list(main_frequencies.keys())
+        amplitudes = {
+            state: circ_quimb.amplitude(state) for state in computational_states
+        }
+        measured_probabilities = {
+            state: abs(amplitude) ** 2 for state, amplitude in amplitudes.items()
+        }
+    else:
+        frequencies = None
+        measured_probabilities = None
+
+    statevector = (
+        circ_quimb.to_dense(backend=self.backend, optimize=self.contractions_optimizer)
+        if return_array
+        else None
+    )
+    return TensorNetworkResult(
+        nqubits=circuit.nqubits,
+        backend=self,
+        measures=frequencies,
+        measured_probabilities=measured_probabilities,
+        prob_type="default",
+        statevector=statevector,
+    )
+
+
+def expectation_observable_symbolic(
+    self, circuit, operators_list, sites_list, coeffs_list, nqubits
+):
+    """
+    Compute the expectation value of a symbolic Hamiltonian on a quantum circuit using tensor network contraction.
+    This method takes a Qibo circuit, converts it to a Quimb tensor network circuit, and evaluates the expectation value
+    of a Hamiltonian specified by three lists of strings: operators, sites, and coefficients.
+    The expectation value is computed by summing the contributions from each term in the Hamiltonian, where each term's
+    expectation is calculated using Quimb's `local_expectation` function.
+
+    Parameters
+    ----------
+    circuit : qibo.models.Circuit
+        The quantum circuit to evaluate, provided as a Qibo circuit object.
+    operators_list : list of str
+        List of operator strings representing the symbolic Hamiltonian terms.
+    sites_list : list of str
+        List of strings, each specifying the qubits (sites) the corresponding operator acts on.
+    coeffs_list : list of str
+        List of strings representing the coefficients for each Hamiltonian term.
+    Returns
+    -------
+    float
+        The real part of the expectation value of the Hamiltonian on the given circuit state.
+    """
+    quimb_circuit = self._qibo_circuit_to_quimb(
+        circuit,
+        quimb_circuit_type=self.circuit_ansatz,
+        gate_opts={"max_bond": self.max_bond_dimension, "cutoff": self.svd_cutoff},
+    )
+
+    expectation_value = 0.0
+    for opstr, sites, coeff in zip(operators_list, sites_list, coeffs_list):
+
+        ops = self._string_to_quimb_operator(opstr)
+        coeff = coeff.real
+
+        exp_values = quimb_circuit.local_expectation(
+            ops,
+            where=sites,
+            backend=self.backend,
+            optimize=self.contractions_optimizer,
+            simplify_sequence="R",
         )
 
-    def configure_tn_simulation(
-        self,
-        ansatz: str = "mps",
-        max_bond_dimension: Optional[int] = None,
-        svd_cutoff: Optional[float] = 1e-10,
-        n_most_frequent_states: int = 100,
-    ):
-        """
-        Configure tensor network simulation.
+        expectation_value = expectation_value + coeff * exp_values
 
-        Args:
-            ansatz : str, optional
-                The tensor network ansatz to use. Default is `None` and, in this case, a
-                generic Circuit Quimb class is used.
-                max_bond_dimension : int, optional
-                The maximum bond dimension for the MPS ansatz. Default is 10.
+    return self.np.real(expectation_value)
 
-        Notes:
-            - The ansatz determines the tensor network structure used for simulation. Currently, only "MPS" is supported.
-            - The `max_bond_dimension` parameter controls the maximum allowed bond dimension for the MPS ansatz.
-        """
-        self.ansatz = ansatz
-        self.max_bond_dimension = max_bond_dimension
-        self.svd_cutoff = svd_cutoff
-        self.n_most_frequent_states = n_most_frequent_states
 
-    @property
-    def circuit_ansatz(self):
-        if self.ansatz == "mps":
-            return qtn.CircuitMPS
-        return qtn.Circuit
+def _qibo_circuit_to_quimb(
+    self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs
+):
+    """
+    Convert a Qibo Circuit to a Quimb Circuit. Measurement gates are ignored. If are given gates not supported by Quimb, an error is raised.
 
-    def setup_backend_specifics(
-        self, quimb_backend="numpy", contractions_optimizer="auto-hq"
-    ):
-        """Setup backend specifics.
-        Args:
-            qimb_backend: str
-                The backend to use for the quimb tensor network simulation.
-            contractions_optimizer: str, optional
-                The contractions_optimizer to use for the quimb tensor network simulation.
-        """
-        # this is not really working because it does not change the inheritance
-        if quimb_backend == "jax":
-            import jax.numpy as jnp
+    Parameters
+    ----------
+    qibo_circ : qibo.models.circuit.Circuit
+        The circuit to convert.
+    quimb_circuit_type : type
+        The Quimb circuit class to use (Circuit, CircuitMPS, etc).
+    circuit_kwargs : dict
+        Extra arguments to pass to the Quimb circuit constructor.
 
-            self.np = jnp
-        elif quimb_backend == "numpy":
-            import numpy as np
+    Returns
+    -------
+    circ : quimb.tensor.circuit.Circuit
+        The converted circuit.
+    """
+    nqubits = qibo_circ.nqubits
+    circ = quimb_circuit_type(nqubits, **circuit_kwargs)
 
-            self.np = np
-        elif quimb_backend == "torch":
-            import torch
+    for gate in qibo_circ.queue:
+        gname = getattr(gate, "name", None)
+        qname = GATE_MAP.get(gname, None)
+        if qname == "measure":
+            continue
+        if qname is None:
+            raise_error(ValueError, f"Gate {gname} not supported in Quimb backend.")
 
-            self.np = torch
+        params = getattr(gate, "parameters", ())
+        qubits = getattr(gate, "qubits", ())
+
+        is_parametrized = isinstance(gate, ParametrizedGate) and getattr(
+            gate, "trainable", True
+        )
+        if is_parametrized:
+            circ.apply_gate(qname, *params, *qubits, parametrized=is_parametrized)
         else:
-            raise_error(ValueError, f"Unsupported quimb backend: {quimb_backend}")
-
-        self.backend = quimb_backend
-        self.contractions_optimizer = contractions_optimizer
-
-    def execute_circuit(
-        self,
-        circuit: Circuit,
-        initial_state=None,
-        nshots=None,
-        return_array=False,
-    ):
-        """
-        Execute a quantum circuit using the specified tensor network ansatz and initial state.
-
-        Args:
-            circuit : QuantumCircuit
-                The quantum circuit to be executed.
-            initial_state : array-like, optional
-                The initial state of the quantum system. Only supported for Matrix Product States (MPS) ansatz.
-            nshots : int, optional
-                The number of shots for sampling the circuit. If None, no sampling is performed, and the full statevector is used.
-            return_array : bool, optional
-                If True, returns the statevector as a dense array. Default is False.
-
-        Returns:
-            TensorNetworkResult
-                An object containing the results of the circuit execution, including:
-                - nqubits: Number of qubits in the circuit.
-                - backend: The backend used for execution.
-                - measures: The measurement frequencies if nshots is specified, otherwise None.
-                - measured_probabilities: A dictionary of computational basis states and their probabilities.
-                - prob_type: The type of probability computation used (currently "default").
-                - statevector: The final statevector as a dense array if return_array is True, otherwise None.
-
-        Raises:
-            ValueError
-                If an initial state is provided but the ansatz is not "MPS".
-
-        Notes:
-            - The ansatz determines the tensor network structure used for simulation. Currently, only "MPS" is supported.
-            - If `initial_state` is provided, it must be compatible with the MPS ansatz.
-            - The `nshots` parameter enables sampling from the circuit's output distribution. If not specified, the full statevector is computed.
-        """
-        if initial_state is not None and self.ansatz == "MPS":
-            initial_state = qtn.tensor_1d.MatrixProductState.from_dense(
-                initial_state, 2
-            )  # 2 is the physical dimension
-        elif initial_state is not None:
-            raise_error(
-                ValueError, "Initial state not None supported only for MPS ansatz."
+            circ.apply_gate(
+                qname,
+                *params,
+                *qubits,
             )
-
-        circ_quimb = self.circuit_ansatz.from_openqasm2_str(
-            circuit.to_qasm(), psi0=initial_state
-        )
-
-        if nshots:
-            frequencies = Counter(circ_quimb.sample(nshots))
-            main_frequencies = {
-                state: count
-                for state, count in frequencies.most_common(self.n_most_frequent_states)
-            }
-            computational_states = list(main_frequencies.keys())
-            amplitudes = {
-                state: circ_quimb.amplitude(state) for state in computational_states
-            }
-            measured_probabilities = {
-                state: abs(amplitude) ** 2 for state, amplitude in amplitudes.items()
-            }
-        else:
-            frequencies = None
-            measured_probabilities = None
-
-        statevector = (
-            circ_quimb.to_dense(
-                backend=self.backend, optimize=self.contractions_optimizer
-            )
-            if return_array
-            else None
-        )
-        return TensorNetworkResult(
-            nqubits=circuit.nqubits,
-            backend=self,
-            measures=frequencies,
-            measured_probabilities=measured_probabilities,
-            prob_type="default",
-            statevector=statevector,
-        )
-
-    def expectation_observable_symbolic(
-        self, circuit, operators_list, sites_list, coeffs_list, nqubits
-    ):
-        """
-        Compute the expectation value of a symbolic Hamiltonian on a quantum circuit using tensor network contraction.
-        This method takes a Qibo circuit, converts it to a Quimb tensor network circuit, and evaluates the expectation value
-        of a Hamiltonian specified by three lists of strings: operators, sites, and coefficients.
-        The expectation value is computed by summing the contributions from each term in the Hamiltonian, where each term's
-        expectation is calculated using Quimb's `local_expectation` function.
-
-        Parameters
-        ----------
-        circuit : qibo.models.Circuit
-            The quantum circuit to evaluate, provided as a Qibo circuit object.
-        operators_list : list of str
-            List of operator strings representing the symbolic Hamiltonian terms.
-        sites_list : list of str
-            List of strings, each specifying the qubits (sites) the corresponding operator acts on.
-        coeffs_list : list of str
-            List of strings representing the coefficients for each Hamiltonian term.
-        Returns
-        -------
-        float
-            The real part of the expectation value of the Hamiltonian on the given circuit state.
-        """
-        quimb_circuit = self._qibo_circuit_to_quimb(
-            circuit,
-            quimb_circuit_type=self.circuit_ansatz,
-            gate_opts={"max_bond": self.max_bond_dimension, "cutoff": self.svd_cutoff},
-        )
-
-        expectation_value = 0.0
-        for opstr, sites, coeff in zip(operators_list, sites_list, coeffs_list):
-
-            ops = self._string_to_quimb_operator(opstr)
-            coeff = coeff.real
-
-            exp_values = quimb_circuit.local_expectation(
-                ops,
-                where=sites,
-                backend=self.backend,
-                optimize=self.contractions_optimizer,
-                simplify_sequence="R",
-            )
-
-            expectation_value = expectation_value + coeff * exp_values
-
-        return self.np.real(expectation_value)
-
-    def _qibo_circuit_to_quimb(
-        self, qibo_circ, quimb_circuit_type=qtn.Circuit, **circuit_kwargs
-    ):
-        """
-        Convert a Qibo Circuit to a Quimb Circuit. Measurement gates are ignored. If are given gates not supported by Quimb, an error is raised.
-
-        Parameters
-        ----------
-        qibo_circ : qibo.models.circuit.Circuit
-            The circuit to convert.
-        quimb_circuit_type : type
-            The Quimb circuit class to use (Circuit, CircuitMPS, etc).
-        circuit_kwargs : dict
-            Extra arguments to pass to the Quimb circuit constructor.
-
-        Returns
-        -------
-        circ : quimb.tensor.circuit.Circuit
-            The converted circuit.
-        """
-        nqubits = qibo_circ.nqubits
-        circ = quimb_circuit_type(nqubits, **circuit_kwargs)
-
-        for gate in qibo_circ.queue:
-            gname = getattr(gate, "name", None)
-            qname = GATE_MAP.get(gname, None)
-            if qname == "measure":
-                continue
-            if qname is None:
-                raise_error(ValueError, f"Gate {gname} not supported in Quimb backend.")
-
-            params = getattr(gate, "parameters", ())
-            qubits = getattr(gate, "qubits", ())
-
-            is_parametrized = isinstance(gate, ParametrizedGate) and getattr(
-                gate, "trainable", True
-            )
-            if is_parametrized:
-                circ.apply_gate(qname, *params, *qubits, parametrized=is_parametrized)
-            else:
-                circ.apply_gate(
-                    qname,
-                    *params,
-                    *qubits,
-                )
-        return circ
-
-    def _string_to_quimb_operator(self, op_str):
-        """
-        Convert a Pauli string (e.g. 'xzy') to a Quimb operator using '&' chaining.
-
-        Parameters
-        ----------
-        op_str : str
-            A string like 'xzy', where each character is one of 'x', 'y', 'z', 'i'.
-
-        Returns
-        -------
-        qu_op : quimb.Qarray
-            The corresponding Quimb operator.
-        """
-        op_str = op_str.lower()
-        op = qu.pauli(op_str[0])
-        for c in op_str[1:]:
-            op = op & qu.pauli(c)
-        return op
+    return circ
 
 
-def QuimbBackend(
-    quimb_backend: str = "numpy", contraction_optimizer="auto-hq"
-) -> QibotnBackend:
+def _string_to_quimb_operator(self, op_str):
+    """
+    Convert a Pauli string (e.g. 'xzy') to a Quimb operator using '&' chaining.
+
+    Parameters
+    ----------
+    op_str : str
+        A string like 'xzy', where each character is one of 'x', 'y', 'z', 'i'.
+
+    Returns
+    -------
+    qu_op : quimb.Qarray
+        The corresponding Quimb operator.
+    """
+    op_str = op_str.lower()
+    op = qu.pauli(op_str[0])
+    for c in op_str[1:]:
+        op = op & qu.pauli(c)
+    return op
+
+
+CLASSES_ROOTS = {"numpy": "Numpy", "torch": "PyTorch", "jax": "Jax"}
+
+METHODS = {
+    "__init__": __init__,
+    "configure_tn_simulation": configure_tn_simulation,
+    "setup_backend_specifics": setup_backend_specifics,
+    "execute_circuit": execute_circuit,
+    "expectation_observable_symbolic": expectation_observable_symbolic,
+    "_qibo_circuit_to_quimb": _qibo_circuit_to_quimb,
+    "_string_to_quimb_operator": _string_to_quimb_operator,
+    "circuit_ansatz": circuit_ansatz,
+}
+
+
+def _generate_backend(quimb_backend: str = "numpy"):
     bases = (QibotnBackend,)
-    methods = {
-        "__init__": __init__,
-        "configure_tn_simulation": configure_tn_simulation,
-        "setup_backend_specifics": setup_backend_specifics,
-        "execute_circuit": execute_circuit,
-        "expectation_observable_symbolic": expectation_observable_symbolic,
-        "_qibo_circuit_to_quimb": _qibo_circuit_to_quimb,
-        "_string_to_quimb_operator": _string_to_quimb_operator,
-        "circuit_ansatz": circuit_ansatz,
-    }
+
     if quimb_backend == "numpy":
         from qibo.backends import NumpyBackend
 
@@ -349,4 +353,22 @@ def QuimbBackend(
     else:
         raise_error(ValueError, f"Unsupported quimb backend: {quimb_backend}")
 
-    return type("QuimbBackend", bases, methods)(quimb_backend, contraction_optimizer)
+    return type(f"Quimb{CLASSES_ROOTS[quimb_backend]}Backend", bases, METHODS)
+
+
+BACKENDS = {}
+for k, v in CLASSES_ROOTS.items():
+    backend_name = f"Quimb{v}Backend"
+    try:
+        backend = _generate_backend(k)
+        BACKENDS[k] = backend
+        globals()[backend_name] = backend
+    except ImportError:
+        continue
+
+
+def __getattr__(name):
+    try:
+        return BACKENDS[name]
+    except KeyError:
+        raise AttributeError(f"module {__name__!r} has no attribute {name!r}") from None

From d4ab3eba52950f09111038d5388a045c9f8d55b4 Mon Sep 17 00:00:00 2001
From: mattia-robbiano <mattiarobbiano@gmail.com>
Date: Thu, 13 Nov 2025 10:45:32 +0200
Subject: [PATCH 32/33] minor improvements to examples, documentation,
 internally used variable names

---
 examples/quimb_intro/quimb_introduction.ipynb | 55 ++++++++++++-------
 src/qibotn/backends/quimb.py                  | 37 ++++++++-----
 2 files changed, 59 insertions(+), 33 deletions(-)

diff --git a/examples/quimb_intro/quimb_introduction.ipynb b/examples/quimb_intro/quimb_introduction.ipynb
index 1e043ac..5eaacc4 100644
--- a/examples/quimb_intro/quimb_introduction.ipynb
+++ b/examples/quimb_intro/quimb_introduction.ipynb
@@ -28,7 +28,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a009a5e0-cfd4-4a49-9f7c-e82f252c6147",
+   "id": "0c5a8939",
    "metadata": {},
    "source": [
     "#### Some hyper parameters"
@@ -36,24 +36,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
-   "id": "b0a1da82",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import cotengra as ctg\n",
-    "ctg_opt = ctg.ReusableHyperOptimizer(\n",
-    "    max_time=10,\n",
-    "    minimize='combo',\n",
-    "    slicing_opts=None,\n",
-    "    parallel=True,\n",
-    "    progbar=True\n",
-    ")\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "id": "64162116-1555-4a68-811c-01593739d622",
    "metadata": {},
    "outputs": [],
@@ -67,7 +50,39 @@
     "# set numpy random seed\n",
     "np.random.seed(42)\n",
     "\n",
-    "quimb_backend.setup_backend_specifics(quimb_backend=\"jax\")"
+    "quimb_backend.setup_backend_specifics(quimb_backend=\"jax\", contractions_optimizer='auto-hq')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "926cfea5",
+   "metadata": {},
+   "source": [
+    "Quimb accepts different methods for optimizing the way it does contractions, that we pass through \"contractions_optimizer\". \n",
+    "We could also define our own cotengra contraction optimizer! \n",
+    "\n",
+    "cotengra is a Python library designed for **optimising contraction trees** and performing efficient contractions of large tensor‐networks.\n",
+    "You can find it here: [https://github.com/jcmgray/cotengra](https://github.com/jcmgray/cotengra)\n",
+    "\n",
+    "For the sake of this tutorial however the default \"auto-hq\" will be fine :) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b0a1da82",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import cotengra as ctg\n",
+    "ctg_opt = ctg.ReusableHyperOptimizer(\n",
+    "    max_time=10,\n",
+    "    minimize='combo',\n",
+    "    slicing_opts=None,\n",
+    "    parallel=True,\n",
+    "    progbar=True\n",
+    ")\n",
+    "# quimb_backend.setup_backend_specifics(quimb_backend=\"jax\", contractions_optimizer='ctg_opt')"
    ]
   },
   {
diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index d72361f..21d54ec 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -20,7 +20,7 @@ GATE_MAP = {
     "rx": "RX",
     "ry": "RY",
     "rz": "RZ",
-    "u3": "U3",  # TODO: check
+    "u3": "U3",
     "cx": "CX",
     "cnot": "CNOT",
     "cy": "CY",
@@ -210,7 +210,10 @@ def expectation_observable_symbolic(
     This method takes a Qibo circuit, converts it to a Quimb tensor network circuit, and evaluates the expectation value
     of a Hamiltonian specified by three lists of strings: operators, sites, and coefficients.
     The expectation value is computed by summing the contributions from each term in the Hamiltonian, where each term's
-    expectation is calculated using Quimb's `local_expectation` function.
+    expectation is calculated using Quimb's `local_expectation` function.         
+    Each operator string must act on all different qubits, i.e., for each term, the corresponding sites tuple must contain unique qubit indices.
+    Example: operators_list = ['xyz', 'xyz'], sites_list = [(1,2,3), (1,2,3)], coeffs_list = [1, 2]
+
 
     Parameters
     ----------
@@ -218,15 +221,23 @@ def expectation_observable_symbolic(
         The quantum circuit to evaluate, provided as a Qibo circuit object.
     operators_list : list of str
         List of operator strings representing the symbolic Hamiltonian terms.
-    sites_list : list of str
-        List of strings, each specifying the qubits (sites) the corresponding operator acts on.
-    coeffs_list : list of str
-        List of strings representing the coefficients for each Hamiltonian term.
+    sites_list : list of tuple of int
+        Tuples each specifying the qubits (sites) the corresponding operator acts on.
+    coeffs_list : list of real/complex
+        The coefficients for each Hamiltonian term.
     Returns
     -------
     float
         The real part of the expectation value of the Hamiltonian on the given circuit state.
     """
+    # Validate that no term acts multiple times on the same qubit (no repeated indices in a sites tuple)
+    for sites in sites_list:
+        if len(sites) != len(set(sites)):
+            raise_error(
+                ValueError,
+                f"Invalid Hamiltonian term sites {sites}: repeated qubit indices are not allowed "
+                "within a single term (e.g. (0,0,0) is invalid).",
+            )
     quimb_circuit = self._qibo_circuit_to_quimb(
         circuit,
         quimb_circuit_type=self.circuit_ansatz,
@@ -276,12 +287,12 @@ def _qibo_circuit_to_quimb(
     circ = quimb_circuit_type(nqubits, **circuit_kwargs)
 
     for gate in qibo_circ.queue:
-        gname = getattr(gate, "name", None)
-        qname = GATE_MAP.get(gname, None)
-        if qname == "measure":
+        gate_name = getattr(gate, "name", None)
+        quimb_gate_name = GATE_MAP.get(gate_name, None)
+        if quimb_gate_name == "measure":
             continue
-        if qname is None:
-            raise_error(ValueError, f"Gate {gname} not supported in Quimb backend.")
+        if quimb_gate_name is None:
+            raise_error(ValueError, f"Gate {gate_name} not supported in Quimb backend.")
 
         params = getattr(gate, "parameters", ())
         qubits = getattr(gate, "qubits", ())
@@ -290,10 +301,10 @@ def _qibo_circuit_to_quimb(
             gate, "trainable", True
         )
         if is_parametrized:
-            circ.apply_gate(qname, *params, *qubits, parametrized=is_parametrized)
+            circ.apply_gate(quimb_gate_name, *params, *qubits, parametrized=is_parametrized)
         else:
             circ.apply_gate(
-                qname,
+                quimb_gate_name,
                 *params,
                 *qubits,
             )

From 24f25d813c27018466c136c615b52967d5a10586 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 13 Nov 2025 08:45:53 +0000
Subject: [PATCH 33/33] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 src/qibotn/backends/quimb.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/qibotn/backends/quimb.py b/src/qibotn/backends/quimb.py
index 21d54ec..b2199d7 100644
--- a/src/qibotn/backends/quimb.py
+++ b/src/qibotn/backends/quimb.py
@@ -210,7 +210,7 @@ def expectation_observable_symbolic(
     This method takes a Qibo circuit, converts it to a Quimb tensor network circuit, and evaluates the expectation value
     of a Hamiltonian specified by three lists of strings: operators, sites, and coefficients.
     The expectation value is computed by summing the contributions from each term in the Hamiltonian, where each term's
-    expectation is calculated using Quimb's `local_expectation` function.         
+    expectation is calculated using Quimb's `local_expectation` function.
     Each operator string must act on all different qubits, i.e., for each term, the corresponding sites tuple must contain unique qubit indices.
     Example: operators_list = ['xyz', 'xyz'], sites_list = [(1,2,3), (1,2,3)], coeffs_list = [1, 2]
 
@@ -301,7 +301,9 @@ def _qibo_circuit_to_quimb(
             gate, "trainable", True
         )
         if is_parametrized:
-            circ.apply_gate(quimb_gate_name, *params, *qubits, parametrized=is_parametrized)
+            circ.apply_gate(
+                quimb_gate_name, *params, *qubits, parametrized=is_parametrized
+            )
         else:
             circ.apply_gate(
                 quimb_gate_name,