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פריסה והפעלה של תבנית לסימולציה אלקטרונית עם מודל ממס משתמע

תבנית זו, שפותחה בשיתוף פעולה עם Cleveland Clinic, מכילה זרימת עבודה לחישוב אנרגיית מצב היסוד ואנרגיית ממסה חופשית של מולקולה בממס משתמע [1]. הסימולציות מבוססות על שיטת אלכסון קוונטי מבוסס דגימה (SQD) [2-6] ועל מודל רצף מקוטב בפורמליזם משוואת אינטגרל (IEF-PCM) של ממס [7].

מדריך זה משתמש בתבנית עם מולקולת מתנול כחומר מומס, שמבנהו האלקטרוני מסומלץ במפורש, ומים כממס, המקורבים כמדיום דיאלקטרי רציף. כדי להתחשב באפקטי קורלציה של אלקטרונים במתנול תוך שמירה על האיזון בין עלות חישובית לדיוק, אנו כוללים רק את האורביטלים σ\sigma, σ\sigma^{*} וזוגות בודדים במרחב הפעיל המסומלץ עם SQD IEF-PCM. בחירת האורביטלים נעשית בשיטת מרחב פעיל ערכיות אטומי (AVAS) תוך שימוש ברכיבי האורביטל האטומי C[2s,2p]‏, O[2s,2p]‏ ו-H[1s]‏, שמניב מרחב פעיל של 14 אלקטרונים ו-12 אורביטלים (14e,12o). האורביטלים הייחוסיים מחושבים עם Hartree Fock קליפה סגורה תוך שימוש בבסיס cc-pvdz.

מבוא לזרימת העבודה

מדריך אינטראקטיבי זה מראה כיצד להעלות את תבנית הפונקציה זו ל-Qiskit Serverless ולהפעיל עומס עבודה לדוגמה. התבנית מובנית כ-Qiskit pattern בארבעה שלבים:

1. איסוף קלט ומיפוי הבעיה

שלב זה מקבל כקלט את הגיאומטריה של המולקולה, המרחב הפעיל שנבחר, מודל הממסה, אפשרויות LUCJ ואפשרויות SQD. לאחר מכן הוא מייצר את קובץ ה-Checkpoint של PySCF, המכיל את נתוני Hartree-Fock (HF) IEF-PCM. נתונים אלה ישמשו בחלק ה-SQD של זרימת העבודה. עבור חלק ה-LUCJ של זרימת העבודה, קטע הקלט גם מייצר את נתוני ה-HF בפאזת גז, המאוחסנים פנימית בפורמט FCIDUMP של PySCF.

המידע מסימולציית ה-HF בפאזת גז והגדרת המרחב הפעיל נלקחים כקלט. חשוב לציין שהוא גם משתמש במידע שהמשתמש הגדיר בקטע הקלט לגבי דיכוי שגיאות, מספר הירי, רמת האופטימיזציה של ה-Transpiler ופריסת ה-Qubit.

הוא מייצר אינטגרלים של אלקטרון אחד ושני אלקטרונים במרחב הפעיל שהוגדר. לאחר מכן האינטגרלים משמשים לביצוע חישובי CCSD קלאסיים, שמחזירים אמפליטודות t2 שבהן אנו משתמשים כדי לפרמטר את ה-Circuit של LUCJ.

2. אופטימיזציה של ה-Circuit

ה-Circuit של LUCJ עובר לאחר מכן Transpile ל-ISA circuit עבור החומרה הייעודית. לאחר מכן מופעל Sampler primitive עם ברירת מחדל של אפשרויות הפחתת שגיאות לניהול ההפעלה.

3. הפעלת ה-Circuit

חישובי LUCJ מחזירים את המחרוזות הבינאריות עבור כל מדידה, כאשר מחרוזות אלה מתאימות לתצורות אלקטרוניות של המערכת הנחקרת. המחרוזות הבינאריות משמשות לאחר מכן כקלט לעיבוד לאחר מכן.

4. עיבוד לאחר מכן באמצעות SQD

שלב אחרון זה מקבל כקלט את קובץ ה-Checkpoint של PySCF המכיל את מידע HF IEF-PCM, את המחרוזות הבינאריות המייצגות את התצורות האלקטרוניות שניבא LUCJ, ואת אפשרויות SQD שהמשתמש הגדיר בקטע הקלט. כפלט, הוא מייצר את אנרגיית ה-SQD IEF-PCM הכוללת של האצווה בעלת האנרגיה הנמוכה ביותר ואנרגיית הממסה החופשית המתאימה.

אפשרויות

עבור תבנית זו עליך לציין אפשרויות ליצירת ה-Circuit של LUCJ ופרמטרי הפעלת SQD.

אפשרויות LUCJ

כאשר ה-Circuit הקוונטי של LUCJ מופעל, נוצרת קבוצת דגימות המייצגות את מצבי הבסיס החישובי מהתפלגות ההסתברות של המערכת המולקולרית. כדי לאזן בין עומק ה-Circuit של LUCJ לביטויו, ה-Qubitים המתאימים לאורביטלים ספיניים בספין הנגדי מקבלים שערים בעלי שני Qubitים ביניהם כאשר Qubitים אלו הם שכנים דרך Qubit עוגן יחיד. כדי ליישם גישה זו על חומרת IBM עם טופולוגיית hex כבד, Qubitים המייצגים אורביטלים ספיניים עם אותו ספין מחוברים דרך טופולוגיית קו שבה כל קו לוקח צורת זיג-זג בשל קישוריות ה-hex הכבד של החומרה הייעודית, בעוד ה-Qubitים המייצגים אורביטלים ספיניים עם ספין מנוגד כוללים חיבור רק בכל Qubit רביעי.

לחץ לפרטים נוספים על האפשרויות הנדרשות:

על המשתמש לספק את מערך initial_layout המתאים ל-Qubitים שמקיימים את דפוס ה-zig-zag הזה בקטע lucj_options של פונקציית SQD IEF-PCM. במקרה של סימולציות SQD IEF-PCM (14e,12o)/cc-pvdz של מתנול, בחרנו את פריסת ה-Qubit הראשונית המתאימה לאלכסון הראשי של Eagle R3 QPU. כאן, 12 האלמנטים הראשונים של מערך initial_layout [0, 14, 18, 19, 20, 33, 39, 40, 41, 53, 60, 61, ...] מתאימים לאורביטלים ספיניים alpha. 12 האלמנטים האחרונים [... 2, 3, 4, 15, 22, 23, 24, 34, 43, 44, 45, 54] מתאימים לאורביטלים ספיניים beta.

חשוב לציין שעל המשתמש לקבוע את number_of_shots, המתאים למספר המדידות ב-Circuit של LUCJ. מספר הירי צריך להיות גדול מספיק מכיוון שהשלב הראשון של נוהל S-CORE מסתמך על הדגימות במגזר החלקיקים הנכון כדי לקבל את הקירוב הראשוני לתפלגות מספר תפוסה של מצב היסוד.

מספר הירי תלוי מאוד במערכת ובחומרה, אך מחקרי SQD בלתי-קוולנטיים, מבוססי פרגמנטים וממס משתמע מצביעים על כך שניתן להגיע לדיוק כימי על ידי ביצוע ההנחיות הבאות:

  • 20,000 - 200,000 ירי עבור מערכות עם פחות מ-16 אורביטלים מולקולריים (32 אורביטלים ספיניים)
  • 200,000 ירי עבור מערכות עם 16 - 18 אורביטלים מולקולריים
  • 200,000 - 2,000,000 ירי עבור מערכות עם יותר מ-18 אורביטלים מולקולריים

המספר הנדרש של ירי מושפע ממספר האורביטלים הספיניים במערכת הנחקרת ומגודל מרחב הילברט המתאים למרחב הפעיל שנבחר במערכת הנחקרת. בדרך כלל, מקרים עם מרחבי הילברט קטנים יותר דורשים פחות ירי. אפשרויות LUCJ זמינות נוספות הן רמת אופטימיזציה של Transpiler ואפשרויות דיכוי שגיאות. שים לב שאפשרויות אלה גם משפיעות על מספר הירי הנדרש והדיוק שיתקבל.

אפשרויות SQD

אפשרויות חשובות בסימולציות SQD כוללות את sqd_iterations‏, number_of_batches ו-samples_per_batch. באופן כללי, מספר קטן יותר של דגימות לאצווה ניתן לפצות עם יותר אצוות (number_of_batches) ויותר איטרציות של S-CORE (sqd_iterations). עם יותר אצוות אנו יכולים לדגום יותר וריאציות של תת-מרחבי תצורה. מכיוון שהאצווה בעלת האנרגיה הנמוכה ביותר נלקחת כפתרון לאנרגיית מצב היסוד של המערכת, יותר אצוות יכולות לשפר את התוצאות דרך סטטיסטיקה טובה יותר. איטרציות נוספות של S-CORE מאפשרות שחזור של יותר תצורות מהתפלגות ה-LUCJ המקורית אם מספר הדגימות במגזר החלקיקים הנכון נמוך. זה יכול לאפשר הפחתה של מספר הדגימות לאצווה.

לחץ למידע נוסף על קביעת אפשרויות SQD:

אסטרטגיה חלופית היא להשתמש ביותר דגימות לאצווה, מה שמבטיח שרוב דגימות LUCJ הראשוניות במרחב החלקיקים הנכון משמשות במהלך נוהל S-CORE, ותת-מרחבים בודדים כוללים מגוון מספיק של תצורות אלקטרוניות. בתורו, זה מצמצם את מספר שלבי S-CORE הנדרשים, כאשר רק שתיים או שלוש איטרציות של SQD נדרשות אם מספר הדגימות לאצווה גדול מספיק. עם זאת, יותר דגימות לאצווה גורמות לעלות חישובית גבוהה יותר של כל שלב אלכסון. לכן, ניתן להשיג את האיזון בין דיוק לעלות חישובית בסימולציות SQD על ידי בחירה אופטימלית של sqd_iterations‏, number_of_batches ו-samples_per_batch.

מחקר SQD IEF-PCM מראה שכאשר משתמשים בשלוש איטרציות של S-CORE, ניתן להגיע לדיוק כימי על ידי ביצוע ההנחיות הבאות:

  • 600 דגימות לאצווה בסימולציות SQD IEF-PCM (14e,12o) של מתנול
  • 1500 דגימות לאצווה בסימולציות SQD IEF-PCM (14e,13o) של מתיל-אמין
  • 6000 דגימות לאצווה בסימולציות SQD IEF-PCM (8e,23o) של מים
  • 16000 דגימות לאצווה בסימולציות SQD IEF-PCM (20e,18o) של אתנול

בדיוק כמו המספר הנדרש של ירי ב-LUCJ, המספר הנדרש של דגימות לאצווה המשמשות בנוהל S-CORE תלוי מאוד במערכת ובחומרה. הדוגמאות לעיל ניתנות לשימוש להערכת נקודת ההתחלה לסמן הייחוס של מספר הדגימות הנדרש לאצווה. המדריך על סמן הייחוס השיטתי של מספר הדגימות הנדרש לאצווה נמצא כאן.

פריסה והפעלה של פונקציית התבנית SQD IEF-PCM

# Added by doQumentation — required packages for this notebook
!pip install -q ffsim numpy pyscf qiskit qiskit-addon-sqd qiskit-ibm-catalog qiskit-ibm-runtime qiskit-serverless solve-solvent

אימות

השתמש ב-qiskit-ibm-catalog כדי לאמת ל-QiskitServerless עם מפתח ה-API שלך (token), שניתן למצוא בלוח המחוונים של IBM Quantum Platform. זה מאפשר את יצירת מופע לקוח serverless להעלאה או הפעלה של הפונקציה שנבחרה:

from qiskit_ibm_catalog import QiskitServerless

serverless = QiskitServerless(
channel="ibm_quantum_platform",
instance="INSTANCE_CRN",
token="YOUR_API_KEY" # Use the 44-character API_KEY you created and saved from the IBM Quantum Platform Home dashboard
)

לחלופין, השתמש ב-save_account() כדי לשמור את האישורים שלך בסביבה מקומית (ראה את המדריך הגדרת חשבון IBM Cloud שלך). שים לב שפעולה זו כותבת את האישורים שלך לאותו קובץ כמו QiskitRuntimeService.save_account():

QiskitServerless.save_account(token="YOUR_API_KEY", channel="ibm_quantum_platform", instance="INSTANCE_CRN")

אם החשבון שמור, אין צורך לספק את ה-token כדי לאמת:

from qiskit_ibm_catalog import QiskitServerless

serverless = QiskitServerless()

העלאת התבנית

כדי להעלות Qiskit Function מותאמת אישית, עליך קודם ליצור מופע של אובייקט QiskitFunction שמגדיר את קוד המקור של הפונקציה. הכותרת תאפשר לך לזהות את הפונקציה לאחר שהיא נמצאת באשכול המרוחק. נקודת הכניסה הראשית היא הקובץ המכיל if __name__ == "__main__". אם זרימת העבודה שלך דורשת קבצי מקור נוספים, ניתן להגדיר ספריית עבודה שתועלה יחד עם נקודת הכניסה.

from qiskit_ibm_catalog import QiskitFunction

template = QiskitFunction(
title="sqd_pcm_template",
entrypoint="sqd_pcm_entrypoint.py",
working_dir="./source_files/", # all files in this directory will be uploaded
dependencies=[
"ffsim==0.0.54",
"pyscf==2.9.0",
"qiskit_addon_sqd==0.10.0",
],
)
print(template)
QiskitFunction(sqd_pcm_template)

לאחר שהמופע מוכן, העלה אותו ל-serverless:

serverless.upload(template)
QiskitFunction(sqd_pcm_template)

כדי לבדוק אם התוכנית הועלתה בהצלחה, השתמש ב-serverless.list():

serverless.list()
[QiskitFunction(sqd_pcm_template),
QiskitFunction(hamiltonian_simulation_template)]

טעינה והרצה של התבנית מרחוק

תבנית הפונקציה הועלתה, אז עכשיו אפשר להריץ אותה מרחוק עם Qiskit Serverless. קודם, טוענים את התבנית לפי שם:

template = serverless.load("sqd_pcm_template")
print(template)
QiskitFunction(sqd_pcm_template)

עכשיו מריצים את התבנית עם הקלטים ברמת הדומיין עבור SQD-IEF PCM. הדוגמה הזו מגדירה עומס עבודה מבוסס מתנול.

molecule = {
"atom": """
O -0.04559 -0.75076 -0.00000;
C -0.04844 0.65398 -0.00000;
H 0.85330 -1.05128 -0.00000;
H -1.08779 0.98076 -0.00000;
H 0.44171 1.06337 0.88811;
H 0.44171 1.06337 -0.88811
""", # Must be specified
"basis": "cc-pvdz", # default is "sto-3g"
"spin": 0, # default is 0
"charge": 0, # default is 0
"verbosity": 0, # default is 0
"number_of_active_orb": 12, # Must be specified
"number_of_active_alpha_elec": 7, # Must be specified
"number_of_active_beta_elec": 7, # Must be specified
"avas_selection": [
"%d O %s" % (k, x) for k in [0] for x in ["2s", "2px", "2py", "2pz"]
]
+ ["%d C %s" % (k, x) for k in [1] for x in ["2s", "2px", "2py", "2pz"]]
+ ["%d H 1s" % k for k in [2, 3, 4, 5]], # default is None
}

solvent_options = {
"method": "IEF-PCM", # other available methods are COSMO, C-PCM, SS(V)PE, see https://manual.q-chem.com/5.4/topic_pcm-em.html
"eps": 78.3553, # value for water
}

lucj_options = {
"initial_layout": [
0,
14,
18,
19,
20,
33,
39,
40,
41,
53,
60,
61,
2,
3,
4,
15,
22,
23,
24,
34,
43,
44,
45,
54,
],
"dynamical_decoupling_choice": True,
"twirling_choice": True,
"number_of_shots": 200000,
"optimization_level": 2,
}

sqd_options = {
"sqd_iterations": 3,
"number_of_batches": 10,
"samples_per_batch": 1000,
"max_davidson_cycles": 200,
}

backend_name = "ibm_sherbrooke"
job = template.run(
backend_name=backend_name,
molecule=molecule,
solvent_options=solvent_options,
lucj_options=lucj_options,
sqd_options=sqd_options,
)
print(job.job_id)
39f8fb70-79b2-43ca-b723-84e6b6135821

בודקים את הסטטוס המפורט של המשימה:

import time

t0 = time.time()
status = job.status()
if status == "QUEUED":
print(f"time = {time.time()-t0:.2f}, status = QUEUED")
while True:
status = job.status()
if status == "QUEUED":
continue
print(f"time = {time.time()-t0:.2f}, status = {status}")
if status == "DONE" or status == "ERROR":
break
time = 2.35, status = DONE

בזמן שהמשימה רצה, אפשר לשלוף לוגים שנוצרו מפלטי logger.info. הם יכולים לספק מידע שימושי לגבי התקדמות זרימת העבודה של SQD IEF-PCM. למשל, חיבורי אורביטל הספין הזהה, או עומק שני-ה-Qubit של מעגל ה-ISA הסופי שמיועד להרצה על חומרה.

print(job.logs())

קריאה לתוצאת המשימה חוסמת את שאר התוכנית עד שתוצאה זמינה. אחרי שהמשימה מסתיימת, אפשר לאחזר את התוצאות. הן כוללות את אנרגיית ה-solvation החינמית, כמו גם מידע על ה-batch עם האנרגיה הנמוכה ביותר, ערך האנרגיה הנמוך ביותר, ומידע שימושי נוסף כמו משך הזמן הכולל של ה-solver.

result = job.result()

result
{'total_energy_hist': array([[-115.14768518, -115.1368396 , -114.19181692, -115.13745429,
-115.1445012 , -114.19673326, -115.1547003 , -114.20563866,
-115.13748344, -115.14764974],
[-115.15768392, -115.15850126, -115.15857275, -115.15770916,
-115.15801684, -115.15822125, -115.15833521, -115.15844051,
-115.15735538, -115.15862354],
[-115.15795148, -115.15847925, -115.15856677, -115.15811156,
-115.15815602, -115.15785171, -115.1583672 , -115.1585533 ,
-115.15833528, -115.15808791]]),
'spin_squared_value_hist': array([[5.37327508e-03, 1.32981759e-02, 1.36214922e-02, 8.84413615e-03,
7.26723578e-03, 1.94875195e-02, 3.03153152e-03, 6.07543106e-03,
1.04951849e-02, 5.36529204e-03],
[6.39397528e-04, 1.36814350e-04, 9.09054260e-05, 5.99361358e-04,
3.64261739e-04, 2.54905866e-04, 2.32540370e-04, 1.53181990e-04,
7.23519739e-04, 6.80737671e-05],
[4.53776416e-04, 1.63043449e-04, 1.05317263e-04, 3.82912836e-04,
3.41047803e-04, 5.18620393e-04, 2.06819142e-04, 1.17086537e-04,
2.32357159e-04, 4.26071537e-04]]),
'solvation_free_energy_hist': array([[-0.00725018, -0.00743955, -0.01132905, -0.0073377 , -0.00722221,
-0.01136705, -0.00719279, -0.01072829, -0.00733404, -0.00725961],
[-0.00719252, -0.00718315, -0.00718074, -0.00719325, -0.00717703,
-0.00718391, -0.00718354, -0.00717928, -0.00719887, -0.0071801 ],
[-0.00719351, -0.00718255, -0.00718198, -0.00718429, -0.00718349,
-0.00718329, -0.0071882 , -0.00718363, -0.00718549, -0.00718814]]),
'occupancy_hist': [[array([0.99712298, 0.99278936, 0.99083163, 0.97328469, 0.98959809,
0.98922134, 0.720333 , 0.25683194, 0.01939338, 0.02840332,
0.00946988, 0.0327204 ]),
array([0.99712298, 0.99278936, 0.99083163, 0.97328469, 0.98959809,
0.98922134, 0.720333 , 0.25683194, 0.01939338, 0.02840332,
0.00946988, 0.0327204 ])],
[array([0.9959042 , 0.9922607 , 0.99018862, 0.99265843, 0.98927447,
0.9900833 , 0.99403876, 0.00989025, 0.01120814, 0.01137717,
0.01152871, 0.01158725]),
array([0.9959042 , 0.9922607 , 0.99018862, 0.99265843, 0.98927447,
0.9900833 , 0.99403876, 0.00989025, 0.01120814, 0.01137717,
0.01152871, 0.01158725])],
[array([0.99590079, 0.99222193, 0.99016753, 0.99265045, 0.98927264,
0.99007179, 0.99407207, 0.00986684, 0.01125181, 0.01141439,
0.01150733, 0.01160243]),
array([0.99590079, 0.99222193, 0.99016753, 0.99265045, 0.98927264,
0.99007179, 0.99407207, 0.00986684, 0.01125181, 0.01141439,
0.01150733, 0.01160243])]],
'lowest_energy_batch': 2,
'lowest_energy_value': -115.1585667736213,
'solvation_free_energy': -0.007181981952470838,
'sci_solver_total_duration': 493.997501373291,
'metadata': {'resources_usage': {'RUNNING: MAPPING': {'CPU_TIME': 6.080063343048096},
'RUNNING: OPTIMIZING_FOR_HARDWARE': {'CPU_TIME': 1.999896764755249},
'RUNNING: WAITING_FOR_QPU': {'CPU_TIME': 6.2850868701934814},
'RUNNING: EXECUTING_QPU': {'QPU_TIME': 21.639373540878296},
'RUNNING: POST_PROCESSING': {'CPU_TIME': 495.40831995010376}},
'num_iterations_executed': 3}}

שימו לב שה-metadata של התוצאה כולל סיכום שימוש במשאבים שמאפשר לכם להעריך טוב יותר את זמן ה-QPU והמעבד הנדרש לכל עומס עבודה (הדוגמה הזו רצה על מכשיר דמה, אז זמני השימוש בפועל עשויים להיות שונים). אחרי שהמשימה מסתיימת, כל הפלט של הלוגים יהיה זמין.

print(job.logs())
2025-06-27 08:42:41,358	INFO job_manager.py:531 -- Runtime env is setting up.
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:45,015: Starting runtime service
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:45,621: Backend: ibm_sherbrooke
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:46,809: Initializing molecule object
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:51,599: Performing CCSD
Parsing /tmp/ray/session_2025-06-27_08-42-13_898146_1/runtime_resources/working_dir_files/_ray_pkg_4bc93dcc58c04b91/output_sqd_pcm/2025-06-27_08-42-45.fcidump.txt
Overwritten attributes get_ovlp get_hcore of <class 'pyscf.scf.hf_symm.SymAdaptedRHF'>
/usr/local/lib/python3.11/site-packages/pyscf/gto/mole.py:1293: UserWarning: Function mol.dumps drops attribute energy_nuc because it is not JSON-serializable
warnings.warn(msg)
/usr/local/lib/python3.11/site-packages/pyscf/gto/mole.py:1293: UserWarning: Function mol.dumps drops attribute intor_symmetric because it is not JSON-serializable
warnings.warn(msg)
converged SCF energy = -115.049680672847
E(CCSD) = -115.1519910037652 E_corr = -0.1023103309180226
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:51,694: Same spin orbital connections: [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 10), (10, 11)]
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:51,694: Opposite spin orbital connections: [(0, 0), (4, 4), (8, 8)]
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:53,718: Optimization level: 2, ops: OrderedDict([('rz', 2438), ('sx', 1496), ('ecr', 766), ('x', 185), ('measure', 24), ('barrier', 1)]), depth: 391
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:53,736: Two-qubit gate depth: 94
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:53,737: Submitting sampler job
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:54,273: Job ID: d1f5j3lqbivc73ebqpj0
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:42:54,313: Job Status: QUEUED
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,813: Starting configuration recovery iteration 0
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,841: Batch 0 subspace dimension: 531441
2025-06-27 08:43:24,844 INFO worker.py:1588 -- Using address 172.17.16.124:6379 set in the environment variable RAY_ADDRESS
2025-06-27 08:43:24,847 INFO worker.py:1723 -- Connecting to existing Ray cluster at address: 172.17.16.124:6379...
2025-06-27 08:43:24,876 INFO worker.py:1908 -- Connected to Ray cluster. View the dashboard at http://172.17.16.124:8265 
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,945: Batch 1 subspace dimension: 519841
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,950: Batch 2 subspace dimension: 543169
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,955: Batch 3 subspace dimension: 532900
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,960: Batch 4 subspace dimension: 534361
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,964: Batch 5 subspace dimension: 531441
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,969: Batch 6 subspace dimension: 540225
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,974: Batch 7 subspace dimension: 524176
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,979: Batch 8 subspace dimension: 537289
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:43:24,983: Batch 9 subspace dimension: 540225
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:09,006: Lowest energy batch: 6
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:09,007: Lowest energy value: -115.15470029849135
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:09,007: Corresponding g_solv value: -0.0071927910374866375
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:09,007: -----------------------------------
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:09,007: Starting configuration recovery iteration 1
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,564: Batch 0 subspace dimension: 413449
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,572: Batch 1 subspace dimension: 399424
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,578: Batch 2 subspace dimension: 438244
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,583: Batch 3 subspace dimension: 422500
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,589: Batch 4 subspace dimension: 409600
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,596: Batch 5 subspace dimension: 404496
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,601: Batch 6 subspace dimension: 410881
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,605: Batch 7 subspace dimension: 442225
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,611: Batch 8 subspace dimension: 409600
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:48:40,618: Batch 9 subspace dimension: 405769
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:49:54,917: Lowest energy batch: 9
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:49:54,917: Lowest energy value: -115.15862353596414
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:49:54,917: Corresponding g_solv value: -0.0071800982859467006
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:49:54,918: -----------------------------------
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:49:54,918: Starting configuration recovery iteration 2
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,501: Batch 0 subspace dimension: 399424
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,508: Batch 1 subspace dimension: 412164
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,514: Batch 2 subspace dimension: 432964
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,519: Batch 3 subspace dimension: 400689
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,524: Batch 4 subspace dimension: 432964
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,529: Batch 5 subspace dimension: 418609
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,533: Batch 6 subspace dimension: 418609
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,538: Batch 7 subspace dimension: 425104
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,543: Batch 8 subspace dimension: 404496
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:50:25,548: Batch 9 subspace dimension: 429025
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:51:37,900: Lowest energy batch: 2
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:51:37,900: Lowest energy value: -115.1585667736213
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:51:37,901: Corresponding g_solv value: -0.007181981952470838
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:51:37,901: -----------------------------------
sqd_pcm_entrypoint.run_function:INFO:2025-06-27 08:51:37,901: SCI_solver totally takes: 493.997501373291 seconds

הצעדים הבאים

המלצות

מקורות

[1] Danil Kaliakin, Akhil Shajan, Fangchun Liang, and Kenneth M. Merz Jr. Implicit Solvent Sample-Based Quantum Diagonalization, The Journal of Physical Chemistry B, 2025, DOI: 10.1021/acs.jpcb.5c01030

[2] Javier Robledo-Moreno, et al., Chemistry Beyond Exact Solutions on a Quantum-Centric Supercomputer, arXiv:2405.05068 [quant-ph].

[3] Jeffery Yu, et al., Quantum-Centric Algorithm for Sample-Based Krylov Diagonalization, arXiv:2501.09702 [quant-ph].

[4] Keita Kanno, et al., Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers, arXiv:2302.11320 [quant-ph].

[5] Kenji Sugisaki, et al., Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer, arXiv:2412.07218 [quant-ph].

[6] Mathias Mikkelsen, Yuya O. Nakagawa, Quantum-selected configuration interaction with time-evolved state, arXiv:2412.13839 [quant-ph].

[7] Herbert, John M. Dielectric continuum methods for quantum chemistry. WIREs Computational Molecular Science, 2021, 11, 1759-0876.

[8] Saki, A. A.; Barison, S.; Fuller, B.; Garrison, J. R.; Glick, J. R.; Johnson, C.; Mezzacapo, A.; Robledo-Moreno, J.; Rossmannek, M.; Schweigert, P. et al. Qiskit addon: sample-based quantum diagonalization, 2024; https://github.com/Qiskit/qiskit-addon-sqd

[9] Asun, Q.; Zhang, X.; Banerjee, S.; Bao, P.; Barbry, M.; Blunt, N. S.; Bogdanov, N. A.; Booth, G. H.; Chen, J.; Cui, Z.-H. PySCF: Python-based Simulations of Chemistry Framework, 2025; https://github.com/pyscf/pyscf

[10] Kevin J. Sung; et al., FFSIM: Faster simulations of fermionic quantum circuits, 2024. https://github.com/qiskit-community/ffsim

%%writefile ./source_files/__init__.py
%%writefile ./source_files/solve_solvent.py

# This code is part of a Qiskit project.
#
# (C) Copyright IBM and Cleveland Clinic 2025
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""Functions for the study of fermionic systems."""

from __future__ import annotations

import warnings

import numpy as np

# DSK Add imports needed for CASCI wrapper
from pyscf import ao2mo, scf, fci
from pyscf.mcscf import avas, casci
from pyscf.solvent import pcm
from pyscf.lib import chkfile, logger

from qiskit_addon_sqd.fermion import (
SCIState,
bitstring_matrix_to_ci_strs,
_check_ci_strs,
)

# DSK Below is the modified CASCI kernel compatible with SQD.
# It utilizes the "fci.selected_ci.kernel_fixed_space"
# as well as enables passing the "batch" and "max_davidson"
# input arguments from "solve_solvent".
# The "batch" contains the CI addresses corresponding to subspaces
# derived from LUCJ and S-CORE calculations.
# The "max_davidson" controls the maximum number of cycles of Davidson's algorithm.

# pylint: disable = unused-argument
def kernel(casci_object, mo_coeff=None, ci0=None, verbose=logger.NOTE, envs=None):
"""CASCI solver compatible with SQD.

Args:
casci_object: CASCI or CASSCF object.
In case of SQD, only CASCI instance is currently incorporated.

mo_coeff : ndarray
orbitals to construct active space Hamiltonian.
In context of SQD, these are either AVAS mo_coeff
or all of the MOs (with option to exclude core MOs).

ci0 : ndarray or custom types FCI solver initial guess.
For SQD the usage of ci0 was not tested.

For external FCI-like solvers, it can be
overloaded different data type. For example, in the state-average
FCI solver, ci0 is a list of ndarray. In other solvers such as
DMRGCI solver, SHCI solver, ci0 are custom types.

kwargs:
envs: dict
In case of SQD this option was not explored,
but in principle this can facilitate the incorporation of the external solvers.

The variable envs is created (for PR 807) to passes MCSCF runtime
environment variables to SHCI solver. For solvers which do not
need this parameter, a kwargs should be created in kernel method
and "envs" pop in kernel function.
"""
if mo_coeff is None:
mo_coeff = casci_object.mo_coeff
if ci0 is None:
ci0 = casci_object.ci

log = logger.new_logger(casci_object, verbose)
t0 = (logger.process_clock(), logger.perf_counter())
log.debug("Start CASCI")

ncas = casci_object.ncas
nelecas = casci_object.nelecas

# The start of SQD version of kernel
# DSK add the read of configurations for batch
ci_strs_sqd = casci_object.batch

# DSK add the input for the maximum number of cycles of Davidson's algorithm
max_davidson = casci_object.max_davidson

# DSK add electron up and down count and norb = ncas
n_up = nelecas[0]
n_dn = nelecas[1]
norb = ncas

# DSK Eigenstate solver info
sqd_verbose = verbose

# DSK ERI read
eri_cas = ao2mo.restore(1, casci_object.get_h2eff(), casci_object.ncas)
t1 = log.timer("integral transformation to CAS space", *t0)

# DSK 1e integrals
h1eff, energy_core = casci_object.get_h1eff()
log.debug("core energy = %.15g", energy_core)
t1 = log.timer("effective h1e in CAS space", *t1)

if h1eff.shape[0] != ncas:
raise RuntimeError(
"Active space size error. nmo=%d ncore=%d ncas=%d" # pylint: disable=consider-using-f-string
% (mo_coeff.shape[1], casci_object.ncore, ncas)
)

# DSK fcisolver needs to be defined in accordance with SQD
# in this software stack it is done in the "solve_solvent" portion of the code.
myci = casci_object.fcisolver
e_cas, sqdvec = fci.selected_ci.kernel_fixed_space(
myci,
h1eff,
eri_cas,
norb,
(n_up, n_dn),
ci_strs=ci_strs_sqd,
verbose=sqd_verbose,
max_cycle=max_davidson,
)

# DSK fcivec is the general name for CI vector assigned by PySCF.
# Depending on type of solver it is either FCI or SCI vector.
# In case of sqd we can call it "sqdvec" for clarity.
# Nonetheless, for further processing PySCF expects
# this data structure to be called fcivec, regardless of the used solver.

fcivec = sqdvec

t1 = log.timer("CI solver", *t1)
e_tot = energy_core + e_cas

# Returns either standard CASCI data or SQD data. Return depends on "sqd_run" True/False.
return e_tot, e_cas, fcivec

# Replace standard CASCI kernel with the SQD-compatible CASCI kernel defined above
casci.kernel = kernel

def solve_solvent(
bitstring_matrix: tuple[np.ndarray, np.ndarray] | np.ndarray,
/,
myeps: float,
mysolvmethod: str,
myavas: list,
num_orbitals: int,
*,
spin_sq: int | None = None,
max_davidson: int = 100,
verbose: int | None = 0,
checkpoint_file: str,
) -> tuple[float, SCIState, list[np.ndarray], float]:
"""Approximate the ground state given molecular integrals and a set of electronic configurations.

Args:
bitstring_matrix: A set of configurations defining the subspace onto which the Hamiltonian
will be projected and diagonalized. This is a 2D array of ``bool`` representations of bit
values such that each row represents a single bitstring. The spin-up configurations
should be specified by column indices in range ``(N, N/2]``, and the spin-down
configurations should be specified by column indices in range ``(N/2, 0]``, where ``N``
is the number of qubits.

(DEPRECATED) The configurations may also be specified by a length-2 tuple of sorted 1D
arrays containing unsigned integer representations of the determinants. The two lists
should represent the spin-up and spin-down orbitals, respectively.

To build PCM model PySCF needs the structure of the molecule. Hence, the electron integrals
(hcore and eri) are not enough to form IEF-PCM simulation. Instead the "start.chk" file is used.
This workflow also requires additional information about solute and solvent,
which is reflected by additional arguments below

myeps: Dielectric parameter of the solvent.
mysolvmethod: Solvent model, which can be IEF-PCM, COSMO, C-PCM, SS(V)PE,
see https://manual.q-chem.com/5.4/topic_pcm-em.html
At the moment only IEF-PCM was tested.
In principle two other models from PySCF "solvent" module can be used as well,
namely SMD and polarizable embedding (PE).
The SMD and PE were not tested yet and their usage requires addition of more
input arguments for "solve_solvent".
myavas: This argument allows user to select active space in solute with AVAS.
The corresponding list should include target atomic orbitals.
If myavas=None, then active space selected based on number of orbitals
derived from ci_strs.
It is assumed that if myavas=None, then the target calculation is either
a) corresponds to full basis case.
b) close to full basis case and only few core orbitals are excluded.
num_orbitals: Number of orbitals, which is essential when myavas = None.
In AVAS case number of orbitals and electrons is derived by AVAS procedure itself.
spin_sq: Target value for the total spin squared for the ground state.
If ``None``, no spin will be imposed.
max_davidson: The maximum number of cycles of Davidson's algorithm
verbose: A verbosity level between 0 and 10
checkpoint_file: Name of the checkpoint file

NOTE: For now open shell functionality is not supported in SQD PCM calculations.
Hence, at the moment solve_solvent does not include open_shell as one of the arguments.

Returns:
- Minimum energy from SCI calculation
- The SCI ground state
- Average occupancy of the alpha and beta orbitals, respectively
- Expectation value of spin-squared
- Solvation free energy

"""
# Unlike the "solve_fermion", the "solve_solvent" utilizes the "checkpoint" file to
# get the starting HF information, which means that "solve_solvent" does not accept
# "hcore" and "eri" as the input arguments.
# Instead "hcore" and "eri" are generated inside of the custom SQD-compatible
# CASCI kernel (defined above).
# The generation of "hcore" and "eri" is based on the information from "checkpoint" file
# as well as "myavas" and "num_orbitals" input arguments.

# DSK this part handles addresses and is identical to "solve_fermion"
if isinstance(bitstring_matrix, tuple):
warnings.warn(
"Passing the input determinants as integers is deprecated. "
"Users should instead pass a bitstring matrix defining the subspace.",
DeprecationWarning,
stacklevel=2,
)
ci_strs = bitstring_matrix
else:
# This will become the default code path after the deprecation period.
ci_strs = bitstring_matrix_to_ci_strs(bitstring_matrix, open_shell=False)
ci_strs = _check_ci_strs(ci_strs)

num_up = format(ci_strs[0][0], "b").count("1")
num_dn = format(ci_strs[1][0], "b").count("1")

# DSK assign verbosity
verbose_ci = verbose

# DSK add information about solute and solvent.
# Since PCM model needs the information about the structure of the molecule
# one cannot use only FCIDUMP. Instead converged HF data can be passed from "checkpoint" file
# along with "mol" object containing the geometry and other information about the solute.

############################################
# This section is specific to "solve_solvent" and is not present in "solve_fermion".
# In case of "solve_fermion" the "eri" and "hcore" are passed directly to
# "fci.selected_ci.kernel_fixed_space".
# In case of "solve_solvent" the incorporation of the polarizable continuum model
# requires utilization of "CASCI.with_solvent"
# data object from PySCF, where underlying CASCI.base_kernel has to be replaced
# with SQD-compatible version.
# Due to these differences in the implementation the "solve_solvent" recovers
# the converged mean field results and "molecule" object from "checkpoint" file
# (instead of using FCIDUMP),
# followed by passing of solute, solvent, and active space information to "CASCI.with_solvent".
# This includes the initiation of "mol", "cm", "mf", and "mc" data structures.

mol = chkfile.load_mol(checkpoint_file)

# DSK Initiation of the solvent model
cm = pcm.PCM(mol)
cm.eps = myeps # solute eps value
cm.method = mysolvmethod # IEF-PCM, COSMO, C-PCM, SS(V)PE,
# see https://manual.q-chem.com/5.4/topic_pcm-em.html

# DSK Read-in converged RHF solution
scf_result_dic = chkfile.load(checkpoint_file, "scf")
mf = scf.RHF(mol).PCM(cm)
mf.__dict__.update(scf_result_dic)

# Identify the active space based on the user input of AVAS or number of orbitals and electrons
if myavas is not None:
orbs = myavas
avas_obj = avas.AVAS(mf, orbs, with_iao=True)
avas_obj.kernel()
ncas, nelecas, _, _, _ = (
avas_obj.ncas,
avas_obj.nelecas,
avas_obj.mo_coeff,
avas_obj.occ_weights,
avas_obj.vir_weights,
)
else:
ncas = num_orbitals
nelecas = (num_up, num_dn)

# Initiate the "CASCI.with_solvent" object
mc = casci.CASCI(mf, ncas=ncas, nelecas=nelecas).PCM(cm)
# Replace mo_coeff with ones produced by AVAS if AVAS is utilized
if myavas is not None:
mc.mo_coeff = avas_obj.mo_coeff
# Read-in the configuration interaction subspace derived from LUCJ and S-CORE
mc.batch = ci_strs
# Assign number of maximum Davidson steps
mc.max_davidson = max_davidson

####### The definition of "fcisolver" object is identical to "solve_fermion" case ########
myci = fci.selected_ci.SelectedCI()
if spin_sq is not None:
myci = fci.addons.fix_spin_(myci, ss=spin_sq)
mc.fcisolver = myci
mc.verbose = verbose_ci
#########################################################################################

# Initiate the "CASCI.with_solvent" simulation with SQD-compatible based CASCI kernel.
mc_result = mc.kernel()

# Get data out of the "CASCI.with_solvent" object
e_sci = mc_result[0]
sci_vec = mc_result[2]
# Here we get additional output comparing to "solve_fermion",
# which is the solvation free energy (G_solv)
g_solv = mc.with_solvent.e

#####################################################
# The remainder of the code in solve_solvent is nearly identical to solve_fermion code.

# However, there are two exceptions in "solve_solvent":

# 1) The dm2 is currently not computed, but can be included if needed
# 2) e_sci is directly output as the result of CASCI.with_solvent object.

# Hence, the two following lines of code are not present in "solve_solvent"
# comparing to the "solve_fermion" code:

# dm2 = myci.make_rdm2(sci_vec, norb, (num_up, num_dn))
# e_sci = np.einsum("pr,pr->", dm1, hcore) + 0.5 * np.einsum("prqs,prqs->", dm2, eri)

# Calculate the avg occupancy of each orbital
dm1 = myci.make_rdm1s(sci_vec, ncas, (num_up, num_dn))
avg_occupancy = [np.diagonal(dm1[0]), np.diagonal(dm1[1])]

# Compute total spin
spin_squared = myci.spin_square(sci_vec, ncas, (num_up, num_dn))[0]

# Convert the PySCF SCIVector to internal format. We access a private field here,
# so we assert that we expect the SCIVector output from kernel_fixed_space to
# have its _strs field populated with alpha and beta strings.
assert isinstance(sci_vec._strs[0], np.ndarray) and isinstance(sci_vec._strs[1], np.ndarray)
assert sci_vec.shape == (len(sci_vec._strs[0]), len(sci_vec._strs[1]))
sci_state = SCIState(
amplitudes=np.array(sci_vec),
ci_strs_a=sci_vec._strs[0],
ci_strs_b=sci_vec._strs[1],
)

return e_sci, sci_state, avg_occupancy, spin_squared, g_solv
%%writefile ./source_files/sqc_pcm_entrypoint.py

# This code is part of a Qiskit project.
#
# (C) Copyright IBM and Cleveland Clinic 2025
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""
SQD-PCM Function Template source code.
"""
from pathlib import Path
from typing import Any
from datetime import datetime
import os
import sys
import json
import logging
import time
import traceback
import numpy as np

import ffsim

from pyscf import gto, scf, mcscf, ao2mo, tools, cc
from pyscf.lib import chkfile
from pyscf.mcscf import avas
from pyscf.solvent import pcm

from qiskit import QuantumCircuit, QuantumRegister
from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager
from qiskit.primitives import BackendSamplerV2

from qiskit_addon_sqd.counts import counts_to_arrays
from qiskit_addon_sqd.configuration_recovery import recover_configurations
from qiskit_addon_sqd.fermion import bitstring_matrix_to_ci_strs
from qiskit_addon_sqd.subsampling import postselect_and_subsample

from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2
from qiskit_serverless import get_arguments, save_result, distribute_task, get, update_status, Job

current_dir = os.path.dirname(os.path.abspath(__file__))
sys.path.insert(0, current_dir)
from solve_solvent import solve_solvent # pylint: disable=wrong-import-position

logger = logging.getLogger(__name__)

def run_function(
backend_name: str,
molecule: dict,
solvent_options: dict,
sqd_options: dict,
lucj_options: dict | None = None,
**kwargs,
) -> dict[str, Any]:
"""
Main entry point for the SQD-PCM (Polarizable Continuum Model) workflow.

This function encapsulates the end-to-end execution of the algorithm.

Args:
backend_name: Identifier for the target backend, required for all
workflows that access IBM Quantum hardware.

molecule: dictionary with molecule information:
- "atom" (str): required field, follows pyscf specification for atomic geometry.
For example, for methanol the value would be::

'''
O -0.04559 -0.75076 -0.00000;
C -0.04844 0.65398 -0.00000;
H 0.85330 -1.05128 -0.00000;
H -1.08779 0.98076 -0.00000;
H 0.44171 1.06337 0.88811;
H 0.44171 1.06337 -0.88811;
'''

- "number_of_active_orb" (int): required field
- "number_of_active_alpha_elec" (int): required field
- "number_of_active_beta_elec" (int): required field
- "basis" (str): optional field, default is "sto-3g"
- "verbosity" (int): optional field, default is 0
- "charge" (int): optional field, default is 0
- "spin" (int): optional field, default is 0
- "avas_selection" (list[str] | None): optional field, default is None

solvent_options: dictionary with solvent options information:
- "method" (str): required field. Method for computing solvent reaction field
for the PCM. Accepted values are: "IEF-PCM", "COSMO",
"C-PCM", "SS(V)PE", see https://manual.q-chem.com/5.4/topic_pcm-em.html
- "eps" (float): required field. Dielectric constant of the solvent in the PCM.

sqd_options: dictionary with sqd options information:
- "sqd_iterations" (int): required field.
- "number_of_batches" (int): required field.
- "samples_per_batch" (int): required field.
- "max_davidson_cycles" (int): required field.

lucj_options: optional dictionary with lucj options information:
- "optimization_level" (int): optional field, default is 2
- "initial_layout" (list[int]): optional field, default is None
- "dynamical_decoupling" (bool): optional field, default is True
- "twirling" (bool): optional field, default is True
- "number_of_shots" (int): optional field, default is 10000

**kwargs
Optional keyword arguments to customize behavior. Existing kwargs include:
- "files_name" (str): optional name for output files (enabled for local testing)
- "testing_backend" (FakeBackendV2): optional fake backend instance to bypass
qiskit runtime service instantiation (enabled for local testing)
- "count_dict_file_name" (str): path to a count dict file to bypass primitive
execution and jump directly to SQD section (enabled for local testing)

Returns:
The function should return the execution results as a dictionary with string keys.
This is to ensure compatibility with ``qiskit_serverless.save_result``.
"""

# Preparation Step: Input validation.
# Do this at the top of the function definition so it fails early if any required
# arguments are missing or invalid.

# Molecule parsing
# Required:
geo = molecule["atom"]
num_active_orb = molecule["number_of_active_orb"]
num_active_alpha = molecule["number_of_active_alpha_elec"]
num_active_beta = molecule["number_of_active_beta_elec"]
# Optional:
input_basis = molecule.get("basis", "sto-3g")
input_verbosity = molecule.get("verbosity", 0)
input_charge = molecule.get("charge", 0)
input_spin = molecule.get("spin", 0)
myavas = molecule.get("avas_selection", None)

# Solvent options parsing
myeps = solvent_options["eps"]
mymethod = solvent_options["method"]

# LUCJ options parsing
if lucj_options is None:
lucj_options = {}
opt_level = lucj_options.get("optimization_level", 2)
initial_layout = lucj_options.get("initial_layout", None)
use_dd = lucj_options.get("dynamical_decoupling", True)
use_twirling = lucj_options.get("twirling", True)
num_shots = lucj_options.get("number_of_shots", True)

# SQD options parsing
iterations = sqd_options["sqd_iterations"]
n_batches = sqd_options["number_of_batches"]
samples_per_batch = sqd_options["samples_per_batch"]
max_davidson_cycles = sqd_options["max_davidson_cycles"]

# kwarg parsing (local testing)
testing_backend = kwargs.get("testing_backend", None)
count_dict_file_name = kwargs.get("count_dict_file_name", None)

files_name = kwargs.get("files_name", datetime.now().strftime("%Y-%m-%d_%H-%M-%S"))
output_path = Path.cwd() / "output_sqd_pcm"
output_path.mkdir(exist_ok=True)
datafiles_name = str(output_path) + "/" + files_name

# --
# Preparation Step: Qiskit Runtime & primitive configuration for
# execution on IBM Quantum hardware.

if testing_backend is None:
# Initialize Qiskit Runtime Service
logger.info("Starting runtime service")
service = QiskitRuntimeService(
channel=os.environ["QISKIT_IBM_CHANNEL"],
instance=os.environ["IBM_CLOUD_INSTANCE"],
token=os.environ["your-API_KEY"], # Use the 44-character API_KEY you created and saved from the IBM Quantum Platform Home dashboard
)
backend = service.backend(backend_name)
logger.info(f"Backend: {backend.name}")

# Set up sampler and corresponding options
sampler = SamplerV2(backend)
sampler.options.dynamical_decoupling.enable = use_dd
sampler.options.twirling.enable_measure = False
sampler.options.twirling.enable_gates = use_twirling
sampler.options.default_shots = num_shots
else:
backend = testing_backend
logger.info(f"Testing backend: {backend.name}")

# Set up backend sampler.
# This doesn't allow running with twirling and dd
sampler = BackendSamplerV2(backend=testing_backend)

# Once the preparation steps are completed, the algorithm can be structured following a
# Qiskit Pattern workflow:
# https://docs.quantum.ibm.com/guides/intro-to-patterns

# --
# Step 1: Map
# In this step, input arguments are used to construct relevant quantum circuits and operators

start_mapping = time.time()
update_status(Job.MAPPING)

# Initialize the molecule object (pyscf)
logger.info("Initializing molecule object")
mol = gto.Mole()
mol.build(
atom=geo,
basis=input_basis,
verbose=input_verbosity,
charge=input_charge,
spin=input_spin,
symmetry=False,
) # Not tested for symmetry calculations

cm = pcm.PCM(mol)
cm.eps = myeps
cm.method = mymethod

mf = scf.RHF(mol).PCM(cm)
# Generation of checkpoint file for the solute and solvent
# which will be used reused in all subsequent sections
checkpoint_file_name = str(datafiles_name + ".chk")
mf.chkfile = checkpoint_file_name
mf.kernel()

# Read-in the information about the molecule
mol = chkfile.load_mol(checkpoint_file_name)

# Read-in RHF data
scf_result_dic = chkfile.load(checkpoint_file_name, "scf")
mf = scf.RHF(mol)
mf.__dict__.update(scf_result_dic)

# LUCJ uses isolated solute
mf.kernel()

# Initialize orbital selection based on user input
if myavas is not None:
orbs = myavas
avas_out = avas.AVAS(mf, orbs, with_iao=True)
avas_out.kernel()
ncas, nelecas = (avas_out.ncas, avas_out.nelecas)
else:
ncas = num_active_orb
nelecas = (
num_active_alpha,
num_active_beta,
)

# LUCJ Step:
# Generate active space
mc = mcscf.CASCI(mf, ncas=ncas, nelecas=nelecas)
if myavas is not None:
mc.mo_coeff = avas_out.mo_coeff
mc.batch = None
# Reliable and most convenient way to do the CCSD on only the active space
# is to create the FCIDUMP file and then run the CCSD calculation only on the
# orbitals stored in the FCIDUMP file.

h1e_cas, ecore = mc.get_h1eff()
h2e_cas = ao2mo.restore(1, mc.get_h2eff(), mc.ncas)

fcidump_file_name = str(datafiles_name + ".fcidump.txt")
tools.fcidump.from_integrals(
fcidump_file_name,
h1e_cas,
h2e_cas,
ncas,
nelecas,
nuc=ecore,
ms=0,
orbsym=[1] * ncas,
)

logger.info("Performing CCSD")
# Read FCIDUMP and perform CCSD on only active space
mf_as = tools.fcidump.to_scf(fcidump_file_name)
mf_as.kernel()

mc_cc = cc.CCSD(mf_as)
mc_cc.kernel()
mc_cc.t1 # pylint: disable=pointless-statement
t2 = mc_cc.t2

n_reps = 2
norb = ncas

if myavas is not None:
nelec = (int(nelecas / 2), int(nelecas / 2))
else:
nelec = nelecas

alpha_alpha_indices = [(p, p + 1) for p in range(norb - 1)]
alpha_beta_indices = [(p, p) for p in range(0, norb, 4)]

logger.info(f"Same spin orbital connections: {alpha_alpha_indices}")
logger.info(f"Opposite spin orbital connections: {alpha_beta_indices}")

# Construct LUCJ op
ucj_op = ffsim.UCJOpSpinBalanced.from_t_amplitudes(
t2, n_reps=n_reps, interaction_pairs=(alpha_alpha_indices, alpha_beta_indices)
)
# Construct circuit
qubits = QuantumRegister(2 * norb, name="q")
circuit = QuantumCircuit(qubits)
circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)
circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)
circuit.measure_all()
end_mapping = time.time()

# --
# Step 2: Optimize
# Transpile circuits to match ISA

start_optimizing = time.time()
update_status(Job.OPTIMIZING_HARDWARE)

pass_manager = generate_preset_pass_manager(
optimization_level=opt_level,
backend=backend,
initial_layout=initial_layout,
)

pass_manager.pre_init = ffsim.qiskit.PRE_INIT
transpiled = pass_manager.run(circuit)

end_optimizing = time.time()
logger.info(
f"Optimization level: {opt_level}, ops: {transpiled.count_ops()}, depth: {transpiled.depth()}"
)

two_q_depth = transpiled.depth(lambda x: x.operation.num_qubits == 2)
logger.info(f"Two-qubit gate depth: {two_q_depth}")

# --
# Step 3: Execute on Hardware
# Submit the underlying Sampler job. Note that this is not the
# actual function job.
if count_dict_file_name is None:
# Submit the LUCJ job
logger.info("Submitting sampler job")
job = sampler.run([transpiled])
logger.info(f"Job ID: {job.job_id()}")
logger.info(f"Job Status: {job.status()}")

start_waiting_qpu = time.time()
while job.status() == "QUEUED":
update_status(Job.WAITING_QPU)
time.sleep(5)

end_waiting_qpu = time.time()
update_status(Job.EXECUTING_QPU)

# Wait until job is complete
result = job.result()
end_executing_qpu = time.time()

pub_result = result[0]
counts_dict = pub_result.data.meas.get_counts()

waiting_qpu_time = end_waiting_qpu - start_waiting_qpu
executing_qpu_time = end_executing_qpu - end_waiting_qpu
else:
# read LUCJ samples from count_dict
logger.info("Skipping sampler, loading counts dict from file")
with open(count_dict_file_name, "r") as file:
count_dict_string = file.read().replace("\n", "")
counts_dict = json.loads(count_dict_string.replace("'", '"'))
waiting_qpu_time = 0
executing_qpu_time = 0

# --
# Step 4: Post-process

start_pp = time.time()
update_status(Job.POST_PROCESSING)

# SQD-PCM section
start = time.time()

# Orbitals, electron, and spin initialization
num_orbitals = ncas
if myavas is not None:
num_elec_a = num_elec_b = int(nelecas / 2)
else:
num_elec_a, num_elec_b = nelecas
spin_sq = input_spin

# Convert counts into bitstring and probability arrays
bitstring_matrix_full, probs_arr_full = counts_to_arrays(counts_dict)

# We set qiskit_serverless to explicitly reserve 1 cpu per thread, as
# the task is CPU-bound and might degrade in performance when sharing
# a core at scale (this might not be the case with smaller examples)
@distribute_task(target={"cpu": 1})
def solve_solvent_parallel(
batches,
myeps,
mysolvmethod,
myavas,
num_orbitals,
spin_sq,
max_davidson,
checkpoint_file,
):
return solve_solvent( # sqd for pyscf
batches,
myeps,
mysolvmethod,
myavas,
num_orbitals,
spin_sq=spin_sq,
max_davidson=max_davidson,
checkpoint_file=checkpoint_file,
)

e_hist = np.zeros((iterations, n_batches)) # energy history
s_hist = np.zeros((iterations, n_batches)) # spin history
g_solv_hist = np.zeros((iterations, n_batches)) # g_solv history
occupancy_hist = []
avg_occupancy = None

num_ran_iter = 0
for i in range(iterations):
logger.info(f"Starting configuration recovery iteration {i}")
# On the first iteration, we have no orbital occupancy information from the
# solver, so we begin with the full set of noisy configurations.
if avg_occupancy is None:
bs_mat_tmp = bitstring_matrix_full
probs_arr_tmp = probs_arr_full

# If we have average orbital occupancy information, we use it to refine the full
# set of noisy configurations
else:
bs_mat_tmp, probs_arr_tmp = recover_configurations(
bitstring_matrix_full, probs_arr_full, avg_occupancy, num_elec_a, num_elec_b
)

# Create batches of subsamples. We post-select here to remove configurations
# with incorrect hamming weight during iteration 0, since no config recovery was performed.
batches = postselect_and_subsample(
bs_mat_tmp,
probs_arr_tmp,
hamming_right=num_elec_a,
hamming_left=num_elec_b,
samples_per_batch=samples_per_batch,
num_batches=n_batches,
)

# Run eigenstate solvers in a loop. This loop should be parallelized for larger problems.
e_tmp = np.zeros(n_batches)
s_tmp = np.zeros(n_batches)
g_solvs_tmp = np.zeros(n_batches)
occs_tmp = []
coeffs = []

res1 = []
for j in range(n_batches):
strs_a, strs_b = bitstring_matrix_to_ci_strs(batches[j])
logger.info(f"Batch {j} subspace dimension: {len(strs_a) * len(strs_b)}")

res1.append(
solve_solvent_parallel(
batches[j],
myeps,
mymethod,
myavas,
num_orbitals,
spin_sq=spin_sq,
max_davidson=max_davidson_cycles,
checkpoint_file=checkpoint_file_name,
)
)

res = get(res1)

for j in range(n_batches):
energy_sci, coeffs_sci, avg_occs, spin, g_solv = res[j]
e_tmp[j] = energy_sci
s_tmp[j] = spin
g_solvs_tmp[j] = g_solv
occs_tmp.append(avg_occs)
coeffs.append(coeffs_sci)

# Combine batch results
avg_occupancy = tuple(np.mean(occs_tmp, axis=0))

# Track optimization history
e_hist[i, :] = e_tmp
s_hist[i, :] = s_tmp
g_solv_hist[i, :] = g_solvs_tmp
occupancy_hist.append(avg_occupancy)

lowest_e_batch_index = np.argmin(e_hist[i, :])

logger.info(f"Lowest energy batch: {lowest_e_batch_index}")
logger.info(f"Lowest energy value: {np.min(e_hist[i, :])}")
logger.info(f"Corresponding g_solv value: {g_solv_hist[i, lowest_e_batch_index]}")
logger.info("-----------------------------------")
num_ran_iter += 1

end_pp = time.time()
end = time.time()
duration = end - start
logger.info(f"SCI_solver totally takes: {duration} seconds")

metadata = {
"resources_usage": {
"RUNNING: MAPPING": {
"CPU_TIME": end_mapping - start_mapping,
},
"RUNNING: OPTIMIZING_FOR_HARDWARE": {
"CPU_TIME": end_optimizing - start_optimizing,
},
"RUNNING: WAITING_FOR_QPU": {
"CPU_TIME": waiting_qpu_time,
},
"RUNNING: EXECUTING_QPU": {
"QPU_TIME": executing_qpu_time,
},
"RUNNING: POST_PROCESSING": {
"CPU_TIME": end_pp - start_pp,
},
},
"num_iterations_executed": num_ran_iter,
}

output = {
"total_energy_hist": e_hist,
"spin_squared_value_hist": s_hist,
"solvation_free_energy_hist": g_solv_hist,
"occupancy_hist": occupancy_hist,
"lowest_energy_batch": lowest_e_batch_index,
"lowest_energy_value": np.min(e_hist[i, :]),
"solvation_free_energy": g_solv_hist[i, lowest_e_batch_index],
"sci_solver_total_duration": duration,
"metadata": metadata,
}

return output

def set_up_logger(my_logger: logging.Logger, level: int = logging.INFO) -> None:
"""Logger setup to communicate logs through serverless."""

log_fmt = "%(module)s.%(funcName)s:%(levelname)s:%(asctime)s: %(message)s"
formatter = logging.Formatter(log_fmt)

# Set propagate to `False` since handlers are to be attached.
my_logger.propagate = False

stream_handler = logging.StreamHandler()
stream_handler.setFormatter(formatter)
my_logger.addHandler(stream_handler)
my_logger.setLevel(level)

# This is the section where `run_function` is called, it's boilerplate code and can be used
# without customization.
if __name__ == "__main__":

# Use serverless helper function to extract input arguments,
input_args = get_arguments()

# Allow to configure logging level
logging_level = input_args.get("logging_level", logging.INFO)
set_up_logger(logger, logging_level)

try:
func_result = run_function(**input_args)
# Use serverless function to save the results that
# will be returned in the job.
save_result(func_result)
except Exception:
save_result(traceback.format_exc())
raise

sys.exit(0)
# 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/sqd_pcm_entrypoint.py") as f1:
with open("./source_files/sqd_pcm_entrypoint.py") as f2:
assert f1.read() == f2.read()

with open("./source_files/solve_solvent.py") as f1:
with open("./source_files/solve_solvent.py") as f2:
assert f1.read() == f2.read()

with open("./source_files/__init__.py") as f1:
with open("./source_files/__init__.py") as f2:
assert f1.read() == f2.read()

shutil.rmtree("./source_files/")