สร้าง function template สำหรับ Hamiltonian simulation

template นี้ครอบคลุม workflow สำหรับจำลองการ time evolution ของ initial state กับ spin-based Hamiltonian ที่ผู้ใช้กำหนด และคืนค่า expectation values ที่ระบุไว้โดยใช้ AQC addon

template นี้มีโครงสร้างเป็น Qiskit pattern ที่มีขั้นตอนดังนี้:

1. รับ input และ map ปัญหา

ส่วนนี้รับ Hamiltonian ที่ต้องการจำลอง, initial state ในรูปแบบ QuantumCircuit, ชุด observables สำหรับประมาณ expectation values และข้อกำหนด options สำหรับ AQC addon ขั้นตอนนี้ตรวจสอบว่า input data ที่จำเป็นทั้งหมดมีอยู่ครบและอยู่ในรูปแบบที่ถูกต้อง

จากนั้น input arguments จะถูกนำไปสร้าง quantum circuits และ operators ที่เกี่ยวข้องสำหรับ workflow โดยจะสร้าง target circuit และหา matrix product state representation ของ circuit นี้โดยใช้ AQC addon หลังจากนั้นจะสร้าง ansatz circuit และปรับให้เหมาะสมด้วย tensor network methods เพื่อผลิต final circuit ที่รัน time evolution ที่เหลือ

2. เตรียม circuits ที่สร้างขึ้นสำหรับการ execution

circuits ที่สร้างจาก AQC addon จะถูก transpile เพื่อรันบน backend ที่เลือก และสร้าง instance ของ EstimatorV2 ด้วยชุด error mitigation options เริ่มต้นสำหรับจัดการการ execution ของ circuit

3. Execution

สุดท้าย ansatz circuit จะถูก transpile และรันบน QPU พร้อมรวบรวมค่าประมาณสำหรับ expectation values ทั้งหมดที่ระบุไว้ และคืนค่าในรูปแบบที่ serialize ได้เพื่อให้ผู้ใช้เข้าถึงได้

เขียน function template

ขั้นแรก ให้เขียน function template สำหรับ Hamiltonian simulation ที่ใช้ AQC-Tensor Qiskit addon เพื่อ map คำอธิบายปัญหาไปยัง circuit ที่มี depth ลดลงสำหรับการรันบน hardware

ตลอดกระบวนการ code จะถูกบันทึกไว้ที่ ./source_files/template_hamiltonian_simulation.py ไฟล์นี้คือ function template ที่สามารถ upload และรันจากระยะไกลด้วย 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)

รวบรวมและตรวจสอบ inputs

เริ่มจากการรับ inputs สำหรับ template ตัวอย่างนี้มี domain-specific inputs ที่เกี่ยวข้องกับ Hamiltonian simulation (เช่น Hamiltonian และ observable) และ capability-specific options (เช่น ต้องการบีบอัด initial layers ของ Trotter circuit ด้วย AQC-Tensor มากแค่ไหน หรือ advanced options สำหรับปรับ error suppression และ mitigation นอกเหนือจากค่า defaults ที่เป็นส่วนหนึ่งของตัวอย่างนี้)

%%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

เมื่อ function template กำลังทำงาน การคืนข้อมูลใน logs ด้วย print statements จะเป็นประโยชน์มาก เพื่อให้ประเมินความคืบหน้าของ workload ได้ดีขึ้น ต่อไปนี้เป็นตัวอย่างง่ายๆ ของการ print estimator_options เพื่อให้มีบันทึก Estimator options จริงที่ใช้ มีตัวอย่างคล้ายกันอีกมากตลอดโปรแกรมเพื่อรายงานความคืบหน้าระหว่าง execution รวมถึงค่าของ objective function ระหว่างส่วน iterative ของ AQC-Tensor และ two-qubit depth ของ final instruction set architecture (ISA) circuit ที่ตั้งใจรันบน hardware

%%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

ตรวจสอบ inputs

ด้านสำคัญของการทำให้ template สามารถนำกลับมาใช้ได้กับ inputs หลากหลายคือการตรวจสอบ input code ต่อไปนี้เป็นตัวอย่างการตรวจสอบว่า stopping fidelity ระหว่าง AQC-Tensor ถูกระบุอย่างเหมาะสมหรือไม่ และถ้าไม่ใช่ ให้คืนค่า error message ที่บอกวิธีแก้ไข

%%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

เตรียม function outputs

ขั้นแรก เตรียม dictionary เพื่อเก็บ function template outputs ทั้งหมด Keys จะถูกเพิ่มเข้า dictionary นี้ตลอด workflow และจะถูกคืนค่าเมื่อโปรแกรมสิ้นสุด

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

output = {}

Appending to ./source_files/template_hamiltonian_simulation.py

Map ปัญหาและ pre-process circuit ด้วย AQC

การ optimize ด้วย AQC-Tensor เกิดขึ้นใน step 1 ของ Qiskit pattern ขั้นแรกสร้าง target state ในตัวอย่างนี้ สร้างจาก target circuit ที่ evolve Hamiltonian เดียวกันในช่วงเวลาเดียวกับส่วน AQC จากนั้นสร้าง ansatz จาก circuit ที่เทียบเท่าแต่มี Trotter steps น้อยกว่า ในส่วนหลักของ AQC algorithm ansatz นั้นจะถูกนำเข้าใกล้ target state แบบ iterative สุดท้าย ผลลัพธ์จะรวมกับ Trotter steps ที่เหลือที่ต้องการเพื่อไปถึง evolution time ที่ต้องการ

สังเกตตัวอย่างเพิ่มเติมของการ logging ที่รวมไว้ใน code ต่อไปนี้

%%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

Optimize the final circuit for execution

หลังจากผ่านขั้นตอน AQC แล้ว final_circuit จะถูก transpile สำหรับฮาร์ดแวร์ ตามปกติ

%%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

Exit early if using dry run mode

ถ้าเลือกโหมด dry run โปรแกรมจะหยุดก่อนที่จะรันบนฮาร์ดแวร์ ซึ่งมีประโยชน์เช่น ถ้าอยากตรวจสอบ two-qubit depth ของ ISA Circuit ก่อนตัดสินใจรันบนฮาร์ดแวร์จริง

%%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

Execute the circuit on hardware

%%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

Save the output

function template นี้จะคืนค่า output ในระดับ domain ที่เกี่ยวข้องกับ workflow การจำลอง Hamiltonian (expectation values) พร้อมกับ metadata สำคัญที่สร้างขึ้นระหว่างกระบวนการ

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

save_result(output)

Appending to ./source_files/template_hamiltonian_simulation.py

Deploy the function to IBM Quantum Platform

ส่วนก่อนหน้าสร้างโปรแกรมสำหรับรันจากระยะไกล โค้ดในส่วนนี้จะอัปโหลดโปรแกรมนั้นไปยัง Qiskit Serverless

ใช้ qiskit-ibm-catalog เพื่อยืนยันตัวตนกับ QiskitServerless ด้วย API key ซึ่งหาได้จากหน้าแดชบอร์ด IBM Quantum Platform แล้วอัปโหลดโปรแกรม

ถ้าต้องการบันทึก credentials ไว้ใช้ทีหลัง ใช้ save_account() ได้ (ดูคู่มือ Set up your IBM Cloud account) โปรดทราบว่าวิธีนี้จะเขียน credentials ลงไฟล์เดียวกับ QiskitRuntimeService.save_account().

from qiskit_ibm_catalog import QiskitServerless, QiskitFunction

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

โปรแกรมนี้มี dependency ของ pip เพิ่มเติม ให้ใส่ไว้ใน array dependencies ตอนสร้าง instance ของ 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)

สุดท้าย ตรวจสอบว่าโปรแกรมอัปโหลดสำเร็จหรือไม่ด้วย serverless.list():

serverless.list()

QiskitFunction(template_hamiltonian_simulation),

Run the function template remotely

function template ถูกอัปโหลดแล้ว จึงสามารถรันจากระยะไกลด้วย Qiskit Serverless ได้ ขั้นแรกโหลด template ตามชื่อ:

template = serverless.load("template_hamiltonian_simulation")

ต่อไปรัน template ด้วย input ระดับ domain สำหรับการจำลอง Hamiltonian ตัวอย่างนี้กำหนดโมเดล XXZ ขนาด 50 Qubit ที่มีค่า coupling แบบสุ่ม พร้อม initial state และ observable

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

ตรวจสอบสถานะของ job:

job.status()

'QUEUED'

หลังจาก job เริ่มรันแล้ว สามารถดึง log ที่สร้างจาก output ของ print() ได้ ข้อมูลเหล่านี้ให้รายละเอียดที่เป็นประโยชน์เกี่ยวกับความคืบหน้าของ workflow การจำลอง Hamiltonian เช่น ค่าของ objective function ระหว่างขั้นตอน iterative ของ AQC หรือ two-qubit depth ของ ISA Circuit สุดท้ายที่จะรันบน hardware

print(job.logs())

No logs yet.

บล็อกส่วนที่เหลือของโปรแกรมไว้จนกว่าจะได้ผลลัพธ์ เมื่อ job เสร็จแล้ว สามารถดึงผลลัพธ์มาได้ ซึ่งรวมถึง output ระดับ domain ของการจำลอง Hamiltonian (ค่าความคาดหวัง) และ metadata ที่มีประโยชน์

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}

หลังจาก job เสร็จสมบูรณ์ output ของ logging ทั้งหมดจะพร้อมใช้งาน

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.

ขั้นตอนถัดไป

คำแนะนำ

สำหรับการศึกษา AQC-Tensor Qiskit addon เพิ่มเติม ลองดู tutorial Improved Trotterized Time Evolution with Approximate Quantum Compilation หรือ qiskit-addon-aqc-tensor repository

%%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

ซอร์สโค้ดโปรแกรมฉบับเต็ม

นี่คือซอร์สโค้ดทั้งหมดของ ./source_files/template_hamiltonian_simulation.py ในรูปแบบ code block เดียว

# 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/")