Bina templat fungsi untuk simulasi Hamiltonian

Templat ini merangkumi aliran kerja untuk mensimulasikan evolusi masa sesuatu keadaan awal terhadap Hamiltonian berasaskan spin yang ditentukan pengguna, dan mengembalikan set nilai jangkaan yang ditetapkan menggunakan addon AQC.

Templat ini disusun sebagai corak Qiskit dengan langkah-langkah berikut:

1. Mengumpul input dan memetakan masalah

Bahagian ini menerima input berupa Hamiltonian yang hendak disimulasikan, keadaan awal dalam bentuk QuantumCircuit, set pemboleh ukur untuk menganggar nilai jangkaan, dan spesifikasi pilihan untuk addon AQC. Langkah ini mengesahkan bahawa semua data input yang diperlukan ada dan berada dalam format yang betul.

Argumen input kemudiannya digunakan untuk membina litar kuantum dan operator yang relevan untuk aliran kerja. Sebuah litar sasaran dicipta dan perwakilan keadaan produk matriks bagi litar ini dijumpai menggunakan addon AQC. Selepas itu, litar ansatz dijana dan dioptimumkan menggunakan kaedah rangkaian tensor, menghasilkan litar akhir yang melaksanakan baki evolusi masa.

2. Menyediakan litar yang dijana untuk pelaksanaan

Litar yang dijana daripada addon AQC kemudiannya ditranspilkan untuk dilaksanakan pada Backend yang dipilih. Sebuah instans EstimatorV2 dicipta dengan set pilihan pengurangan ralat lalai untuk menguruskan pelaksanaan litar.

3. Pelaksanaan

Akhir sekali, litar ansatz ditranspilkan dan dilaksanakan pada QPU serta mengumpul anggaran untuk semua nilai jangkaan yang ditentukan, yang dikembalikan dalam format boleh siri untuk diakses oleh pengguna.

Tulis templat fungsi

Pertama, tulis templat fungsi untuk simulasi Hamiltonian yang menggunakan addon Qiskit AQC-Tensor untuk memetakan huraian masalah kepada litar kedalaman berkurangan untuk dilaksanakan pada perkakasan.

Sepanjang proses ini, kod disimpan ke ./source_files/template_hamiltonian_simulation.py. Fail ini ialah templat fungsi yang boleh anda muat naik dan jalankan dari jauh dengan Qiskit Serverless.

# Added by doQumentation — required packages for this notebook
!pip install -q mergedeep numpy qiskit qiskit-addon-aqc-tensor qiskit-addon-utils qiskit-ibm-catalog qiskit-ibm-runtime qiskit-serverless quimb scipy

# This cell is hidden from users, it just creates a new folder
from pathlib import Path

Path("./source_files").mkdir(exist_ok=True)

Kumpul dan sahkan input

Mulakan dengan mendapatkan input untuk templat. Contoh ini mempunyai input khusus domain yang relevan untuk simulasi Hamiltonian (seperti Hamiltonian dan pemboleh ukur) dan pilihan khusus keupayaan (seperti berapa banyak anda ingin memampatkan lapisan awal litar Trotter menggunakan AQC-Tensor, atau pilihan lanjutan untuk melaraskan penindasan dan pengurangan ralat di luar tetapan lalai yang merupakan sebahagian daripada contoh ini).

%%writefile ./source_files/template_hamiltonian_simulation.py

from qiskit import QuantumCircuit
from qiskit_serverless import get_arguments, save_result

# Extract parameters from arguments
#
# Do this at the top of the program so it fails early if any required arguments are missing or invalid.

arguments = get_arguments()

dry_run = arguments.get("dry_run", False)
backend_name = arguments["backend_name"]

aqc_evolution_time = arguments["aqc_evolution_time"]
aqc_ansatz_num_trotter_steps = arguments["aqc_ansatz_num_trotter_steps"]
aqc_target_num_trotter_steps = arguments["aqc_target_num_trotter_steps"]

remainder_evolution_time = arguments["remainder_evolution_time"]
remainder_num_trotter_steps = arguments["remainder_num_trotter_steps"]

# Stop if this fidelity is achieved
aqc_stopping_fidelity = arguments.get("aqc_stopping_fidelity", 1.0)
# Stop after this number of iterations, even if stopping fidelity is not achieved
aqc_max_iterations = arguments.get("aqc_max_iterations", 500)

hamiltonian = arguments["hamiltonian"]
observable = arguments["observable"]
initial_state = arguments.get("initial_state", QuantumCircuit(hamiltonian.num_qubits))

Writing ./source_files/template_hamiltonian_simulation.py

%%writefile --append ./source_files/template_hamiltonian_simulation.py

import numpy as np
import json
from mergedeep import merge

# Configure `EstimatorOptions`, to control the parameters of the hardware experiment
#
# Set default options
estimator_default_options = {
    "resilience": {
        "measure_mitigation": True,
        "zne_mitigation": True,
        "zne": {
            "amplifier": "gate_folding",
            "noise_factors": [1, 2, 3],
            "extrapolated_noise_factors": list(np.linspace(0, 3, 31)),
            "extrapolator": ["exponential", "linear", "fallback"],
        },
        "measure_noise_learning": {
            "num_randomizations": 512,
            "shots_per_randomization": 512,
        },
    },
    "twirling": {
        "enable_gates": True,
        "enable_measure": True,
        "num_randomizations": 300,
        "shots_per_randomization": 100,
        "strategy": "active",
    },
}
# Merge with user-provided options
estimator_options = merge(
    arguments.get("estimator_options", {}), estimator_default_options
)

Appending to ./source_files/template_hamiltonian_simulation.py

Apabila templat fungsi sedang berjalan, adalah berguna untuk mengembalikan maklumat dalam log menggunakan pernyataan cetak, supaya anda dapat menilai kemajuan beban kerja dengan lebih baik. Berikut ialah contoh mudah percetakan estimator_options supaya ada rekod pilihan Estimator sebenar yang digunakan. Terdapat banyak lagi contoh serupa sepanjang program untuk melaporkan kemajuan semasa pelaksanaan, termasuk nilai fungsi objektif semasa komponen berulang AQC-Tensor, dan kedalaman dua Qubit litar set arahan seni bina (ISA) akhir yang dimaksudkan untuk dilaksanakan pada perkakasan.

%%writefile --append ./source_files/template_hamiltonian_simulation.py

print("estimator_options =", json.dumps(estimator_options, indent=4))

Appending to ./source_files/template_hamiltonian_simulation.py

Sahkan input

Aspek penting dalam memastikan templat boleh digunakan semula merentasi pelbagai input ialah pengesahan input. Kod berikut ialah contoh pengesahan bahawa kesetiaan berhenti semasa AQC-Tensor telah ditetapkan dengan sewajarnya dan jika tidak, mengembalikan mesej ralat yang bermaklumat tentang cara membetulkan ralat tersebut.

%%writefile --append ./source_files/template_hamiltonian_simulation.py

# Perform parameter validation

if not 0.0 < aqc_stopping_fidelity <= 1.0:
    raise ValueError(
        f"Invalid stopping fidelity: {aqc_stopping_fidelity}.  It must be a positive float no greater than 1."
    )

Appending to ./source_files/template_hamiltonian_simulation.py

Sediakan output fungsi

Pertama, sediakan kamus untuk menyimpan semua output templat fungsi. Kunci akan ditambah ke kamus ini sepanjang aliran kerja, dan ia dikembalikan pada penghujung program.

%%writefile --append ./source_files/template_hamiltonian_simulation.py

output = {}

Appending to ./source_files/template_hamiltonian_simulation.py

Petakan masalah dan pra-proses litar dengan AQC

Pengoptimuman AQC-Tensor berlaku dalam langkah 1 corak Qiskit. Pertama, keadaan sasaran dibina. Dalam contoh ini, ia dibina daripada litar sasaran yang mengevolusi Hamiltonian yang sama untuk tempoh masa yang sama seperti bahagian AQC. Kemudian, ansatz dijana daripada litar setara tetapi dengan langkah Trotter yang lebih sedikit. Dalam bahagian utama algoritma AQC, ansatz itu secara berulang didekatkan kepada keadaan sasaran. Akhirnya, hasilnya digabungkan dengan baki langkah Trotter yang diperlukan untuk mencapai masa evolusi yang dikehendaki.

Perhatikan contoh tambahan pengelogan yang digabungkan dalam kod berikut.

%%writefile --append ./source_files/template_hamiltonian_simulation.py

import os
os.environ["NUMBA_CACHE_DIR"] = "/data"

import datetime
import quimb.tensor
from scipy.optimize import OptimizeResult, minimize
from qiskit.synthesis import SuzukiTrotter
from qiskit_addon_utils.problem_generators import generate_time_evolution_circuit
from qiskit_addon_aqc_tensor.ansatz_generation import (
    generate_ansatz_from_circuit,
    AnsatzBlock,
)
from qiskit_addon_aqc_tensor.simulation import (
    tensornetwork_from_circuit,
    compute_overlap,
)
from qiskit_addon_aqc_tensor.simulation.quimb import QuimbSimulator
from qiskit_addon_aqc_tensor.objective import OneMinusFidelity

print("Hamiltonian:", hamiltonian)
print("Observable:", observable)
simulator_settings = QuimbSimulator(quimb.tensor.CircuitMPS, autodiff_backend="jax")

# Construct the AQC target circuit
aqc_target_circuit = initial_state.copy()
if aqc_evolution_time:
    aqc_target_circuit.compose(
        generate_time_evolution_circuit(
            hamiltonian,
            synthesis=SuzukiTrotter(reps=aqc_target_num_trotter_steps),
            time=aqc_evolution_time,
        ),
        inplace=True,
    )

# Construct matrix-product state representation of the AQC target state
aqc_target_mps = tensornetwork_from_circuit(aqc_target_circuit, simulator_settings)
print("Target MPS maximum bond dimension:", aqc_target_mps.psi.max_bond())
output["target_bond_dimension"] = aqc_target_mps.psi.max_bond()

# Generate an ansatz and initial parameters from a Trotter circuit with fewer steps
aqc_good_circuit = initial_state.copy()
if aqc_evolution_time:
    aqc_good_circuit.compose(
        generate_time_evolution_circuit(
            hamiltonian,
            synthesis=SuzukiTrotter(reps=aqc_ansatz_num_trotter_steps),
            time=aqc_evolution_time,
        ),
        inplace=True,
    )
aqc_ansatz, aqc_initial_parameters = generate_ansatz_from_circuit(aqc_good_circuit)
print("Number of AQC parameters:", len(aqc_initial_parameters))
output["num_aqc_parameters"] = len(aqc_initial_parameters)

# Calculate the fidelity of ansatz circuit vs. the target state, before optimization
good_mps = tensornetwork_from_circuit(aqc_good_circuit, simulator_settings)
starting_fidelity = abs(compute_overlap(good_mps, aqc_target_mps)) ** 2
print("Starting fidelity of AQC portion:", starting_fidelity)
output["aqc_starting_fidelity"] = starting_fidelity

# Optimize the ansatz parameters by using MPS calculations
def callback(intermediate_result: OptimizeResult):
    fidelity = 1 - intermediate_result.fun
    print(f"{datetime.datetime.now()} Intermediate result: Fidelity {fidelity:.8f}")
    if intermediate_result.fun < stopping_point:
        raise StopIteration

objective = OneMinusFidelity(aqc_target_mps, aqc_ansatz, simulator_settings)
stopping_point = 1.0 - aqc_stopping_fidelity

result = minimize(
    objective,
    aqc_initial_parameters,
    method="L-BFGS-B",
    jac=True,
    options={"maxiter": aqc_max_iterations},
    callback=callback,
)
if result.status not in (
    0,
    1,
    99,
):  # 0 => success; 1 => max iterations reached; 99 => early termination via StopIteration
    raise RuntimeError(
        f"Optimization failed: {result.message} (status={result.status})"
    )
print(f"Done after {result.nit} iterations.")
output["num_iterations"] = result.nit
aqc_final_parameters = result.x
output["aqc_final_parameters"] = list(aqc_final_parameters)

# Construct an optimized circuit for initial portion of time evolution
aqc_final_circuit = aqc_ansatz.assign_parameters(aqc_final_parameters)

# Calculate fidelity after optimization
aqc_final_mps = tensornetwork_from_circuit(aqc_final_circuit, simulator_settings)
aqc_fidelity = abs(compute_overlap(aqc_final_mps, aqc_target_mps)) ** 2
print("Fidelity of AQC portion:", aqc_fidelity)
output["aqc_fidelity"] = aqc_fidelity

# Construct final circuit, with remainder of time evolution
final_circuit = aqc_final_circuit.copy()
if remainder_evolution_time:
    remainder_circuit = generate_time_evolution_circuit(
        hamiltonian,
        synthesis=SuzukiTrotter(reps=remainder_num_trotter_steps),
        time=remainder_evolution_time,
    )
    final_circuit.compose(remainder_circuit, inplace=True)

Appending to ./source_files/template_hamiltonian_simulation.py

Optimumkan litar akhir untuk pelaksanaan

Selepas bahagian AQC aliran kerja, final_circuit ditranspilkan untuk perkakasan seperti biasa.

%%writefile --append ./source_files/template_hamiltonian_simulation.py

from qiskit_ibm_runtime import QiskitRuntimeService
from qiskit.transpiler import generate_preset_pass_manager

service = QiskitRuntimeService()
backend = service.backend(backend_name)

# Transpile PUBs (circuits and observables) to match ISA
pass_manager = generate_preset_pass_manager(backend=backend, optimization_level=3)
isa_circuit = pass_manager.run(final_circuit)
isa_observable = observable.apply_layout(isa_circuit.layout)

isa_2qubit_depth = isa_circuit.depth(lambda x: x.operation.num_qubits == 2)
print("ISA circuit two-qubit depth:", isa_2qubit_depth)
output["twoqubit_depth"] = isa_2qubit_depth

Appending to ./source_files/template_hamiltonian_simulation.py

Keluar awal jika menggunakan mod dry run

Jika mod dry run telah dipilih, program dihentikan sebelum dilaksanakan pada perkakasan. Ini berguna jika, contohnya, anda ingin memeriksa kedalaman dua Qubit litar ISA terlebih dahulu sebelum memutuskan untuk melaksanakan pada perkakasan.

%%writefile --append ./source_files/template_hamiltonian_simulation.py

# Exit now if dry run; don't execute on hardware
if dry_run:
    import sys

    print("Exiting before hardware execution since `dry_run` is True.")
    save_result(output)
    sys.exit(0)

Appending to ./source_files/template_hamiltonian_simulation.py

Laksanakan litar pada perkakasan

%%writefile --append ./source_files/template_hamiltonian_simulation.py

# ## Step 3: Execute quantum experiments on backend
from qiskit_ibm_runtime import EstimatorV2 as Estimator

estimator = Estimator(backend, options=estimator_options)

# Submit the underlying Estimator job. Note that this is not the
# actual function job.
job = estimator.run([(isa_circuit, isa_observable)])
print("Job ID:", job.job_id())
output["job_id"] = job.job_id()

# Wait until job is complete
hw_results = job.result()
hw_results_dicts = [pub_result.data.__dict__ for pub_result in hw_results]

# Save hardware results to serverless output dictionary
output["hw_results"] = hw_results_dicts

# Reorganize expectation values
hw_expvals = [pub_result_data["evs"].tolist() for pub_result_data in hw_results_dicts]

# Save expectation values to Qiskit Serverless
print("Hardware expectation values", hw_expvals)
output["hw_expvals"] = hw_expvals[0]

Appending to ./source_files/template_hamiltonian_simulation.py

Simpan output

Templat fungsi ini mengembalikan output peringkat domain yang relevan untuk aliran kerja simulasi Hamiltonian ini (nilai jangkaan) di samping metadata penting yang dihasilkan sepanjang proses.

%%writefile --append ./source_files/template_hamiltonian_simulation.py

save_result(output)

Appending to ./source_files/template_hamiltonian_simulation.py

Erahkan fungsi ke IBM Quantum Platform

Bahagian sebelumnya mencipta program untuk dijalankan dari jauh. Kod dalam bahagian ini memuat naik program tersebut ke Qiskit Serverless.

Gunakan qiskit-ibm-catalog untuk mengesahkan diri ke QiskitServerless dengan kunci API anda, yang boleh anda temui di papan pemuka IBM Quantum Platform, dan muat naik program tersebut.

Anda boleh menggunakan save_account() secara pilihan untuk menyimpan kelayakan anda (lihat panduan Sediakan akaun IBM Cloud anda). Perhatikan bahawa ini menulis kelayakan anda ke fail yang sama seperti QiskitRuntimeService.save_account().

from qiskit_ibm_catalog import QiskitServerless, QiskitFunction

# Authenticate to the remote cluster and submit the pattern for remote execution
serverless = QiskitServerless()

Program ini mempunyai kebergantungan pip tersuai. Tambahkannya ke tatasusunan dependencies semasa membina instans QiskitFunction:

template = QiskitFunction(
    title="template_hamiltonian_simulation",
    entrypoint="template_hamiltonian_simulation.py",
    working_dir="./source_files/",
    dependencies=[
        "qiskit-addon-utils~=0.1.0",
        "qiskit-addon-aqc-tensor[quimb-jax]~=0.1.2",
        "mergedeep==1.3.4",
    ],
)

serverless.upload(template)

QiskitFunction(template_hamiltonian_simulation)

Akhirnya, untuk menyemak sama ada program berjaya dimuat naik, gunakan serverless.list():

serverless.list()

QiskitFunction(template_hamiltonian_simulation),

Jalankan templat fungsi dari jauh

Templat fungsi telah dimuat naik, jadi anda boleh menjalankannya dari jauh dengan Qiskit Serverless. Pertama, muat templat mengikut nama:

template = serverless.load("template_hamiltonian_simulation")

Seterusnya, jalankan templat dengan input peringkat domain untuk simulasi Hamiltonian. Contoh ini menentukan model XXZ 50-Qubit dengan gandingan rawak, dan keadaan awal serta pemboleh ukur.

from itertools import chain
import numpy as np
from qiskit.quantum_info import SparsePauliOp

L = 50

# Generate the edge list for this spin-chain
edges = [(i, i + 1) for i in range(L - 1)]
# Generate an edge-coloring so we can make hw-efficient circuits
edges = edges[::2] + edges[1::2]

# Generate random coefficients for our XXZ Hamiltonian
np.random.seed(0)
Js = np.random.rand(L - 1) + 0.5 * np.ones(L - 1)

hamiltonian = SparsePauliOp.from_sparse_list(
    chain.from_iterable(
        [
            [
                ("XX", (i, j), Js[i] / 2),
                ("YY", (i, j), Js[i] / 2),
                ("ZZ", (i, j), Js[i]),
            ]
            for i, j in edges
        ]
    ),
    num_qubits=L,
)
observable = SparsePauliOp.from_sparse_list(
    [("ZZ", (L // 2 - 1, L // 2), 1.0)], num_qubits=L
)

from qiskit import QuantumCircuit

initial_state = QuantumCircuit(L)
for i in range(L):
    if i % 2:
        initial_state.x(i)

job = template.run(
    dry_run=True,
    initial_state=initial_state,
    hamiltonian=hamiltonian,
    observable=observable,
    backend_name="ibm_fez",
    estimator_options={},
    aqc_evolution_time=0.2,
    aqc_ansatz_num_trotter_steps=1,
    aqc_target_num_trotter_steps=32,
    remainder_evolution_time=0.2,
    remainder_num_trotter_steps=4,
    aqc_max_iterations=300,
)
print(job.job_id)

853b0edb-d63f-4629-be71-398b6dcf33cb

Semak status kerja:

job.status()

'QUEUED'

Selepas kerja berjalan, anda boleh mengambil log yang dicipta daripada output print(). Log ini boleh memberikan maklumat berguna tentang kemajuan aliran kerja simulasi Hamiltonian. Contohnya, nilai fungsi objektif semasa komponen berulang AQC, atau kedalaman dua Qubit litar ISA akhir yang dimaksudkan untuk dilaksanakan pada perkakasan.

print(job.logs())

No logs yet.

Sekat baki program sehingga keputusan tersedia. Selepas kerja selesai, anda boleh mendapatkan semula hasilnya. Ini termasuk output peringkat domain simulasi Hamiltonian (nilai jangkaan) dan metadata berguna.

result = job.result()

del result[
    "aqc_final_parameters"
]  # the list is too long to conveniently display here
result

{'target_bond_dimension': 5,
 'num_aqc_parameters': 816,
 'aqc_starting_fidelity': 0.9914382555614002,
 'num_iterations': 72,
 'aqc_fidelity': 0.9998108844412502,
 'twoqubit_depth': 33}

Selepas kerja selesai, keseluruhan output log akan tersedia.

print(job.logs())

2024-12-17 14:50:15,580	INFO job_manager.py:531 -- Runtime env is setting up.
estimator_options = {
    "resilience": {
        "measure_mitigation": true,
        "zne_mitigation": true,
        "zne": {
            "amplifier": "gate_folding",
            "noise_factors": [
                1,
                2,
                3
            ],
            "extrapolated_noise_factors": [
                0.0,
                0.1,
                0.2,
                0.30000000000000004,
                0.4,
                0.5,
                0.6000000000000001,
                0.7000000000000001,
                0.8,
                0.9,
                1.0,
                1.1,
                1.2000000000000002,
                1.3,
                1.4000000000000001,
                1.5,
                1.6,
                1.7000000000000002,
                1.8,
                1.9000000000000001,
                2.0,
                2.1,
                2.2,
                2.3000000000000003,
                2.4000000000000004,
                2.5,
                2.6,
                2.7,
                2.8000000000000003,
                2.9000000000000004,
                3.0
            ],
            "extrapolator": [
                "exponential",
                "linear",
                "fallback"
            ]
        },
        "measure_noise_learning": {
            "num_randomizations": 512,
            "shots_per_randomization": 512
        }
    },
    "twirling": {
        "enable_gates": true,
        "enable_measure": true,
        "num_randomizations": 300,
        "shots_per_randomization": 100,
        "strategy": "active"
    }
}
Hamiltonian: SparsePauliOp(['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXX', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYY', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZ', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'XXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'YYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXI', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYI', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IXXIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IYYIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII'],
              coeffs=[0.52440675+0.j, 0.52440675+0.j, 1.0488135 +0.j, 0.55138169+0.j,
 0.55138169+0.j, 1.10276338+0.j, 0.4618274 +0.j, 0.4618274 +0.j,
 0.9236548 +0.j, 0.46879361+0.j, 0.46879361+0.j, 0.93758721+0.j,
 0.73183138+0.j, 0.73183138+0.j, 1.46366276+0.j, 0.64586252+0.j,
 0.64586252+0.j, 1.29172504+0.j, 0.53402228+0.j, 0.53402228+0.j,
 1.06804456+0.j, 0.28551803+0.j, 0.28551803+0.j, 0.57103606+0.j,
 0.2601092 +0.j, 0.2601092 +0.j, 0.5202184 +0.j, 0.63907838+0.j,
 0.63907838+0.j, 1.27815675+0.j, 0.73930917+0.j, 0.73930917+0.j,
 1.47861834+0.j, 0.48073968+0.j, 0.48073968+0.j, 0.96147936+0.j,
 0.30913721+0.j, 0.30913721+0.j, 0.61827443+0.j, 0.32167664+0.j,
 0.32167664+0.j, 0.64335329+0.j, 0.51092416+0.j, 0.51092416+0.j,
 1.02184832+0.j, 0.38227781+0.j, 0.38227781+0.j, 0.76455561+0.j,
 0.47807517+0.j, 0.47807517+0.j, 0.95615033+0.j, 0.2593949 +0.j,
 0.2593949 +0.j, 0.5187898 +0.j, 0.55604786+0.j, 0.55604786+0.j,
 1.11209572+0.j, 0.72187404+0.j, 0.72187404+0.j, 1.44374808+0.j,
 0.42975395+0.j, 0.42975395+0.j, 0.8595079 +0.j, 0.5988156 +0.j,
 0.5988156 +0.j, 1.1976312 +0.j, 0.58338336+0.j, 0.58338336+0.j,
 1.16676672+0.j, 0.35519128+0.j, 0.35519128+0.j, 0.71038256+0.j,
 0.40771418+0.j, 0.40771418+0.j, 0.81542835+0.j, 0.60759468+0.j,
 0.60759468+0.j, 1.21518937+0.j, 0.52244159+0.j, 0.52244159+0.j,
 1.04488318+0.j, 0.57294706+0.j, 0.57294706+0.j, 1.14589411+0.j,
 0.6958865 +0.j, 0.6958865 +0.j, 1.391773  +0.j, 0.44172076+0.j,
 0.44172076+0.j, 0.88344152+0.j, 0.51444746+0.j, 0.51444746+0.j,
 1.02889492+0.j, 0.71279832+0.j, 0.71279832+0.j, 1.42559664+0.j,
 0.29356465+0.j, 0.29356465+0.j, 0.5871293 +0.j, 0.66630992+0.j,
 0.66630992+0.j, 1.33261985+0.j, 0.68500607+0.j, 0.68500607+0.j,
 1.37001215+0.j, 0.64957928+0.j, 0.64957928+0.j, 1.29915856+0.j,
 0.64026459+0.j, 0.64026459+0.j, 1.28052918+0.j, 0.56996051+0.j,
 0.56996051+0.j, 1.13992102+0.j, 0.72233446+0.j, 0.72233446+0.j,
 1.44466892+0.j, 0.45733097+0.j, 0.45733097+0.j, 0.91466194+0.j,
 0.63711684+0.j, 0.63711684+0.j, 1.27423369+0.j, 0.53421697+0.j,
 0.53421697+0.j, 1.06843395+0.j, 0.55881775+0.j, 0.55881775+0.j,
 1.1176355 +0.j, 0.558467  +0.j, 0.558467  +0.j, 1.116934  +0.j,
 0.59091015+0.j, 0.59091015+0.j, 1.1818203 +0.j, 0.46851598+0.j,
 0.46851598+0.j, 0.93703195+0.j, 0.28011274+0.j, 0.28011274+0.j,
 0.56022547+0.j, 0.58531893+0.j, 0.58531893+0.j, 1.17063787+0.j,
 0.31446315+0.j, 0.31446315+0.j, 0.6289263 +0.j])
Observable: SparsePauliOp(['IIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIII'],
              coeffs=[1.+0.j])
Target MPS maximum bond dimension: 5
Number of AQC parameters: 816
Starting fidelity of AQC portion: 0.9914382555614002
2024-12-17 14:52:23.400028 Intermediate result: Fidelity 0.99764093
2024-12-17 14:52:23.429669 Intermediate result: Fidelity 0.99788003
2024-12-17 14:52:23.459674 Intermediate result: Fidelity 0.99795970
2024-12-17 14:52:23.489666 Intermediate result: Fidelity 0.99799067
2024-12-17 14:52:23.518545 Intermediate result: Fidelity 0.99803401
2024-12-17 14:52:23.546952 Intermediate result: Fidelity 0.99809821
2024-12-17 14:52:23.575271 Intermediate result: Fidelity 0.99824660
2024-12-17 14:52:23.604049 Intermediate result: Fidelity 0.99845326
2024-12-17 14:52:23.632709 Intermediate result: Fidelity 0.99870497
2024-12-17 14:52:23.660527 Intermediate result: Fidelity 0.99891442
2024-12-17 14:52:23.688273 Intermediate result: Fidelity 0.99904488
2024-12-17 14:52:23.716105 Intermediate result: Fidelity 0.99914438
2024-12-17 14:52:23.744336 Intermediate result: Fidelity 0.99922827
2024-12-17 14:52:23.773399 Intermediate result: Fidelity 0.99929071
2024-12-17 14:52:23.801482 Intermediate result: Fidelity 0.99932432
2024-12-17 14:52:23.830466 Intermediate result: Fidelity 0.99936460
2024-12-17 14:52:23.860738 Intermediate result: Fidelity 0.99938891
2024-12-17 14:52:23.889958 Intermediate result: Fidelity 0.99940607
2024-12-17 14:52:23.918703 Intermediate result: Fidelity 0.99941965
2024-12-17 14:52:23.949744 Intermediate result: Fidelity 0.99944337
2024-12-17 14:52:23.980871 Intermediate result: Fidelity 0.99946875
2024-12-17 14:52:24.012124 Intermediate result: Fidelity 0.99949009
2024-12-17 14:52:24.044359 Intermediate result: Fidelity 0.99952191
2024-12-17 14:52:24.075840 Intermediate result: Fidelity 0.99953669
2024-12-17 14:52:24.106303 Intermediate result: Fidelity 0.99955242
2024-12-17 14:52:24.139329 Intermediate result: Fidelity 0.99958412
2024-12-17 14:52:24.169725 Intermediate result: Fidelity 0.99960176
2024-12-17 14:52:24.198749 Intermediate result: Fidelity 0.99961606
2024-12-17 14:52:24.227874 Intermediate result: Fidelity 0.99963811
2024-12-17 14:52:24.256818 Intermediate result: Fidelity 0.99964383
2024-12-17 14:52:24.285889 Intermediate result: Fidelity 0.99964717
2024-12-17 14:52:24.315228 Intermediate result: Fidelity 0.99966064
2024-12-17 14:52:24.345322 Intermediate result: Fidelity 0.99966517
2024-12-17 14:52:24.374921 Intermediate result: Fidelity 0.99967089
2024-12-17 14:52:24.404309 Intermediate result: Fidelity 0.99968305
2024-12-17 14:52:24.432664 Intermediate result: Fidelity 0.99968889
2024-12-17 14:52:24.461639 Intermediate result: Fidelity 0.99969997
2024-12-17 14:52:24.491244 Intermediate result: Fidelity 0.99971666
2024-12-17 14:52:24.520354 Intermediate result: Fidelity 0.99972441
2024-12-17 14:52:24.549965 Intermediate result: Fidelity 0.99973561
2024-12-17 14:52:24.583464 Intermediate result: Fidelity 0.99973811
2024-12-17 14:52:24.617537 Intermediate result: Fidelity 0.99974074
2024-12-17 14:52:24.652247 Intermediate result: Fidelity 0.99974467
2024-12-17 14:52:24.686831 Intermediate result: Fidelity 0.99974991
2024-12-17 14:52:24.725476 Intermediate result: Fidelity 0.99975230
2024-12-17 14:52:24.764637 Intermediate result: Fidelity 0.99975373
2024-12-17 14:52:24.802499 Intermediate result: Fidelity 0.99975552
2024-12-17 14:52:24.839960 Intermediate result: Fidelity 0.99975885
2024-12-17 14:52:24.877472 Intermediate result: Fidelity 0.99976469
2024-12-17 14:52:24.916233 Intermediate result: Fidelity 0.99976517
2024-12-17 14:52:24.993750 Intermediate result: Fidelity 0.99976875
2024-12-17 14:52:25.034953 Intermediate result: Fidelity 0.99976887
2024-12-17 14:52:25.076197 Intermediate result: Fidelity 0.99977244
2024-12-17 14:52:25.112340 Intermediate result: Fidelity 0.99977638
2024-12-17 14:52:25.149947 Intermediate result: Fidelity 0.99977828
2024-12-17 14:52:25.190049 Intermediate result: Fidelity 0.99978174
2024-12-17 14:52:25.310903 Intermediate result: Fidelity 0.99978222
2024-12-17 14:52:25.347512 Intermediate result: Fidelity 0.99978508
2024-12-17 14:52:25.385201 Intermediate result: Fidelity 0.99978543
2024-12-17 14:52:25.457436 Intermediate result: Fidelity 0.99978770
2024-12-17 14:52:25.497133 Intermediate result: Fidelity 0.99978818
2024-12-17 14:52:25.541179 Intermediate result: Fidelity 0.99978913
2024-12-17 14:52:25.584791 Intermediate result: Fidelity 0.99978937
2024-12-17 14:52:25.621484 Intermediate result: Fidelity 0.99979068
2024-12-17 14:52:25.655847 Intermediate result: Fidelity 0.99979211
2024-12-17 14:52:25.691710 Intermediate result: Fidelity 0.99979700
2024-12-17 14:52:25.767711 Intermediate result: Fidelity 0.99979759
2024-12-17 14:52:25.804517 Intermediate result: Fidelity 0.99979807
2024-12-17 14:52:25.839394 Intermediate result: Fidelity 0.99980236
2024-12-17 14:52:25.874438 Intermediate result: Fidelity 0.99980296
2024-12-17 14:52:25.909900 Intermediate result: Fidelity 0.99980320
2024-12-17 14:52:26.713044 Intermediate result: Fidelity 0.99980320
Done after 72 iterations.
Fidelity of AQC portion: 0.9998108844412502
ISA circuit two-qubit depth: 33
Exiting before hardware execution since `dry_run` is True.

Langkah seterusnya

Cadangan

Untuk menyelami lebih dalam addon Qiskit AQC-Tensor, lihat tutorial Improved Trotterized Time Evolution with Approximate Quantum Compilation atau repositori qiskit-addon-aqc-tensor.

%%writefile ./source_files/template_hamiltonian_simulation_full.py

from qiskit import QuantumCircuit
from qiskit_serverless import get_arguments, save_result

# Extract parameters from arguments
#
# Do this at the top of the program so it fails early if any required arguments are missing or invalid.

arguments = get_arguments()

dry_run = arguments.get("dry_run", False)
backend_name = arguments["backend_name"]

aqc_evolution_time = arguments["aqc_evolution_time"]
aqc_ansatz_num_trotter_steps = arguments["aqc_ansatz_num_trotter_steps"]
aqc_target_num_trotter_steps = arguments["aqc_target_num_trotter_steps"]

remainder_evolution_time = arguments["remainder_evolution_time"]
remainder_num_trotter_steps = arguments["remainder_num_trotter_steps"]

# Stop if this fidelity is achieved
aqc_stopping_fidelity = arguments.get("aqc_stopping_fidelity", 1.0)
# Stop after this number of iterations, even if stopping fidelity is not achieved
aqc_max_iterations = arguments.get("aqc_max_iterations", 500)

hamiltonian = arguments["hamiltonian"]
observable = arguments["observable"]
initial_state = arguments.get("initial_state", QuantumCircuit(hamiltonian.num_qubits))

import numpy as np
import json
from mergedeep import merge

# Configure `EstimatorOptions`, to control the parameters of the hardware experiment
#
# Set default options
estimator_default_options = {
    "resilience": {
        "measure_mitigation": True,
        "zne_mitigation": True,
        "zne": {
            "amplifier": "gate_folding",
            "noise_factors": [1, 2, 3],
            "extrapolated_noise_factors": list(np.linspace(0, 3, 31)),
            "extrapolator": ["exponential", "linear", "fallback"],
        },
        "measure_noise_learning": {
            "num_randomizations": 512,
            "shots_per_randomization": 512,
        },
    },
    "twirling": {
        "enable_gates": True,
        "enable_measure": True,
        "num_randomizations": 300,
        "shots_per_randomization": 100,
        "strategy": "active",
    },
}
# Merge with user-provided options
estimator_options = merge(
    arguments.get("estimator_options", {}), estimator_default_options
)

print("estimator_options =", json.dumps(estimator_options, indent=4))

# Perform parameter validation

if not 0.0 < aqc_stopping_fidelity <= 1.0:
    raise ValueError(
        f"Invalid stopping fidelity: {aqc_stopping_fidelity}.  It must be a positive float no greater than 1."
    )

output = {}

import os
os.environ["NUMBA_CACHE_DIR"] = "/data"

import datetime
import quimb.tensor
from scipy.optimize import OptimizeResult, minimize
from qiskit.synthesis import SuzukiTrotter
from qiskit_addon_utils.problem_generators import generate_time_evolution_circuit
from qiskit_addon_aqc_tensor.ansatz_generation import (
    generate_ansatz_from_circuit,
    AnsatzBlock,
)
from qiskit_addon_aqc_tensor.simulation import (
    tensornetwork_from_circuit,
    compute_overlap,
)
from qiskit_addon_aqc_tensor.simulation.quimb import QuimbSimulator
from qiskit_addon_aqc_tensor.objective import OneMinusFidelity

print("Hamiltonian:", hamiltonian)
print("Observable:", observable)
simulator_settings = QuimbSimulator(quimb.tensor.CircuitMPS, autodiff_backend="jax")

# Construct the AQC target circuit
aqc_target_circuit = initial_state.copy()
if aqc_evolution_time:
    aqc_target_circuit.compose(
        generate_time_evolution_circuit(
            hamiltonian,
            synthesis=SuzukiTrotter(reps=aqc_target_num_trotter_steps),
            time=aqc_evolution_time,
        ),
        inplace=True,
    )

# Construct matrix-product state representation of the AQC target state
aqc_target_mps = tensornetwork_from_circuit(aqc_target_circuit, simulator_settings)
print("Target MPS maximum bond dimension:", aqc_target_mps.psi.max_bond())
output["target_bond_dimension"] = aqc_target_mps.psi.max_bond()

# Generate an ansatz and initial parameters from a Trotter circuit with fewer steps
aqc_good_circuit = initial_state.copy()
if aqc_evolution_time:
    aqc_good_circuit.compose(
        generate_time_evolution_circuit(
            hamiltonian,
            synthesis=SuzukiTrotter(reps=aqc_ansatz_num_trotter_steps),
            time=aqc_evolution_time,
        ),
        inplace=True,
    )
aqc_ansatz, aqc_initial_parameters = generate_ansatz_from_circuit(aqc_good_circuit)
print("Number of AQC parameters:", len(aqc_initial_parameters))
output["num_aqc_parameters"] = len(aqc_initial_parameters)

# Calculate the fidelity of ansatz circuit vs. the target state, before optimization
good_mps = tensornetwork_from_circuit(aqc_good_circuit, simulator_settings)
starting_fidelity = abs(compute_overlap(good_mps, aqc_target_mps)) ** 2
print("Starting fidelity of AQC portion:", starting_fidelity)
output["aqc_starting_fidelity"] = starting_fidelity

# Optimize the ansatz parameters by using MPS calculations
def callback(intermediate_result: OptimizeResult):
    fidelity = 1 - intermediate_result.fun
    print(f"{datetime.datetime.now()} Intermediate result: Fidelity {fidelity:.8f}")
    if intermediate_result.fun < stopping_point:
        raise StopIteration

objective = OneMinusFidelity(aqc_target_mps, aqc_ansatz, simulator_settings)
stopping_point = 1.0 - aqc_stopping_fidelity

result = minimize(
    objective,
    aqc_initial_parameters,
    method="L-BFGS-B",
    jac=True,
    options={"maxiter": aqc_max_iterations},
    callback=callback,
)
if result.status not in (
    0,
    1,
    99,
):  # 0 => success; 1 => max iterations reached; 99 => early termination via StopIteration
    raise RuntimeError(
        f"Optimization failed: {result.message} (status={result.status})"
    )
print(f"Done after {result.nit} iterations.")
output["num_iterations"] = result.nit
aqc_final_parameters = result.x
output["aqc_final_parameters"] = list(aqc_final_parameters)

# Construct an optimized circuit for initial portion of time evolution
aqc_final_circuit = aqc_ansatz.assign_parameters(aqc_final_parameters)

# Calculate fidelity after optimization
aqc_final_mps = tensornetwork_from_circuit(aqc_final_circuit, simulator_settings)
aqc_fidelity = abs(compute_overlap(aqc_final_mps, aqc_target_mps)) ** 2
print("Fidelity of AQC portion:", aqc_fidelity)
output["aqc_fidelity"] = aqc_fidelity

# Construct final circuit, with remainder of time evolution
final_circuit = aqc_final_circuit.copy()
if remainder_evolution_time:
    remainder_circuit = generate_time_evolution_circuit(
        hamiltonian,
        synthesis=SuzukiTrotter(reps=remainder_num_trotter_steps),
        time=remainder_evolution_time,
    )
    final_circuit.compose(remainder_circuit, inplace=True)

from qiskit_ibm_runtime import QiskitRuntimeService
from qiskit.transpiler import generate_preset_pass_manager

service = QiskitRuntimeService()
backend = service.backend(backend_name)

# Transpile PUBs (circuits and observables) to match ISA
pass_manager = generate_preset_pass_manager(backend=backend, optimization_level=3)
isa_circuit = pass_manager.run(final_circuit)
isa_observable = observable.apply_layout(isa_circuit.layout)

isa_2qubit_depth = isa_circuit.depth(lambda x: x.operation.num_qubits == 2)
print("ISA circuit two-qubit depth:", isa_2qubit_depth)
output["twoqubit_depth"] = isa_2qubit_depth

# Exit now if dry run; don't execute on hardware
if dry_run:
    import sys

    print("Exiting before hardware execution since `dry_run` is True.")
    save_result(output)
    sys.exit(0)

# ## Step 3: Execute quantum experiments on backend
from qiskit_ibm_runtime import EstimatorV2 as Estimator

estimator = Estimator(backend, options=estimator_options)

# Submit the underlying Estimator job. Note that this is not the
# actual function job.
job = estimator.run([(isa_circuit, isa_observable)])
print("Job ID:", job.job_id())
output["job_id"] = job.job_id()

# Wait until job is complete
hw_results = job.result()
hw_results_dicts = [pub_result.data.__dict__ for pub_result in hw_results]

# Save hardware results to serverless output dictionary
output["hw_results"] = hw_results_dicts

# Reorganize expectation values
hw_expvals = [pub_result_data["evs"].tolist() for pub_result_data in hw_results_dicts]

# Save expectation values to Qiskit Serverless
output["hw_expvals"] = hw_expvals[0]

save_result(output)

Overwriting ./source_files/template_hamiltonian_simulation_full.py

Kod sumber program penuh

Berikut ialah keseluruhan sumber ./source_files/template_hamiltonian_simulation.py dalam satu blok kod.

# This cell is hidden from users.  It verifies both source listings are identical then deletes the working folder we created
import shutil

with open("./source_files/template_hamiltonian_simulation.py") as f1:
    with open("./source_files/template_hamiltonian_simulation_full.py") as f2:
        assert f1.read() == f2.read()

shutil.rmtree("./source_files/")