804 lines
71 KiB
Plaintext
804 lines
71 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "656bb283-ac6d-48d2-a029-3c417c9961f8",
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"metadata": {},
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"source": [
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"## Introduction to Quantum Matcha Tea backend in QiboTN\n",
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"\n",
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"#### Some imports"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"id": "6722d94e-e311-48f9-b6df-c6d829bf67fb",
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"metadata": {},
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"outputs": [],
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"source": [
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"import time\n",
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"import numpy as np\n",
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"from scipy import stats\n",
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"\n",
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"import qibo\n",
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"from qibo import Circuit, gates, hamiltonians\n",
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"from qibo.backends import construct_backend\n",
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"\n",
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"from qmatchatea import QCConvergenceParameters"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a009a5e0-cfd4-4a49-9f7c-e82f252c6147",
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"metadata": {},
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"source": [
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"#### Some hyper parameters"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"id": "64162116-1555-4a68-811c-01593739d622",
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"metadata": {},
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"outputs": [],
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"source": [
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"# construct qibotn backend\n",
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"qmatcha_backend = construct_backend(backend=\"qibotn\", platform=\"qmatchatea\")\n",
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"\n",
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"# set number of qubits\n",
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"nqubits = 4\n",
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"\n",
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"# set numpy random seed\n",
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"np.random.seed(42)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "252f5cd1-5932-4de6-8076-4a357d50ebad",
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"metadata": {},
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"source": [
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"#### Constructing a parametric quantum circuit"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"id": "4a22a172-f50d-411d-afa3-fa61937c7b3a",
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"metadata": {},
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"outputs": [],
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"source": [
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"def build_circuit(nqubits, nlayers):\n",
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" \"\"\"Construct a parametric quantum circuit.\"\"\"\n",
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" circ = Circuit(nqubits)\n",
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" for _ in range(nlayers):\n",
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" for q in range(nqubits):\n",
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" circ.add(gates.RY(q=q, theta=0.))\n",
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" circ.add(gates.RZ(q=q, theta=0.))\n",
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" [circ.add(gates.CNOT(q%nqubits, (q+1)%nqubits) for q in range(nqubits))]\n",
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" circ.add(gates.M(*range(nqubits)))\n",
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" return circ"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"id": "76f23c57-6d08-496b-9a27-52fb63bbfcb1",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0: ─RY─RZ─o─────X─RY─RZ─o─────X─RY─RZ─o─────X─M─\n",
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"1: ─RY─RZ─X─o───|─RY─RZ─X─o───|─RY─RZ─X─o───|─M─\n",
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"2: ─RY─RZ───X─o─|─RY─RZ───X─o─|─RY─RZ───X─o─|─M─\n",
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"3: ─RY─RZ─────X─o─RY─RZ─────X─o─RY─RZ─────X─o─M─\n"
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]
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}
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],
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"source": [
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"circuit = build_circuit(nqubits=nqubits, nlayers=3)\n",
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"circuit.draw()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"id": "07b2c097-cea2-42ec-8f1d-b4bbb5b71d98",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Setting random parameters\n",
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"circuit.set_parameters(\n",
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" parameters=np.random.uniform(-np.pi, np.pi, len(circuit.get_parameters())),\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fd0cea52-03f5-4366-a01a-a5a84aa8ebc7",
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"metadata": {},
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"source": [
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"#### Setting up the tensor network simulator\n",
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"\n",
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"Depending on the simulator, various parameters can be set. In the case of Quantum Matcha, we direclty exploit the `qmatchatea` interface and we construct a `QCConvergenceParameters` object (for more info [this is the link to the qmatchatea code](https://baltig.infn.it/quantum_matcha_tea/py_api_quantum_matcha_tea/-/blob/master/qmatchatea/utils/utils.py?ref_type=heads#L540))."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"id": "34452bfd-2287-4b38-8099-e072239eab74",
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"metadata": {},
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"outputs": [],
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"source": [
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"# We first define the useful objects \n",
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"convergence_parameters = QCConvergenceParameters(cut_ratio=1e-6, max_bond_dimension=50)\n",
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"\n",
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"# And then call the dedicate configuration function\n",
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"qmatcha_backend.configure_tn_simulation(\n",
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" convergence_params=convergence_parameters,\n",
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" ansatz=\"MPS\",\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "648d85b8-445d-4081-aeed-1691fbae67be",
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"metadata": {},
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"source": [
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"#### Executing through the backend\n",
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"\n",
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"The `backend.execute_circuit` method can be used then. We can simulate results in three ways:\n",
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"1. reconstruction of the final state (statevector like, only if `nqubits < 20` due to Quantum Matcha Tea setup);\n",
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"2. computation of the relevant probabilities of the final state. There are three way of doing so, but we will see it directly into the docstrings;\n",
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"3. reconstruction of the relevant state's frequencies (only if `nshots` is not `None`)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "221ef886-5578-4200-a019-dcafa51aada3",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"\u001b[0;31mSignature:\u001b[0m\n",
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"\u001b[0mqmatcha_backend\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexecute_circuit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
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"\u001b[0;34m\u001b[0m \u001b[0mcircuit\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
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"\u001b[0;34m\u001b[0m \u001b[0minitial_state\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
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"\u001b[0;34m\u001b[0m \u001b[0mnshots\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
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"\u001b[0;34m\u001b[0m \u001b[0mprob_type\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
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"\u001b[0;34m\u001b[0m \u001b[0mreturn_array\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
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"\u001b[0;34m\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mprob_kwargs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
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"\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mDocstring:\u001b[0m\n",
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"Execute a Qibo quantum circuit using tensor network simulation.\n",
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"\n",
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"This method returns a ``TensorNetworkResult`` object, which provides:\n",
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" - Reconstruction of the system state (if the system size is < 20).\n",
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" - Frequencies (if the number of shots is specified).\n",
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" - Probabilities computed using various methods.\n",
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"\n",
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"The following probability computation methods are available, as implemented\n",
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"in Quantum Matcha Tea:\n",
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" - **\"E\" (Even):** Probabilities are computed by evenly descending the probability tree,\n",
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" pruning branches (states) with probabilities below a threshold.\n",
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" - **\"G\" (Greedy):** Probabilities are computed by following the most probable states\n",
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" in descending order until reaching a given coverage (sum of probabilities).\n",
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" - **\"U\" (Unbiased):** An optimal probability measure that is unbiased and designed\n",
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" for best performance. See https://arxiv.org/abs/2401.10330 for details.\n",
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"\n",
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"Args:\n",
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" circuit: A Qibo circuit to execute.\n",
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" initial_state: The initial state of the system (default is the vacuum state\n",
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" for tensor network simulations).\n",
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" nshots: The number of shots for shot-noise simulation (optional).\n",
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" prob_type: The probability computation method. Must be one of:\n",
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" - \"E\" (Even)\n",
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" - \"G\" (Greedy)\n",
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" - \"U\" (Unbiased) [default].\n",
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" prob_kwargs: Additional parameters required for probability computation:\n",
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" - For \"U\", requires ``num_samples``.\n",
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" - For \"E\" and \"G\", requires ``prob_threshold``.\n",
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"\n",
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"Returns:\n",
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" TensorNetworkResult: An object with methods to reconstruct the state,\n",
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" compute probabilities, and generate frequencies.\n",
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"\u001b[0;31mFile:\u001b[0m ~/Documents/PhD/qibotn/src/qibotn/backends/qmatchatea.py\n",
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"\u001b[0;31mType:\u001b[0m method\n"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"qmatcha_backend.execute_circuit?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"id": "f271d3f3-c7f2-49b3-94e2-d6e843a169d0",
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"metadata": {},
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"outputs": [],
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"source": [
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"circuit = build_circuit(nqubits=4, nlayers=2)\n",
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"\n",
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"# Setting random parameters\n",
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"circuit.set_parameters(\n",
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" parameters=np.random.uniform(-np.pi, np.pi, len(circuit.get_parameters())),\n",
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")\n",
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"\n",
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"# We first define the useful objects \n",
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"convergence_parameters = QCConvergenceParameters(cut_ratio=1e-12, max_bond_dimension=1100)\n",
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"\n",
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"# And then call the dedicate configuration function\n",
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"qmatcha_backend.configure_tn_simulation(\n",
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" convergence_params=convergence_parameters,\n",
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" ansatz=\"MPS\",\n",
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")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"id": "35a244c3-adba-4b8b-b28c-0ab592b0f7cf",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{'nqubits': 4,\n",
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" 'backend': QMatchaTeaBackend(),\n",
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" 'measures': None,\n",
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" 'measured_probabilities': {'U': {'0000': (0.0, 0.06042361322153613),\n",
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" '0001': (0.06042361322153613, 0.16103484648184754),\n",
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" '0010': (0.1610348464818476, 0.3885436985884956),\n",
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" '0011': (0.3885436985884956, 0.4596882048691001),\n",
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" '0100': (0.4596882048691, 0.46449216980829905),\n",
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" '0101': (0.46449216980829905, 0.47672801247815266),\n",
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" '0110': (0.47672801247815266, 0.5016979158974251),\n",
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" '0111': (0.5016979158974251, 0.5398303779135739),\n",
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" '1000': (0.539830377913574, 0.6539396910265846),\n",
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" '1001': (0.6539396910265846, 0.7584098289087688),\n",
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" '1010': (0.7584098289087688, 0.7781986778747929),\n",
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" '1011': (0.7781986778747929, 0.8661307878495997),\n",
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" '1100': (0.8661307878495996, 0.8908084103632258),\n",
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" '1101': (0.8908084103632258, 0.9107085647613623),\n",
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" '1110': (0.9107085647613623, 0.9481703292728131),\n",
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" '1111': (0.9481703292728131, 0.9999999999999999)},\n",
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" 'E': [None],\n",
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" 'G': [None]},\n",
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" 'prob_type': 'U',\n",
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" 'statevector': array([-0.13931487-0.20252155j, -0.21974897+0.25655351j,\n",
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" 0.02884164-0.06302479j, -0.15237615+0.03819857j,\n",
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" -0.3172761 -0.35615268j, -0.10121749+0.09769272j,\n",
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" 0.14826026-0.0546699j , -0.1814861 -0.06726486j,\n",
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" -0.10907416+0.29784906j, 0.30276076+0.11316387j,\n",
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" 0.07771728+0.07871383j, -0.12379363+0.0676409j ,\n",
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" -0.21860099+0.15283362j, 0.06862868+0.28848261j,\n",
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" -0.04640848-0.18968056j, -0.22262942-0.04760056j])}"
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]
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},
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"execution_count": 23,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Simple execution (defaults)\n",
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"outcome = qmatcha_backend.execute_circuit(circuit=circuit, return_array=True)\n",
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"\n",
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"# Print outcome\n",
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"vars(outcome)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"id": "60501c3d-2a44-421f-b434-4a508714b132",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{'nqubits': 4,\n",
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" 'backend': QMatchaTeaBackend(),\n",
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" 'measures': None,\n",
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" 'measured_probabilities': {'U': [None],\n",
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" 'E': [None],\n",
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" 'G': {'0010': 0.227508852106648,\n",
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" '0011': 0.07114450628060452,\n",
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" '1000': 0.227508852106648,\n",
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" '1001': 0.07114450628060452,\n",
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" '0000': 0.06042361322153613,\n",
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" '0001': 0.1006112332603114}},\n",
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" 'prob_type': 'G',\n",
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" 'statevector': array([-0.13931487-0.20252155j, -0.21974897+0.25655351j,\n",
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" 0.02884164-0.06302479j, -0.15237615+0.03819857j,\n",
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" -0.3172761 -0.35615268j, -0.10121749+0.09769272j,\n",
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" 0.14826026-0.0546699j , -0.1814861 -0.06726486j,\n",
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" -0.10907416+0.29784906j, 0.30276076+0.11316387j,\n",
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" 0.07771728+0.07871383j, -0.12379363+0.0676409j ,\n",
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" -0.21860099+0.15283362j, 0.06862868+0.28848261j,\n",
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" -0.04640848-0.18968056j, -0.22262942-0.04760056j])}"
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]
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},
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"execution_count": 26,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
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"# Execution with a specific probability type\n",
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"# We use here \"E\", which is cutting some of the components if under a threshold\n",
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"outcome = qmatcha_backend.execute_circuit(\n",
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" circuit=circuit,\n",
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" prob_type=\"G\",\n",
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" prob_threshold=0.9,\n",
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" return_array=True,\n",
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")\n",
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"\n",
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"# Print outcome\n",
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"vars(outcome)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "84ec0b48-f6b4-495c-93b8-8e42d1a8b0df",
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"metadata": {},
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"source": [
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"---\n",
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"\n",
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"One can access to the specific contents of the simulation outcome."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"id": "c0443efc-21ef-4ed5-9cf4-785d204a1881",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Probabilities:\n",
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" [0.22750885 0.07114451 0.22750885 0.07114451 0.06042361 0.10061123]\n",
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"\n",
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"State:\n",
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" [-0.13931487-0.20252155j -0.21974897+0.25655351j 0.02884164-0.06302479j\n",
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" -0.15237615+0.03819857j -0.3172761 -0.35615268j -0.10121749+0.09769272j\n",
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" 0.14826026-0.0546699j -0.1814861 -0.06726486j -0.10907416+0.29784906j\n",
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" 0.30276076+0.11316387j 0.07771728+0.07871383j -0.12379363+0.0676409j\n",
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" -0.21860099+0.15283362j 0.06862868+0.28848261j -0.04640848-0.18968056j\n",
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" -0.22262942-0.04760056j]\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(f\"Probabilities:\\n {outcome.probabilities()}\\n\")\n",
|
|
"print(f\"State:\\n {outcome.state()}\\n\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9f477388-ca45-409a-a0ce-6603ec294e42",
|
|
"metadata": {},
|
|
"source": [
|
|
"---\n",
|
|
"\n",
|
|
"But frequencies cannot be accessed, since no shots have been set."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 28,
|
|
"id": "8a868f3e-8383-47ee-a93a-27c5f85e48c5",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# print(f\"Frequencies:\\n {outcome.frequencies()}\\n\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "8e9413c7-602a-44ed-a50c-1c3dd4dd7494",
|
|
"metadata": {},
|
|
"source": [
|
|
"---\n",
|
|
"\n",
|
|
"We can then repeat the execution by setting the number of shots"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 29,
|
|
"id": "68122cd3-662f-4fd1-bb9c-d33b6f5448dd",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"{'nqubits': 4,\n",
|
|
" 'backend': QMatchaTeaBackend(),\n",
|
|
" 'measures': {'0000': 75,\n",
|
|
" '0001': 113,\n",
|
|
" '0010': 202,\n",
|
|
" '0011': 59,\n",
|
|
" '0100': 9,\n",
|
|
" '0101': 14,\n",
|
|
" '0110': 30,\n",
|
|
" '0111': 37,\n",
|
|
" '1000': 130,\n",
|
|
" '1001': 113,\n",
|
|
" '1010': 19,\n",
|
|
" '1011': 95,\n",
|
|
" '1100': 19,\n",
|
|
" '1101': 26,\n",
|
|
" '1110': 39,\n",
|
|
" '1111': 44},\n",
|
|
" 'measured_probabilities': {'U': [None],\n",
|
|
" 'E': {'0000': 0.06042361322153613,\n",
|
|
" '0001': 0.1006112332603114,\n",
|
|
" '0010': 0.227508852106648,\n",
|
|
" '0011': 0.07114450628060452,\n",
|
|
" '1000': 0.11410931311301056,\n",
|
|
" '1001': 0.10447013788218423,\n",
|
|
" '1011': 0.08793210997480687,\n",
|
|
" '1111': 0.05182967072718676},\n",
|
|
" 'G': [None]},\n",
|
|
" 'prob_type': 'E',\n",
|
|
" 'statevector': None}"
|
|
]
|
|
},
|
|
"execution_count": 29,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Execution with a specific probability type\n",
|
|
"# We use here \"E\", which is cutting some of the components if under a threshold\n",
|
|
"outcome = qmatcha_backend.execute_circuit(\n",
|
|
" circuit=circuit,\n",
|
|
" nshots=1024,\n",
|
|
" prob_type=\"E\",\n",
|
|
" prob_threshold=0.05,\n",
|
|
")\n",
|
|
"\n",
|
|
"# Print outcome\n",
|
|
"vars(outcome)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 30,
|
|
"id": "ef0e9591-ccca-4cdd-a81b-2bfb3caaf3d0",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Frequencies:\n",
|
|
" {'0000': 75, '0001': 113, '0010': 202, '0011': 59, '0100': 9, '0101': 14, '0110': 30, '0111': 37, '1000': 130, '1001': 113, '1010': 19, '1011': 95, '1100': 19, '1101': 26, '1110': 39, '1111': 44}\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# And then finally access frequencies!\n",
|
|
"print(f\"Frequencies:\\n {outcome.frequencies()}\\n\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "7fe725ff-533e-4648-9f8d-9cb6c0826354",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Testing the performances"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 31,
|
|
"id": "9e9632d5-28dd-4846-8457-c579d0cb9453",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"qmatcha_range = range(2, 100, 2)\n",
|
|
"qibojit_threshold = 28\n",
|
|
"qibojit_range = range(2, qibojit_threshold, 2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "4e6b1126-32ab-418d-b760-44ff62048f70",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"qmatcha_times, qmatcha_errs = [], []\n",
|
|
"qibojit_times, qibojit_errs = [], []\n",
|
|
"\n",
|
|
"qibojit_backend = construct_backend(\"qibojit\", platform=\"numba\")\n",
|
|
"qibo.set_threads(2)\n",
|
|
"\n",
|
|
"\n",
|
|
"for q in qmatcha_range:\n",
|
|
" print(f\"Executing for {q} qubits\")\n",
|
|
" # Build the circuit\n",
|
|
" circuit = build_circuit(q, 1)\n",
|
|
"\n",
|
|
" reasonable_exp = min(13, int(q / 2))\n",
|
|
" \n",
|
|
" qmatcha_backend.configure_tn_simulation(\n",
|
|
" convergence_params=QCConvergenceParameters(max_bond_dimension=2**reasonable_exp),\n",
|
|
" ansatz=\"MPS\"\n",
|
|
" )\n",
|
|
"\n",
|
|
" tmp_qmatcha_times, tmp_qibojit_times = [], [] \n",
|
|
" for i in range(20):\n",
|
|
" # Set random parameters\n",
|
|
" circuit.set_parameters(parameters=np.random.uniform(-np.pi, np.pi, len(circuit.get_parameters())))\n",
|
|
" \n",
|
|
" # Measure QMatcha execution time\n",
|
|
" print(f\"1. ---- QMatcha\") if i == 0 else None\n",
|
|
" start_time = time.time()\n",
|
|
" outcome = qmatcha_backend.execute_circuit(circuit=circuit)\n",
|
|
" tmp_qmatcha_times.append(time.time() - start_time)\n",
|
|
"\n",
|
|
" if q < qibojit_threshold:\n",
|
|
" \n",
|
|
" if i == 0:\n",
|
|
" outcome = qibojit_backend.execute_circuit(circuit=circuit)\n",
|
|
" \n",
|
|
" # Measure Qibojit execution time\n",
|
|
" print(f\"2. ---- Qibojit\") if i == 0 else None\n",
|
|
" start_time = time.time()\n",
|
|
" outcome = qibojit_backend.execute_circuit(circuit=circuit)\n",
|
|
" tmp_qibojit_times.append(time.time() - start_time)\n",
|
|
" \n",
|
|
" qmatcha_times.append(np.median(tmp_qmatcha_times))\n",
|
|
" qmatcha_errs.append(stats.median_abs_deviation(tmp_qmatcha_times))\n",
|
|
" \n",
|
|
" if q < qibojit_threshold:\n",
|
|
" qibojit_times.append(np.median(tmp_qibojit_times))\n",
|
|
" qibojit_errs.append(stats.median_abs_deviation(tmp_qibojit_times))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 32,
|
|
"id": "5620f476-1bc7-4cf8-9868-b127c715b6ec",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Saving data\n",
|
|
"# np.save(arr=qmatcha_times, file=\"qmatcha_times\")\n",
|
|
"# np.save(arr=qibojit_times, file=\"qibojit_times\")\n",
|
|
"# np.save(arr=qmatcha_errs, file=\"qmatcha_errs\")\n",
|
|
"# np.save(arr=qibojit_errs, file=\"qibojit_errs\")\n",
|
|
"\n",
|
|
"qmatcha_times = np.load(\"qmatcha_times.npy\")\n",
|
|
"qmatcha_errs = np.load(\"qmatcha_errs.npy\")\n",
|
|
"qibojit_times = np.load(\"qibojit_times.npy\")\n",
|
|
"qibojit_errs = np.load(\"qibojit_errs.npy\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 33,
|
|
"id": "32d605e9-672a-40b6-8a1a-eb17bbc3c45e",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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\n",
|
|
"text/plain": [
|
|
"<Figure size 600x450 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"plt.figure(figsize=(6, 6 * 6/8))\n",
|
|
"plt.title(\"Simple test of CPU 12th Gen Intel® Core™ i7-1260P\")\n",
|
|
"plt.errorbar(qmatcha_range, qmatcha_times, yerr=qmatcha_errs, marker=\"o\", color=\"red\", label=\"QMatcha-numpy\", alpha=0.7)\n",
|
|
"plt.errorbar(qibojit_range, qibojit_times, yerr=qibojit_errs, marker=\"o\", color=\"blue\", label=\"Qibojit-numba\", alpha=0.7)\n",
|
|
"plt.legend()\n",
|
|
"plt.xlabel(\"Qubits\")\n",
|
|
"plt.ylabel(\"Time [s]\")\n",
|
|
"plt.grid(True)\n",
|
|
"plt.yscale(\"log\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "dd84f1f3-7aa5-4ad1-ae09-81e0aff75b5b",
|
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"metadata": {},
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"source": [
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"### Compute expectation values"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 34,
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"id": "0b46e315-7786-4247-bd2a-83ea1c5842eb",
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"metadata": {},
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"outputs": [],
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"source": [
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"from qibo.symbols import Z, X"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"id": "37385485-e8a3-4ab0-ad44-bcc4e9da24ca",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0: ─RY─RZ─o─────X─RY─RZ─o─────X─M─\n",
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"1: ─RY─RZ─X─o───|─RY─RZ─X─o───|─M─\n",
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"2: ─RY─RZ───X─o─|─RY─RZ───X─o─|─M─\n",
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"3: ─RY─RZ─────X─o─RY─RZ─────X─o─M─\n"
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]
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}
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],
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"source": [
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"# We are going to compute the expval of an Hamiltonian\n",
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"# On the state prepared by the following circuit\n",
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"circuit.draw()\n",
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"\n",
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"circuit.set_parameters(\n",
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" np.random.randn(len(circuit.get_parameters()))\n",
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")"
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]
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},
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{
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"cell_type": "code",
|
|
"execution_count": 36,
|
|
"id": "ddecc910-7804-4199-8577-a7db38a16db8",
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"metadata": {},
|
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"outputs": [],
|
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"source": [
|
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"# We can create an Hamiltonian form\n",
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"form = 0.5 * Z(0) * Z(1) +- 1.5 * X(0) * Z(2) + Z(3)\n",
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"hamiltonian = hamiltonians.SymbolicHamiltonian(form)"
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]
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|
},
|
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{
|
|
"cell_type": "code",
|
|
"execution_count": 37,
|
|
"id": "a6599df3-989e-4131-8664-3451d0cc4372",
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"metadata": {},
|
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"outputs": [
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{
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"data": {
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|
"text/plain": [
|
|
"\u001b[0;31mSignature:\u001b[0m \u001b[0mqmatcha_backend\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpectation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcircuit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mobservable\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mDocstring:\u001b[0m\n",
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"Compute the expectation value of a Qibo-friendly ``observable`` on\n",
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|
"the Tensor Network constructed from a Qibo ``circuit``.\n",
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|
"\n",
|
|
"This method takes a Qibo-style symbolic Hamiltonian (e.g., `X(0)*Z(1) + 2.0*Y(2)*Z(0)`)\n",
|
|
"as the observable, converts it into a Quantum Matcha Tea (qmatchatea) observable\n",
|
|
"(using `TNObsTensorProduct` and `TNObsWeightedSum`), and computes its expectation\n",
|
|
"value using the provided circuit.\n",
|
|
"\n",
|
|
"Args:\n",
|
|
" circuit: A Qibo quantum circuit object on which the expectation value\n",
|
|
" is computed. The circuit should be compatible with the qmatchatea\n",
|
|
" Tensor Network backend.\n",
|
|
" observable: The observable whose expectation value we want to compute.\n",
|
|
" This must be provided in the symbolic Hamiltonian form supported by Qibo\n",
|
|
" (e.g., `X(0)*Y(1)` or `Z(0)*Z(1) + 1.5*Y(2)`).\n",
|
|
"\n",
|
|
"Returns:\n",
|
|
" qibotn.TensorNetworkResult class, providing methods to retrieve\n",
|
|
" probabilities, frequencies and state always according to the chosen\n",
|
|
" simulation setup.\n",
|
|
"\u001b[0;31mFile:\u001b[0m ~/Documents/PhD/qibotn/src/qibotn/backends/qmatchatea.py\n",
|
|
"\u001b[0;31mType:\u001b[0m method\n"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"qmatcha_backend.expectation?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 38,
|
|
"id": "163b70a3-814a-4a62-a98a-2ffca933a544",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"-0.27540575238693377"
|
|
]
|
|
},
|
|
"execution_count": 38,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"qmatcha_backend.expectation(\n",
|
|
" circuit=circuit,\n",
|
|
" observable=hamiltonian,\n",
|
|
")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 39,
|
|
"id": "2d8c4a9c-eca3-49d0-bdbf-ab054172c4e5",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"-0.275405752386936"
|
|
]
|
|
},
|
|
"execution_count": 39,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Try with Qibo\n",
|
|
"\n",
|
|
"hamiltonian = hamiltonians.SymbolicHamiltonian(form)\n",
|
|
"hamiltonian.expectation(circuit().state())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "94df291c-9ddc-4b2e-8442-5fca00784bd8",
|
|
"metadata": {},
|
|
"source": [
|
|
"They match! 🥳"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"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": "3.10.0"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|