Construiește un șablon de funcție pentru simularea Hamiltonian
Acest șablon încapsulează un flux de lucru pentru a simula evoluția în timp a unei stări inițiale față de un Hamiltonian bazat pe spin definit de utilizator și returnează un set de valori de așteptare specificate, folosind componenta suplimentară AQC.
Acest șablon este structurat ca un tipar Qiskit cu următorii pași:
1. Colectarea intrărilor și maparea problemei
Această secțiune primește ca intrare Hamiltonianul de simulat, o stare inițială sub forma unui QuantumCircuit, un set de observabile pentru estimarea valorilor de așteptare și o specificație de opțiuni pentru componenta suplimentară AQC. Acest pas validează că toate datele de intrare obligatorii sunt prezente și că se află în formatul corect.
Argumentele de intrare sunt apoi folosite pentru a construi circuitele cuantice și operatorii relevanți pentru flux. Se creează un circuit țintă și se găsește o reprezentare de tip produs matricial al stărilor pentru acest circuit folosind componenta suplimentară AQC. Ulterior, un circuit ansatz este generat și optimizat folosind metode de rețele tensoriale, producând un circuit final care execută restul evoluției în timp.
2. Pregătirea circuitelor generate pentru execuție
Circuitele generate de componenta suplimentară AQC sunt apoi transpilate pentru a fi executate pe un Backend ales. O instanță EstimatorV2 este creată cu un set implicit de opțiuni de atenuare a erorilor pentru a gestiona execuția circuitului.
3. Execuție
În final, circuitul ansatz este transpilat și executat pe un QPU și colectează estimări pentru toate valorile de așteptare specificate, care sunt returnate într-un format serializabil pentru a fi accesate de utilizator.
Scrie șablonul de funcție
Mai întâi, scrie un șablon de funcție pentru simularea Hamiltonian care folosește componenta suplimentară AQC-Tensor Qiskit pentru a mapa descrierea problemei la un circuit de adâncime redusă pentru execuție pe hardware.
Pe parcurs, codul este salvat în ./source_files/template_hamiltonian_simulation.py. Acest fișier este șablonul de funcție pe care îl poți încărca și rula de la distanță cu 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)
Colectează și validează intrările
Începe prin obținerea intrărilor pentru șablon. Acest exemplu are intrări specifice domeniului, relevante pentru simularea Hamiltonian (cum ar fi Hamiltonianul și observabilul), și opțiuni specifice capacității (cum ar fi cât de mult vrei să comprimi straturile inițiale ale circuitului Trotter folosind AQC-Tensor, sau opțiuni avansate pentru ajustarea fină a suprimării și atenuării erorilor față de valorile implicite care fac parte din acest exemplu).
%%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
Când șablonul de funcție rulează, este util să returnezi informații în jurnale folosind instrucțiuni print, astfel încât să poți evalua mai bine progresul sarcinii de lucru. Mai jos este un exemplu simplu de afișare a estimator_options, astfel încât să existe o înregistrare a opțiunilor efective ale Estimator utilizate. Există multe alte exemple similare în cadrul programului pentru a raporta progresul în timpul execuției, inclusiv valoarea funcției obiectiv în componenta iterativă a AQC-Tensor și adâncimea pe doi qubiți a circuitului final din arhitectura setului de instrucțiuni (ISA) destinat execuției pe 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
Validarea intrărilor
Un aspect important al asigurării că șablonul poate fi reutilizat pentru o gamă largă de intrări este validarea intrărilor. Codul următor este un exemplu de verificare a faptului că fidelitatea de oprire în AQC-Tensor a fost specificată corespunzător și, în caz contrar, returnează un mesaj de eroare informativ despre cum să corectezi eroarea.
%%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
Pregătirea ieșirilor funcției
Mai întâi, pregătește un dicționar care să conțină toate ieșirile șablonului de funcție. Cheile vor fi adăugate în acest dicționar pe parcursul fluxului de lucru și acesta este returnat la sfârșitul programului.
%%writefile --append ./source_files/template_hamiltonian_simulation.py
output = {}
Appending to ./source_files/template_hamiltonian_simulation.py
Maparea problemei și preprocesarea circuitului cu AQC
Optimizarea AQC-Tensor are loc în pasul 1 al unui tipar Qiskit. Mai întâi, se construiește o stare țintă. În acest exemplu, aceasta este construită dintr-un circuit țintă care evoluează același Hamiltonian pentru aceeași perioadă de timp ca și porțiunea AQC. Apoi, un ansatz este generat dintr-un circuit echivalent, dar cu mai puțini pași Trotter. În partea principală a algoritmului AQC, acel ansatz este adus iterativ mai aproape de starea țintă. În final, rezultatul este combinat cu restul pașilor Trotter necesari pentru a atinge timpul de evoluție dorit.
Observă exemplele suplimentare de jurnalizare încorporate în codul următor.
%%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
Optimizează circuitul final pentru execuție
După etapa AQC din flux, final_circuit este transpilat pentru hardware în mod obișnuit.
%%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
Ieșire anticipată în modul dry run
Dacă a fost selectat modul dry run, programul se oprește înainte de execuția pe hardware. Acest lucru poate fi util dacă, de exemplu, vrei să inspectezi mai întâi adâncimea two-qubit a circuitului ISA înainte de a decide să execuți pe 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
Execută circuitul pe 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
Salvează rezultatul
Acest șablon de funcție returnează rezultatele relevante la nivel de domeniu pentru acest flux de simulare Hamiltonian (valori de așteptare), împreună cu metadatele importante generate pe parcurs.
%%writefile --append ./source_files/template_hamiltonian_simulation.py
save_result(output)
Appending to ./source_files/template_hamiltonian_simulation.py
Deployează funcția pe IBM Quantum Platform
Secțiunea anterioară a creat un program care urmează să fie rulat de la distanță. Codul din această secțiune încarcă acel program în Qiskit Serverless.
Folosește qiskit-ibm-catalog pentru a te autentifica la QiskitServerless cu cheia ta API, pe care o găsești pe panoul de control IBM Quantum Platform, și încarcă programul.
Poți folosi opțional save_account() pentru a-ți salva credențialele (vezi ghidul Configurează-ți contul IBM Cloud). Reține că aceasta scrie credențialele tale în același fișier ca QiskitRuntimeService.save_account().
from qiskit_ibm_catalog import QiskitServerless, QiskitFunction
# Authenticate to the remote cluster and submit the pattern for remote execution
serverless = QiskitServerless()
Acest program are dependențe pip personalizate. Adaugă-le într-un array dependencies atunci când construiești instanța 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)
În final, pentru a verifica dacă programul a fost încărcat cu succes, folosește serverless.list():
serverless.list()
QiskitFunction(template_hamiltonian_simulation),
Rulează șablonul de funcție de la distanță
Șablonul de funcție a fost încărcat, astfel că îl poți rula de la distanță cu Qiskit Serverless. Mai întâi, încarcă șablonul după nume:
template = serverless.load("template_hamiltonian_simulation")
Apoi, rulează șablonul cu intrările de nivel de domeniu pentru simularea Hamiltonian. Acest exemplu specifică un model XXZ de 50 de Qubit cu cuplaje aleatoare, o stare inițială și un observabil.
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
Verifică starea jobului:
job.status()
'QUEUED'
După ce jobul rulează, poți prelua jurnalele create din ieșirile print(). Acestea pot oferi informații utile despre progresul fluxului de lucru pentru simularea Hamiltonian. De exemplu, valoarea funcției obiectiv pe parcursul componentei iterative a AQC sau adâncimea pe doi Qubiți a circuitului ISA final destinat execuției pe hardware.
print(job.logs())
No logs yet.
Blochează restul programului până când un rezultat este disponibil. După ce jobul este finalizat, poți recupera rezultatele. Acestea includ ieșirea de nivel de domeniu a simulării Hamiltonian (valoarea de așteptare) și metadate utile.
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}
După finalizarea jobului, întreaga ieșire de jurnal va fi disponibilă.
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.
Pași următori
Recomandări
Pentru o prezentare mai detaliată a addon-ului Qiskit AQC-Tensor, consultă tutorialul Improved Trotterized Time Evolution with Approximate Quantum Compilation sau depozitul qiskit-addon-aqc-tensor.
%%writefile ./source_files/template_hamiltonian_simulation_full.py
from qiskit import QuantumCircuit
from qiskit_serverless import get_arguments, save_result
# Extract parameters from arguments
#
# Do this at the top of the program so it fails early if any required arguments are missing or invalid.
arguments = get_arguments()
dry_run = arguments.get("dry_run", False)
backend_name = arguments["backend_name"]
aqc_evolution_time = arguments["aqc_evolution_time"]
aqc_ansatz_num_trotter_steps = arguments["aqc_ansatz_num_trotter_steps"]
aqc_target_num_trotter_steps = arguments["aqc_target_num_trotter_steps"]
remainder_evolution_time = arguments["remainder_evolution_time"]
remainder_num_trotter_steps = arguments["remainder_num_trotter_steps"]
# Stop if this fidelity is achieved
aqc_stopping_fidelity = arguments.get("aqc_stopping_fidelity", 1.0)
# Stop after this number of iterations, even if stopping fidelity is not achieved
aqc_max_iterations = arguments.get("aqc_max_iterations", 500)
hamiltonian = arguments["hamiltonian"]
observable = arguments["observable"]
initial_state = arguments.get("initial_state", QuantumCircuit(hamiltonian.num_qubits))
import numpy as np
import json
from mergedeep import merge
# Configure `EstimatorOptions`, to control the parameters of the hardware experiment
#
# Set default options
estimator_default_options = {
"resilience": {
"measure_mitigation": True,
"zne_mitigation": True,
"zne": {
"amplifier": "gate_folding",
"noise_factors": [1, 2, 3],
"extrapolated_noise_factors": list(np.linspace(0, 3, 31)),
"extrapolator": ["exponential", "linear", "fallback"],
},
"measure_noise_learning": {
"num_randomizations": 512,
"shots_per_randomization": 512,
},
},
"twirling": {
"enable_gates": True,
"enable_measure": True,
"num_randomizations": 300,
"shots_per_randomization": 100,
"strategy": "active",
},
}
# Merge with user-provided options
estimator_options = merge(
arguments.get("estimator_options", {}), estimator_default_options
)
print("estimator_options =", json.dumps(estimator_options, indent=4))
# Perform parameter validation
if not 0.0 < aqc_stopping_fidelity <= 1.0:
raise ValueError(
f"Invalid stopping fidelity: {aqc_stopping_fidelity}. It must be a positive float no greater than 1."
)
output = {}
import os
os.environ["NUMBA_CACHE_DIR"] = "/data"
import datetime
import quimb.tensor
from scipy.optimize import OptimizeResult, minimize
from qiskit.synthesis import SuzukiTrotter
from qiskit_addon_utils.problem_generators import generate_time_evolution_circuit
from qiskit_addon_aqc_tensor.ansatz_generation import (
generate_ansatz_from_circuit,
AnsatzBlock,
)
from qiskit_addon_aqc_tensor.simulation import (
tensornetwork_from_circuit,
compute_overlap,
)
from qiskit_addon_aqc_tensor.simulation.quimb import QuimbSimulator
from qiskit_addon_aqc_tensor.objective import OneMinusFidelity
print("Hamiltonian:", hamiltonian)
print("Observable:", observable)
simulator_settings = QuimbSimulator(quimb.tensor.CircuitMPS, autodiff_backend="jax")
# Construct the AQC target circuit
aqc_target_circuit = initial_state.copy()
if aqc_evolution_time:
aqc_target_circuit.compose(
generate_time_evolution_circuit(
hamiltonian,
synthesis=SuzukiTrotter(reps=aqc_target_num_trotter_steps),
time=aqc_evolution_time,
),
inplace=True,
)
# Construct matrix-product state representation of the AQC target state
aqc_target_mps = tensornetwork_from_circuit(aqc_target_circuit, simulator_settings)
print("Target MPS maximum bond dimension:", aqc_target_mps.psi.max_bond())
output["target_bond_dimension"] = aqc_target_mps.psi.max_bond()
# Generate an ansatz and initial parameters from a Trotter circuit with fewer steps
aqc_good_circuit = initial_state.copy()
if aqc_evolution_time:
aqc_good_circuit.compose(
generate_time_evolution_circuit(
hamiltonian,
synthesis=SuzukiTrotter(reps=aqc_ansatz_num_trotter_steps),
time=aqc_evolution_time,
),
inplace=True,
)
aqc_ansatz, aqc_initial_parameters = generate_ansatz_from_circuit(aqc_good_circuit)
print("Number of AQC parameters:", len(aqc_initial_parameters))
output["num_aqc_parameters"] = len(aqc_initial_parameters)
# Calculate the fidelity of ansatz circuit vs. the target state, before optimization
good_mps = tensornetwork_from_circuit(aqc_good_circuit, simulator_settings)
starting_fidelity = abs(compute_overlap(good_mps, aqc_target_mps)) ** 2
print("Starting fidelity of AQC portion:", starting_fidelity)
output["aqc_starting_fidelity"] = starting_fidelity
# Optimize the ansatz parameters by using MPS calculations
def callback(intermediate_result: OptimizeResult):
fidelity = 1 - intermediate_result.fun
print(f"{datetime.datetime.now()} Intermediate result: Fidelity {fidelity:.8f}")
if intermediate_result.fun < stopping_point:
raise StopIteration
objective = OneMinusFidelity(aqc_target_mps, aqc_ansatz, simulator_settings)
stopping_point = 1.0 - aqc_stopping_fidelity
result = minimize(
objective,
aqc_initial_parameters,
method="L-BFGS-B",
jac=True,
options={"maxiter": aqc_max_iterations},
callback=callback,
)
if result.status not in (
0,
1,
99,
): # 0 => success; 1 => max iterations reached; 99 => early termination via StopIteration
raise RuntimeError(
f"Optimization failed: {result.message} (status={result.status})"
)
print(f"Done after {result.nit} iterations.")
output["num_iterations"] = result.nit
aqc_final_parameters = result.x
output["aqc_final_parameters"] = list(aqc_final_parameters)
# Construct an optimized circuit for initial portion of time evolution
aqc_final_circuit = aqc_ansatz.assign_parameters(aqc_final_parameters)
# Calculate fidelity after optimization
aqc_final_mps = tensornetwork_from_circuit(aqc_final_circuit, simulator_settings)
aqc_fidelity = abs(compute_overlap(aqc_final_mps, aqc_target_mps)) ** 2
print("Fidelity of AQC portion:", aqc_fidelity)
output["aqc_fidelity"] = aqc_fidelity
# Construct final circuit, with remainder of time evolution
final_circuit = aqc_final_circuit.copy()
if remainder_evolution_time:
remainder_circuit = generate_time_evolution_circuit(
hamiltonian,
synthesis=SuzukiTrotter(reps=remainder_num_trotter_steps),
time=remainder_evolution_time,
)
final_circuit.compose(remainder_circuit, inplace=True)
from qiskit_ibm_runtime import QiskitRuntimeService
from qiskit.transpiler import generate_preset_pass_manager
service = QiskitRuntimeService()
backend = service.backend(backend_name)
# Transpile PUBs (circuits and observables) to match ISA
pass_manager = generate_preset_pass_manager(backend=backend, optimization_level=3)
isa_circuit = pass_manager.run(final_circuit)
isa_observable = observable.apply_layout(isa_circuit.layout)
isa_2qubit_depth = isa_circuit.depth(lambda x: x.operation.num_qubits == 2)
print("ISA circuit two-qubit depth:", isa_2qubit_depth)
output["twoqubit_depth"] = isa_2qubit_depth
# Exit now if dry run; don't execute on hardware
if dry_run:
import sys
print("Exiting before hardware execution since `dry_run` is True.")
save_result(output)
sys.exit(0)
# ## Step 3: Execute quantum experiments on backend
from qiskit_ibm_runtime import EstimatorV2 as Estimator
estimator = Estimator(backend, options=estimator_options)
# Submit the underlying Estimator job. Note that this is not the
# actual function job.
job = estimator.run([(isa_circuit, isa_observable)])
print("Job ID:", job.job_id())
output["job_id"] = job.job_id()
# Wait until job is complete
hw_results = job.result()
hw_results_dicts = [pub_result.data.__dict__ for pub_result in hw_results]
# Save hardware results to serverless output dictionary
output["hw_results"] = hw_results_dicts
# Reorganize expectation values
hw_expvals = [pub_result_data["evs"].tolist() for pub_result_data in hw_results_dicts]
# Save expectation values to Qiskit Serverless
output["hw_expvals"] = hw_expvals[0]
save_result(output)
Overwriting ./source_files/template_hamiltonian_simulation_full.py
Codul sursă complet al programului
Iată întregul cod sursă al fișierului ./source_files/template_hamiltonian_simulation.py într-un singur bloc de cod.
# 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/")