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해밀턴 시뮬레이션을 위한 Qiskit 함수 템플릿 구축

이 템플릿은 사용자가 정의한 스핀 기반 해밀토니언에 대한 초기 상태의 시간 진화를 시뮬레이션하는 워크플로를 캡슐화하며, AQC-Tensor Qiskit 애드온을 사용하여 지정된 기대값 집합을 반환합니다.

이 템플릿은 다음 단계로 구성된 키스킷 패턴으로 구성되어 있습니다:

1. 입력 수집 및 문제 매핑

이 섹션에서는 시뮬레이션할 해밀턴, QuantumCircuit 형태의 초기 상태, 기대값을 추정하기 위한 관측 변수 세트, AQC 애드온의 옵션 사양을 입력으로 사용합니다. 이 단계에서는 필요한 모든 입력 데이터가 존재하고 올바른 형식인지 확인합니다.

그런 다음 입력 인수는 워크플로에 적합한 양자 회로와 연산자를 구성하는 데 사용됩니다. 대상 회로가 생성되고 AQC 애드온을 사용하여 이 회로의 행렬 곱 상태 표현을 찾습니다. 그 후 텐서 네트워크 방법을 사용하여 안사츠 회로를 생성하고 최적화하여 나머지 시간 진화를 실행하는 최종 회로를 생성합니다.

2. 생성된 회로를 실행할 수 있도록 준비한다

그런 다음 AQC 애드온에서 생성된 회로를 트랜스파일링하여 선택한 백엔드에서 실행합니다. 인스턴스는 EstimatorV2 인스턴스는 회로 실행을 관리하기 위한 기본 오류 완화 옵션 세트로 생성됩니다.

3. 실행

마지막으로, ansatz 회로는 트랜스파일링되어 QPU에서 실행되고 지정된 모든 기대값에 대한 추정치를 수집하며, 사용자가 액세스할 수 있도록 직렬화 가능한 형식으로 반환됩니다.

함수 템플릿을 작성하세요

먼저, AQC-Tensor Qiskit 애드온을 사용하여 문제 설명을 하드웨어에서 실행 가능한 축소 깊이 회로로 매핑하는 해밀턴 시뮬레이션용 함수 템플릿을 작성하십시오.

이 페이지를 다운로드하여 노트북 편집기에서 로컬로 열어보면, 일부 코드 셀에 ‘magic’ 명령어가 포함되어 있는 것을 %%writefile확인할 수 있습니다. 이 매직 커맨드는 코드를 에 저장합니다 ./source_files/template_hamiltonian_simulation.py. 이는 Qiskit Serverless 에 업로드하여 원격으로 실행할 수 있는 함수 템플릿입니다.

입력을 수집하고 검증합니다

템플릿에 대한 입력값을 가져오는 것부터 시작하세요. 이 예제에는 해밀턴 시뮬레이션과 관련된 도메인별 입력(예: 해밀턴 및 관측 가능)과 기능별 옵션(예: AQC-Tensor를 사용하여 트로터 회로의 초기 레이어를 얼마나 압축할지 또는 이 예제의 일부인 기본값 이상으로 오류 억제 및 완화를 미세 조정하는 고급 옵션)이 있습니다.

./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))
./source_files/template_hamiltonian_simulation.py (appended)
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
)

함수 템플릿이 실행 중일 때 인쇄 문을 사용하여 로그에 정보를 반환하면 워크로드의 진행 상황을 더 잘 평가할 수 있습니다. 다음은 실제 사용된 견적서 옵션을 기록할 수 있도록 estimator_options 을 출력하는 간단한 예제입니다. 프로그램 전체에 걸쳐 실행 중 진행 상황을 보고하는 유사한 예가 더 많이 있으며, 여기에는 AQC-Tensor의 반복 구성 요소 중 목적 함수의 값과 하드웨어에서 실행하기 위한 최종 명령 집합 아키텍처(ISA) 회로의 2쿼비트 깊이 등이 포함됩니다.

./source_files/template_hamiltonian_simulation.py (appended)
print("estimator_options =", json.dumps(estimator_options, indent=4))

입력값을 검증하십시오

다양한 입력에서 템플릿을 재사용할 수 있도록 하는 데 있어 중요한 측면은 입력 유효성 검사입니다. 다음 코드는 AQC-Tensor 중 중지 충실도가 적절하게 지정되었는지 확인하고, 그렇지 않은 경우 오류 해결 방법에 대한 정보성 오류 메시지를 반환하는 예제입니다.

./source_files/template_hamiltonian_simulation.py (appended)
# Perform parameter validation

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

함수 출력을 준비하십시오

먼저 모든 함수 템플릿 출력을 담을 사전을 준비합니다. 키는 워크플로 전반에 걸쳐 이 사전에 추가되며, 프로그램이 끝날 때 반환됩니다.

./source_files/template_hamiltonian_simulation.py (appended)
output = {}

문제를 매핑하고 AQC로 회로를 전처리합니다

AQC-텐서 최적화는 키스킷 패턴의 1단계에서 이루어집니다. 먼저 대상 상태를 구성합니다. 이 예제에서는 AQC 부분과 동일한 기간 동안 동일한 해밀턴을 진화시키는 타겟 회로로 구성됩니다. 그런 다음 등가 회로에서 안사츠가 생성되지만 트로터 단계가 더 적습니다. AQC 알고리즘의 주요 부분에서는 해당 안사츠가 반복적으로 목표 상태에 가까워집니다. 마지막으로, 원하는 진화 시간에 도달하는 데 필요한 나머지 트로터 단계와 결과를 결합합니다.

다음 코드에 포함된 로깅의 추가 예시를 참고하세요.

./source_files/template_hamiltonian_simulation.py (appended)
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)

최종 회로를 실행에 최적화하십시오

워크플로의 AQC 부분 이후에는 final_circuit 하드웨어에 대해서는 평소와 같이 변환 됩니다.

./source_files/template_hamiltonian_simulation.py (appended)
from qiskit_serverless import get_runtime_service
from qiskit.transpiler import generate_preset_pass_manager

service = get_runtime_service()
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

드라이 런 모드를 사용할 경우 조기에 종료하십시오

드라이 실행 모드를 선택한 경우 하드웨어에서 실행하기 전에 프로그램이 중지됩니다. 예를 들어 하드웨어에서 실행을 결정하기 전에 먼저 ISA 회로의 2쿼비트 깊이를 검사하려는 경우 유용할 수 있습니다.

./source_files/template_hamiltonian_simulation.py (appended)
# 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)

회로를 하드웨어에서 실행하다

./source_files/template_hamiltonian_simulation.py (appended)
# ## 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]

출력 저장

이 함수 템플릿은 이 해밀턴 시뮬레이션 워크플로에 대한 관련 도메인 수준 출력(기대값)과 함께 그 과정에서 생성된 중요한 메타데이터를 반환합니다.

./source_files/template_hamiltonian_simulation.py (appended)
save_result(output)

함수를 IBM Quantum Platform 에 배포하세요

이전 섹션에서는 원격으로 실행할 프로그램을 만들었습니다. 이 섹션의 코드는 해당 프로그램을 키스킷 서버리스에 업로드합니다.

qiskit-ibm-catalog 을 사용하여 IBM 퀀텀 플랫폼 대시보드에서 찾을 수 있는 API 키로 QiskitServerless 에 인증하고 프로그램을 업로드합니다.

선택적으로 를 사용하여 save_account() 자격 증명을 저장할 수 있습니다( IBM Cloud 계정 설정 가이드 참조). 참고: 이 명령어는 사용자 자격 증명을 동일한 파일에 QiskitRuntimeService.save_account()기록합니다.

from qiskit_ibm_catalog import QiskitServerless, QiskitFunction

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

이 프로그램에는 사용자 지정 pip 종속성이 있습니다. QiskitFunction 인스턴스를 구성할 때 dependencies 배열에 추가합니다:

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)

Output:

QiskitFunction(template_hamiltonian_simulation)

마지막으로 프로그램이 성공적으로 업로드되었는지 확인하려면 serverless.list() 을 사용합니다:

serverless.list()

Output:

 QiskitFunction(template_hamiltonian_simulation),

함수 템플릿을 원격으로 실행하십시오

함수 템플릿이 업로드되었으므로 키스킷 서버리스에서 원격으로 실행할 수 있습니다. 먼저 템플릿을 이름으로 로드합니다:

template = serverless.load("template_hamiltonian_simulation")

다음으로 해밀턴 시뮬레이션을 위한 도메인 수준 입력으로 템플릿을 실행합니다. 이 예는 무작위 커플링과 초기 상태 및 관측 가능한 50-큐비트 XXZ 모델을 지정합니다.

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)

Output:

853b0edb-d63f-4629-be71-398b6dcf33cb

작업 상태를 확인합니다:

job.status()

Output:

'QUEUED'

작업이 실행된 후 print() 출력에서 생성된 로그를 가져올 수 있습니다. 이를 통해 해밀턴 시뮬레이션 워크플로우의 진행 상황에 대한 실행 가능한 정보를 얻을 수 있습니다. 예를 들어, AQC의 반복 구성 요소 중 목적 함수의 값 또는 하드웨어에서 실행하기 위한 최종 ISA 회로의 2쿼비트 깊이입니다.

print(job.logs())

Output:

No logs yet.

결과가 나올 때까지 나머지 프로그램을 차단합니다. 작업이 완료되면 결과를 검색할 수 있습니다. 여기에는 해밀턴 시뮬레이션의 도메인 수준 출력(기대값)과 유용한 메타데이터가 포함됩니다.

result = job.result()

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

Output:

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

작업이 완료되면 전체 로깅 출력을 사용할 수 있습니다.

print(job.logs())

Output:

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.

다음 단계

권장사항

AQC-텐서 키스킷 애드온에 대해 자세히 알아보려면 근사 양자 컴파일로 트로터화된 시간 진화 개선 자습서 또는 qiskit-addon-aqc-tensor 리포지토리를 확인하시기 바랍니다.

  • 다음은 하나의 코드 블록으로 된 ./source_files/template_hamiltonian_simulation.py 의 전체 소스입니다.

    ./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 hardware experiment's parameters
#
# 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.transpiler import generate_preset_pass_manager
from qiskit_ibm_catalog import QiskitFunctionsCatalog
from qiskit_serverless import get_runtime_service

service = get_runtime_service()
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)
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