433 lines
179 KiB
Plaintext
433 lines
179 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "eb419bc5-908c-4f0d-a4ff-c4d13f04e332",
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"metadata": {
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"tags": []
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},
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"source": [
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"# Heisenberg chain\n",
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"*Usage estimate: 2 minutes on IBM Cusco (NOTE: This is an estimate only. Your runtime may vary.)*"
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]
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},
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{
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"cell_type": "markdown",
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"id": "49d868bf",
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"metadata": {},
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"source": [
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"## Background\n",
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"\n",
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"In this tutorial, we will show how to build, deploy, and run a `Qiskit Pattern` for simulating a Heisenberg chain and estimating its ground state energy. For more information on `Qiskit Patterns` and how `Qiskit Serverless` can be used to deploy them to the cloud for managed execution, visit our [docs page on the IBM Quantum Platform](https://docs.quantum.ibm.com/run/quantum-serverless)."
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]
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},
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{
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"cell_type": "markdown",
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"id": "bc52f763",
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"metadata": {},
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"source": [
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"## Requirements\n",
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"\n",
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"Before starting this tutorial, ensure that you have the following installed:\n",
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"\n",
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"* Qiskit SDK 1.2 or later, with visualization support (`pip install 'qiskit[visualization]'`)\n",
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"* Qiskit Runtime 0.28 or later (`pip install qiskit-ibm-runtime`) 0.22 or later"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a46e9e3e",
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"metadata": {},
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"source": [
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"## Setup"
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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": null,
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"id": "e7754922",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"from scipy.optimize import minimize\n",
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"from typing import Union, Sequence\n",
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"\n",
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"\n",
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"from qiskit import QuantumCircuit\n",
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"from qiskit.quantum_info import SparsePauliOp\n",
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"from qiskit.primitives.base import BaseEstimator, BaseEstimatorV2\n",
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"from qiskit.circuit.library import XGate\n",
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"from qiskit.circuit.library import EfficientSU2\n",
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"from qiskit.transpiler import PassManager\n",
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"from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
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"\n",
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"from qiskit_ibm_runtime import QiskitRuntimeService\n",
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"from qiskit_ibm_runtime.transpiler.passes.scheduling import (\n",
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" ALAPScheduleAnalysis,\n",
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" PadDynamicalDecoupling,\n",
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")\n",
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"from qiskit_ibm_runtime import Session, Estimator\n",
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"\n",
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"from qiskit_serverless import IBMServerlessProvider, QiskitPattern\n",
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"\n",
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"\n",
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"def visualize_results(results):\n",
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" plt.plot(results[\"cost_history\"], lw=2)\n",
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" plt.xlabel(\"Iteration\")\n",
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" plt.ylabel(\"Energy\")\n",
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" plt.show()\n",
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"\n",
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"\n",
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"def build_callback(\n",
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" ansatz: QuantumCircuit,\n",
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" hamiltonian: SparsePauliOp,\n",
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" estimator: Union[BaseEstimator, BaseEstimatorV2],\n",
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" callback_dict: dict,\n",
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"):\n",
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" def callback(current_vector):\n",
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" # Keep track of the number of iterations\n",
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" callback_dict[\"iters\"] += 1\n",
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" # Set the prev_vector to the latest one\n",
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" callback_dict[\"prev_vector\"] = current_vector\n",
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" # Compute the value of the cost function at the current vector\n",
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" # This adds an additional function evaluation\n",
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" if isinstance(estimator, BaseEstimator):\n",
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" current_cost = (\n",
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" estimator.run(\n",
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" ansatz, hamiltonian, parameter_values=current_vector\n",
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" )\n",
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" .result()\n",
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" .values[0]\n",
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" )\n",
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" else:\n",
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" current_cost = (\n",
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" estimator.run([(ansatz, hamiltonian, [current_vector])])\n",
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" .result()[0]\n",
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" .data.evs[0]\n",
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" )\n",
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" callback_dict[\"cost_history\"].append(current_cost)\n",
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" # Print to screen on single line\n",
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" print(\n",
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" \"Iters. done: {} [Current cost: {}]\".format(\n",
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" callback_dict[\"iters\"], current_cost\n",
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" ),\n",
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" end=\"\\r\",\n",
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" flush=True,\n",
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" )\n",
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"\n",
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" return callback"
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]
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},
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{
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"cell_type": "markdown",
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"id": "132fb15f-10b4-4d7e-83d8-f512a6f675d1",
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"metadata": {},
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"source": [
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"## Step 1: Map classical inputs to a quantum problem\n",
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"\n",
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"* Input: Number of spins\n",
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"* Output: Ansatz and Hamiltonian modeling the Heisenberg chain\n",
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"\n",
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"Construct an ansatz and Hamiltonian which model a 10-spin Heisenberg chain. First, we import some generic packages and create a couple of helper functions."
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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": null,
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"id": "7e8d2f10-f1d6-4ec2-bac9-9db23499c9e1",
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"metadata": {},
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"outputs": [],
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"source": [
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"num_spins = 10\n",
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"ansatz = EfficientSU2(num_qubits=num_spins, reps=3)\n",
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"\n",
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"# Remember to insert your token in the QiskitRuntimeService constructor\n",
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"service = QiskitRuntimeService()\n",
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"backend = service.least_busy(\n",
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" operational=True, min_num_qubits=num_spins, simulator=False\n",
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")\n",
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"\n",
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"coupling = backend.target.build_coupling_map()\n",
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"reduced_coupling = coupling.reduce(list(range(num_spins)))\n",
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"\n",
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"edge_list = reduced_coupling.graph.edge_list()\n",
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"ham_list = []\n",
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"\n",
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"for edge in edge_list:\n",
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" ham_list.append((\"ZZ\", edge, 0.5))\n",
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" ham_list.append((\"YY\", edge, 0.5))\n",
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" ham_list.append((\"XX\", edge, 0.5))\n",
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"\n",
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"for qubit in reduced_coupling.physical_qubits:\n",
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" ham_list.append((\"Z\", [qubit], np.random.random() * 2 - 1))\n",
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"\n",
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"hamiltonian = SparsePauliOp.from_sparse_list(ham_list, num_qubits=num_spins)\n",
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"\n",
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"ansatz.draw(\"mpl\", style=\"iqp\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ab79119b-5e56-49d8-a20e-1c8e665baec0",
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"metadata": {},
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"source": [
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"## Step 2: Optimize problem for quantum hardware execution\n",
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"\n",
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"* Input: Abstract circuit, observable\n",
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"* Output: Target circuit and observable, optimized for the selected QPU\n",
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"\n",
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"Use the `generate_preset_pass_manager` function from Qiskit to automatically generate an optimization routine for our circuit with respect to the selected QPU. We choose `optimization_level=3`, which provides the highest level of optimization of the preset pass managers. We also include `ALAPScheduleAnalysis` and `PadDynamicalDecoupling` scheduling passes to suppress decoherence errors."
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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": null,
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"id": "a0a5f1c8-5c31-4d9f-ae81-37bd67271d44",
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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": [
|
|
"<Figure size 4228.38x521.733 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 3,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"target = backend.target\n",
|
|
"pm = generate_preset_pass_manager(optimization_level=3, backend=backend)\n",
|
|
"pm.scheduling = PassManager(\n",
|
|
" [\n",
|
|
" ALAPScheduleAnalysis(durations=target.durations()),\n",
|
|
" PadDynamicalDecoupling(\n",
|
|
" durations=target.durations(),\n",
|
|
" dd_sequences=[XGate(), XGate()],\n",
|
|
" pulse_alignment=target.pulse_alignment,\n",
|
|
" ),\n",
|
|
" ]\n",
|
|
")\n",
|
|
"ansatz_ibm = pm.run(ansatz)\n",
|
|
"observable_ibm = hamiltonian.apply_layout(ansatz_ibm.layout)\n",
|
|
"ansatz_ibm.draw(\"mpl\", scale=0.6, style=\"iqp\", fold=-1, idle_wires=False)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9e889d0b-30b5-4e6b-84c9-d1f096abf132",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Step 3: Execute using Qiskit primitives\n",
|
|
"\n",
|
|
"* Input: Target circuit and observable\n",
|
|
"* Output: Results of optimization\n",
|
|
"\n",
|
|
"Minimize the estimated ground state energy of the system by optimizing the circuit parameters. Use the `Estimator` primitive from Qiskit Runtime to evaluate the cost function during optimization.\n",
|
|
"\n",
|
|
"Since we optimized the circuit for the backend in Step 2, we can avoid doing transpilation on the Runtime server by setting `skip_transpilation=True` and passing the optimized circuit. For this demo, we will run on a QPU using `qiskit-ibm-runtime` primitives. To run with `qiskit` statevector-based primitives, replace the block of code using Qiskit IBM Runtime primitives with the commented block."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "4c4b1b0b-5c61-4587-986c-7a9108bc2505",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# SciPy minimizer routine\n",
|
|
"def cost_func(\n",
|
|
" params: Sequence,\n",
|
|
" ansatz: QuantumCircuit,\n",
|
|
" hamiltonian: SparsePauliOp,\n",
|
|
" estimator: Union[BaseEstimator, BaseEstimatorV2],\n",
|
|
") -> float:\n",
|
|
" \"\"\"Ground state energy evaluation.\"\"\"\n",
|
|
" if isinstance(estimator, BaseEstimatorV2):\n",
|
|
" return (\n",
|
|
" estimator.run([(ansatz, hamiltonian, [params])])\n",
|
|
" .result()[0]\n",
|
|
" .data.evs[0]\n",
|
|
" )\n",
|
|
" else:\n",
|
|
" return (\n",
|
|
" estimator.run(ansatz, hamiltonian, parameter_values=params)\n",
|
|
" .result()\n",
|
|
" .values[0]\n",
|
|
" )\n",
|
|
"\n",
|
|
"\n",
|
|
"num_params = ansatz_ibm.num_parameters\n",
|
|
"params = 2 * np.pi * np.random.random(num_params)\n",
|
|
"\n",
|
|
"callback_dict = {\n",
|
|
" \"prev_vector\": None,\n",
|
|
" \"iters\": 0,\n",
|
|
" \"cost_history\": [],\n",
|
|
"}\n",
|
|
"\n",
|
|
"# Evaluate the problem using a QPU via Qiskit IBM Runtime\n",
|
|
"with Session(backend=backend) as session:\n",
|
|
" estimator = Estimator()\n",
|
|
" callback = build_callback(\n",
|
|
" ansatz_ibm, observable_ibm, estimator, callback_dict\n",
|
|
" )\n",
|
|
" res = minimize(\n",
|
|
" cost_func,\n",
|
|
" x0=params,\n",
|
|
" args=(ansatz_ibm, observable_ibm, estimator),\n",
|
|
" callback=callback,\n",
|
|
" method=\"cobyla\",\n",
|
|
" options={\"maxiter\": 100},\n",
|
|
" )\n",
|
|
"\n",
|
|
"visualize_results(callback_dict)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "33abbb3f-6245-4610-a05d-e2bc4cc551f0",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Step 4: Post-process and return result in desired classical format\n",
|
|
"\n",
|
|
"* Input: Ground state energy estimates during optimization\n",
|
|
"* Output: Estimated ground state energy"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "e5b58771-d543-4e75-9746-fbc7b28e4360",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Estimated ground state energy: -2.594437119769288\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(f'Estimated ground state energy: {res[\"fun\"]}')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "4548f97e-352e-4a8e-b2c7-3c85f12099ab",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Deploy the Qiskit Pattern to the cloud\n",
|
|
"\n",
|
|
"To do this, move the source code above to a file, `./source/heisenberg.py`, wrap the code in a script which takes inputs and returns the final solution, and finally upload it to a remote cluster using the `QiskitPattern` class from `Qiskit Serverless`. For guidance on specifying external dependencies, passing input arguments, and more, check out the [Qiskit Serverless guides](https://qiskit.github.io/qiskit-serverless/getting_started/index.html).\n",
|
|
"\n",
|
|
"The input to the Pattern is the number of spins in the chain. The output is an estimation of the ground state energy of the system."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "970c51c8-dac5-4b64-9f20-4067666dfddc",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Authenticate to the remote cluster and submit the pattern for remote execution\n",
|
|
"serverless = IBMServerlessProvider()\n",
|
|
"heisenberg_pattern = QiskitPattern(\n",
|
|
" title=\"ibm/heisenberg\",\n",
|
|
" entrypoint=\"heisenberg.py\",\n",
|
|
" working_dir=\"./source/\",\n",
|
|
")\n",
|
|
"serverless.upload(heisenberg_pattern)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e1b5c8d0-229a-4a39-8a8a-daf1762fca54",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Run the Qiskit Pattern as a managed service\n",
|
|
"\n",
|
|
"Once we have uploaded the pattern to the cloud, we can easily run it using the `IBMServerlessProvider` client."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "9d9e5218-bdfe-4897-8920-7d0578a32c7f",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Run the pattern on the remote cluster\n",
|
|
"\n",
|
|
"job = serverless.run(\"ibm/heisenberg\")\n",
|
|
"solution = job.result()\n",
|
|
"\n",
|
|
"print(solution)\n",
|
|
"print(job.logs())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c14b0e0a",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Tutorial survey\n",
|
|
"\n",
|
|
"Please take one minute to provide feedback on this tutorial. Your insights will help us improve our content offerings and user experience.\n",
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"\n",
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"[Link to survey](https://your.feedback.ibm.com/jfe/form/SV_bfuBwfNeeFBxnim)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c1c57978",
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"metadata": {},
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"source": [
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"© IBM Corp. 2023, 2024"
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]
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}
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],
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"metadata": {
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|
"description": "Build, deploy, and run a Qiskit Pattern for simulating a Heisenberg chain and estimating its ground state energy.",
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"kernelspec": {
|
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"display_name": "Python 3",
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"language": "python",
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|
"name": "python3"
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},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
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"version": 3
|
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},
|
|
"file_extension": ".py",
|
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"mimetype": "text/x-python",
|
|
"name": "python",
|
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"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3"
|
|
},
|
|
"platform": "cloud",
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"title": "Heisenberg chain"
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},
|
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"nbformat": 4,
|
|
"nbformat_minor": 5
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|
}
|