בניית תבנית פונקציה לסימולציית המילטוניאן
תבנית זו עוטפת זרימת עבודה לסימולציית התפתחות זמן של מצב התחלתי מול המילטוניאן מבוסס ספין שמוגדר על ידי המשתמש, ומחזירה קבוצת ערכי ציפייה מוגדרים בעזרת תוסף AQC.
תבנית זו בנויה כ-Qiskit pattern עם השלבים הבאים:
1. איסוף קלט ומיפוי הבעיה
חלק זה מקבל כקלט את ההמילטוניאן לסימולציה, מצב התחלתי בצורת QuantumCircuit, קבוצת אופרטורים להערכת ערכי ציפייה, ומפרט אפשרויות לתוסף AQC. שלב זה מאמת שכל נתוני הקלט הנדרשים קיימים ושהם בפורמט הנכון.
ארגומנטי הקלט משמשים לאחר מכן לבניית מעגלים קוונטיים ואופרטורים רלוונטיים לזרימת העבודה. נוצר מעגל מטרה, ומוצגת ייצוג מצב מכפלת מטריצות (MPS) של המעגל הזה בעזרת תוסף AQC. בהמשך, נוצר מעגל ansatz ומבוצעת אופטימיזציה שלו בשיטות רשת טנסורים, ומייצרת מעגל סופי שמבצע את שארית התפתחות הזמן.
2. הכנת המעגלים שנוצרו לביצוע
המעגלים שנוצרו על ידי תוסף AQC עוברים טרנספילציה לביצוע על backend שנבחר. נוצר מופע של EstimatorV2 עם קבוצת אפשרויות ברירת מחדל להפחתת שגיאות לניהול ביצוע המעגל.
3. ביצוע
לבסוף, מעגל ה-ansatz עובר טרנספילציה ומורץ על QPU ואוסף אומדנים עבור כל ערכי הציפייה המוגדרים, המוחזרים בפורמט הניתן לסריאליזציה לגישה על ידי המשתמש.
כתיבת תבנית הפונקציה
ראשית, כתוב תבנית פונקציה לסימולציית המילטוניאן שמשתמשת ב-תוסף AQC-Tensor של Qiskit כדי למפות את תיאור הבעיה למעגל בעומק מצומצם לביצוע על חומרה.
לאורך כל הדרך, הקוד נשמר ב-./source_files/template_hamiltonian_simulation.py. קובץ זה הוא תבנית הפונקציה שאתה יכול להעלות ולהריץ מרחוק עם 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)
איסוף ואימות הקלטים
התחל בקבלת הקלטים לתבנית. לדוגמה זו יש קלטים ספציפיים לתחום הרלוונטיים לסימולציית המילטוניאן (כגון ההמילטוניאן והאופרטור) ואפשרויות ספציפיות ליכולת (כגון כמה רוצים לדחוס את השכבות הראשוניות של מעגל Trotter בעזרת AQC-Tensor, או אפשרויות מתקדמות לכוונון עדין של דיכוי ומיפחתת שגיאות מעבר לברירות המחדל שהן חלק מדוגמה זו).
%%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
כאשר תבנית הפונקציה פועלת, מועיל להחזיר מידע בלוגים באמצעות הצהרות print, כדי שתוכל להעריך טוב יותר את התקדמות עומס העבודה. להלן דוגמה פשוטה להדפסת estimator_options כדי שתהיה רשומה של אפשרויות ה-Estimator בפועל שבהן נעשה שימוש. ישנן דוגמאות דומות רבות נוספות לאורך התוכנית לדיווח על התקדמות במהלך הביצוע, כולל ערך פונקציית המטרה במהלך הרכיב האיטרטיבי של AQC-Tensor, ועומק שני-הקיוביטים של מעגל ה-ISA (ארכיטקטורת קבוצת ההוראות) הסופי המיועד לביצוע על חומרה.
%%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
אימות הקלטים
היבט חשוב להבטחת שהתבנית ניתנת לשימוש חוזר על פני טווח קלטים הוא אימות קלט. הקוד הבא הוא דוגמה לאימות שנאמנות העצירה במהלך AQC-Tensor צוינה כראוי, ואם לא, החזרת הודעת שגיאה אינפורמטיבית על כיצד לתקן את השגיאה.
%%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
הכנת פלטי הפונקציה
ראשית, הכן מילון כדי לשמור את כל פלטי תבנית הפונקציה. מפתחות יתווספו למילון זה לאורך זרימת העבודה, והוא מוחזר בסוף התוכנית.
%%writefile --append ./source_files/template_hamiltonian_simulation.py
output = {}
Appending to ./source_files/template_hamiltonian_simulation.py
מיפוי הבעיה ועיבוד מקדים של המעגל עם AQC
אופטימיזציית AQC-Tensor מתרחשת בשלב 1 של Qiskit pattern. ראשית, נבנה מצב מטרה. בדוגמה זו, הוא נבנה ממעגל מטרה שמפתח את אותו המילטוניאן לאותה תקופת זמן כמו חלק ה-AQC. לאחר מכן, נוצר ansatz ממעגל שקול אך עם פחות צעדי Trotter. בחלק הראשי של אלגוריתם AQC, ה-ansatz הזה מובא באופן איטרטיבי קרוב יותר למצב המטרה. לבסוף, התוצאה משולבת עם שאר צעדי Trotter הנדרשים להגיע לזמן ההתפתחות הרצוי.
שים לב לדוגמאות נוספות של רישום (logging) המשולבות בקוד הבא.
%%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
אופטימיזציה של המעגל הסופי לביצוע
לאחר חלק AQC של זרימת העבודה, ה-final_circuit עובר טרנספילציה לחומרה כרגיל.
%%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
יציאה מוקדמת אם משתמשים במצב ריצה יבשה
אם נבחר מצב ריצה יבשה, התוכנית נעצרת לפני ביצוע על חומרה. זה יכול להיות שימושי אם, למשל, רוצים תחילה לבדוק את עומק שני-הקיוביטים של מעגל ה-ISA לפני קבלת החלטה לבצע על חומרה.
%%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
ביצוע המעגל על חומרה
%%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
שמירת הפלט
תבנית פונקציה זו מחזירה את הפלט הרלוונטי לתחום עבור זרימת עבודה זו של סימולציית המילטוניאן (ערכי ציפייה) בנוסף למטא-דאטה חשוב שנוצר בדרך.
%%writefile --append ./source_files/template_hamiltonian_simulation.py
save_result(output)
Appending to ./source_files/template_hamiltonian_simulation.py
פריסת הפונקציה ב-IBM Quantum Platform
החלק הקודם יצר תוכנית להרצה מרחוק. הקוד בחלק זה מעלה את התוכנית הזו ל-Qiskit Serverless.
השתמש ב-qiskit-ibm-catalog לאימות ב-QiskitServerless עם מפתח ה-API שלך, שניתן למצוא בלוח המחוונים של IBM Quantum Platform, ולהעלאת התוכנית.
ניתן לבחרית להשתמש ב-save_account() לשמירת האישורים שלך (ראה את מדריך הגדרת חשבון IBM Cloud שלך). שים לב שפעולה זו כותבת את האישורים שלך לאותו הקובץ כמו QiskitRuntimeService.save_account().
from qiskit_ibm_catalog import QiskitServerless, QiskitFunction
# Authenticate to the remote cluster and submit the pattern for remote execution
serverless = QiskitServerless()
לתוכנית זו יש תלויות pip מותאמות אישית. הוסף אותן למערך dependencies בעת בניית מופע ה-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)
לבסוף, כדי לבדוק אם התוכנית הועלתה בהצלחה, השתמש ב-serverless.list():
serverless.list()
QiskitFunction(template_hamiltonian_simulation),
הרצת תבנית הפונקציה מרחוק
תבנית הפונקציה הועלתה, כך שניתן להריץ אותה מרחוק עם Qiskit Serverless. ראשית, טען את התבנית לפי שם:
template = serverless.load("template_hamiltonian_simulation")
לאחר מכן, הרץ את התבנית עם קלטים ברמת התחום לסימולציית המילטוניאן. דוגמה זו מציינת מודל XXZ של 50 קיוביטים עם קישורים אקראיים, מצב התחלתי ואופרטור.
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
בדוק את סטטוס המשימה:
job.status()
'QUEUED'
לאחר שהמשימה פועלת, ניתן לאחזר לוגים שנוצרו מפלטי print(). אלה יכולים לספק מידע פעיל לגבי התקדמות זרימת העבודה של סימולציית המילטוניאן. לדוגמה, ערך פונקציית המטרה במהלך הרכיב האיטרטיבי של AQC, או עומק שני-הקיוביטים של מעגל ה-ISA הסופי המיועד לביצוע על חומרה.
print(job.logs())
No logs yet.
חסום את שאר התוכנית עד שתוצאה תהיה זמינה. לאחר שהמשימה מסתיימת, ניתן לאחזר את התוצאות. אלה כוללות את הפלט ברמת התחום של סימולציית המילטוניאן (ערך ציפייה) ומטא-דאטה שימושי.
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}
לאחר השלמת המשימה, כל פלט הרישום יהיה זמין.
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.
השלבים הבאים
המלצות
לצלילה עמוקה יותר לתוסף AQC-Tensor של Qiskit, עיין בהדרכה שיפור התפתחות זמן Trotterized עם קומפילציה קוונטית מקורבת או במאגר 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
קוד המקור המלא של התוכנית
הנה המקור המלא של ./source_files/template_hamiltonian_simulation.py כבלוק קוד אחד.
# 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/")