Gumawa ng function template para sa Hamiltonian simulation

Ang template na ito ay sumasaklaw sa isang workflow para sa pag-simulate ng time evolution ng isang initial state laban sa isang user-defined spin-based Hamiltonian at nagbabalik ng isang hanay ng mga tinukoy na expectation values gamit ang AQC addon.

Ang template na ito ay nakabalangkas bilang isang Qiskit pattern na may mga sumusunod na hakbang:

1. Pangongolekta ng input at pag-map ng problema

Ang seksyong ito ay tumatanggap bilang input ng Hamiltonian na isi-simulate, isang initial state sa anyo ng QuantumCircuit, isang hanay ng mga observable para sa pag-estimate ng expectation values, at isang pagtukoy ng mga opsyon para sa AQC addon. Bine-validate ng hakbang na ito na lahat ng kinakailangang input data ay naroroon at nasa tamang format.

Ang mga input argument ay ginagamit pagkatapos upang buuin ang mga kaugnay na quantum circuit at operator para sa workflow. Isang target circuit ang nilikha at isang matrix product state representation ng circuit na ito ang natagpuan gamit ang AQC addon. Kasunod nito, isang ansatz circuit ang nalilikha at ino-optimize gamit ang tensor network methods, na nagpo-produce ng final circuit na nag-e-execute ng natitirang bahagi ng time evolution.

2. Paghahanda ng mga nabuong circuit para sa execution

Ang mga nabuong circuit mula sa AQC addon ay ini-transpile para ma-execute sa isang piniling backend. Isang EstimatorV2 instance ang nilikha na may default na hanay ng mga error mitigation option para pamahalaan ang circuit execution.

3. Execution

Sa huli, ang ansatz circuit ay ini-transpile at ine-execute sa isang QPU at nangongolekta ng mga estimate para sa lahat ng tinukoy na expectation values, na ibinabalik sa isang serializable na format para ma-access ng user.

Isulat ang function template

Una, sumulat ng function template para sa Hamiltonian simulation na gumagamit ng AQC-Tensor Qiskit addon para i-map ang paglalarawan ng problema sa isang reduced-depth circuit para sa execution sa hardware.

Sa buong proseso, ang code ay sine-save sa ./source_files/template_hamiltonian_simulation.py. Ang file na ito ang function template na maaari mong i-upload at patakbuhin nang remote gamit ang 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)

Pangolektahin at i-validate ang mga input

Magsimula sa pamamagitan ng pagkuha ng mga input para sa template. Ang halimbawang ito ay may mga domain-specific na input na may kaugnayan sa Hamiltonian simulation (tulad ng Hamiltonian at observable) at mga capability-specific na opsyon (tulad ng kung gaano karami ang gusto mong i-compress ang mga initial layer ng Trotter circuit gamit ang AQC-Tensor, o mga advanced na opsyon para sa fine-tuning ng error suppression at mitigation na lampas sa mga default na bahagi ng halimbawang ito).

%%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

Kapag tumatakbo ang function template, kapaki-pakinabang na magbalik ng impormasyon sa mga log sa pamamagitan ng paggamit ng mga print statement, para mas madali mong masuri ang progreso ng workload. Sumusunod ay isang simpleng halimbawa ng pag-print ng estimator_options para may rekord ang mga aktwal na Estimator option na ginamit. Marami pang katulad na halimbawa sa buong programa para mag-ulat ng progreso sa panahon ng execution, kabilang ang halaga ng objective function sa panahon ng iterative na bahagi ng AQC-Tensor, at ang two-qubit depth ng final instruction set architecture (ISA) circuit na nilayong i-execute sa 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

I-validate ang mga input

Isang mahalagang aspeto ng pagtitiyak na ang template ay maaaring magamit muli sa iba't ibang input ay ang input validation. Ang sumusunod na code ay isang halimbawa ng pag-verify na ang stopping fidelity sa panahon ng AQC-Tensor ay naitakda nang tama at kung hindi, nagbababalik ng impormatibong mensahe ng error kung paano ayusin ang error.

%%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

Ihanda ang mga output ng function

Una, maghanda ng dictionary para hawakan ang lahat ng output ng function template. Ang mga key ay idadagdag sa dictionary na ito sa buong workflow, at ibinabalik ito sa katapusan ng programa.

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

output = {}

Appending to ./source_files/template_hamiltonian_simulation.py

I-map ang problema at i-pre-process ang circuit gamit ang AQC

Ang AQC-Tensor optimization ay nagaganap sa hakbang 1 ng isang Qiskit pattern. Una, isang target state ang binubuo. Sa halimbawang ito, ito ay binubuo mula sa isang target circuit na nag-e-evolve ng parehong Hamiltonian para sa parehong tagal ng panahon tulad ng bahagi ng AQC. Pagkatapos, isang ansatz ang nalilikha mula sa isang katumbas na circuit ngunit na may mas kaunting mga Trotter step. Sa pangunahing bahagi ng AQC algorithm, ang ansatz na iyon ay paulit-ulit na inilalapit sa target state. Sa wakas, ang resulta ay pinagsama sa natitirang mga Trotter step na kailangan para maabot ang nais na evolution time.

Tandaan ang mga karagdagang halimbawa ng logging na naka-incorporate sa sumusunod na code.

%%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

I-optimize ang final circuit para sa execution

Pagkatapos ng bahagi ng AQC ng workflow, ang final_circuit ay ini-transpile para sa hardware tulad ng karaniwan.

%%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

Lumabas nang maaga kung gumagamit ng dry run mode

Kung pinili ang dry run mode, ang programa ay titigil bago mag-execute sa hardware. Maaari itong maging kapaki-pakinabang kung, halimbawa, nais mo munang suriin ang two-qubit depth ng ISA circuit bago magpasya na mag-execute sa hardware.

%%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

I-execute ang circuit sa 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

I-save ang output

Ang function template na ito ay nagbabalik ng kaugnay na domain-level na output para sa Hamiltonian simulation workflow na ito (expectation values) kasama ang mahahalagang metadata na nabuong sa proseso.

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

save_result(output)

Appending to ./source_files/template_hamiltonian_simulation.py

I-deploy ang function sa IBM Quantum Platform

Ginawa ng nakaraang seksyon ang isang program na tatakbo nang malayo. Ang code sa seksyong ito ay nag-a-upload ng program na iyon sa Qiskit Serverless.

Gamitin ang qiskit-ibm-catalog para mag-authenticate sa QiskitServerless gamit ang iyong API key, na makikita sa IBM Quantum Platform dashboard, at i-upload ang program.

Maaari kang gumamit ng save_account() para i-save ang iyong mga kredensyal (tingnan ang gabay na Set up your IBM Cloud account). Tandaan na isusulat nito ang iyong mga kredensyal sa parehong file tulad ng QiskitRuntimeService.save_account().

from qiskit_ibm_catalog import QiskitServerless, QiskitFunction

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

Ang program na ito ay may custom na pip dependencies. Idagdag ang mga ito sa isang dependencies array kapag ginagawa ang QiskitFunction instance:

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)

Sa huli, para suriin kung matagumpay na na-upload ang program, gamitin ang serverless.list():

serverless.list()

QiskitFunction(template_hamiltonian_simulation),

Patakbuhin ang function template nang malayo

Na-upload na ang function template, kaya maaari mo na itong patakbuhin nang malayo gamit ang Qiskit Serverless. Una, i-load ang template ayon sa pangalan:

template = serverless.load("template_hamiltonian_simulation")

Susunod, patakbuhin ang template gamit ang mga domain-level na input para sa Hamiltonian simulation. Sa halimbawang ito, tinutukoy ang isang 50-qubit na XXZ model na may random na couplings, at isang initial state at 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

Suriin ang status ng job:

job.status()

'QUEUED'

Pagkatapos na tumatakbo na ang job, maaari kang kumuha ng mga log na nagmula sa mga print() na output. Makapagbibigay ito ng kapaki-pakinabang na impormasyon tungkol sa progreso ng Hamiltonian simulation workflow. Halimbawa, ang halaga ng objective function sa panahon ng iterative na bahagi ng AQC, o ang two-qubit depth ng panghuling ISA circuit na nilalayon para sa execution sa hardware.

print(job.logs())

No logs yet.

I-block ang natitirang bahagi ng program hanggang may available na resulta. Pagkatapos matapos ang job, maaari mong makuha ang mga resulta. Kasama rito ang domain-level na output ng Hamiltonian simulation (expectation value) at mga kapaki-pakinabang na metadata.

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}

Pagkatapos makumpleto ang job, ang buong logging output ay magiging available na.

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.

Mga Susunod na Hakbang

Mga Rekomendasyon

Para sa mas malalim na pag-aaral ng AQC-Tensor Qiskit addon, tingnan ang tutorial na Improved Trotterized Time Evolution with Approximate Quantum Compilation o ang 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

Buong source code ng programa

Narito ang buong source ng ./source_files/template_hamiltonian_simulation.py bilang isang code block.

# 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/")