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Implante e execute um template para simulação de estrutura eletrônica com modelo de solvente implícito

Este template, desenvolvido em colaboração com a Cleveland Clinic, consiste em um fluxo de trabalho para calcular a energia do estado fundamental e a energia livre de solvatação de uma molécula em um solvente implícito [1]. Essas simulações são baseadas no método de diagonalização quântica por amostragem (SQD) [2-6] e no modelo de contínuo polarizável com formalismo de equação integral (IEF-PCM) para solvente [7].

Este guia utiliza o template com a molécula de metanol como soluto — cuja estrutura eletrônica é simulada explicitamente — e água como solvente, aproximada como um meio dielétrico contínuo. Para considerar os efeitos de correlação eletrônica no metanol, mantendo o equilíbrio entre o custo computacional e a precisão, incluímos apenas os orbitais σ\sigma, σ\sigma^{*} e de pares isolados no espaço ativo simulado com SQD IEF-PCM. Essa seleção de orbitais é feita com o método de espaço ativo de valência atômica (AVAS) usando os componentes de orbital atômico C[2s,2p], O[2s,2p] e H[1s], o que resulta no espaço ativo de 14 elétrons e 12 orbitais (14e,12o). Os orbitais de referência são calculados com Hartree-Fock de camada fechada usando o conjunto de bases cc-pvdz.

Introdução ao fluxo de trabalho

Este guia interativo mostra como fazer o upload deste template de função para o Qiskit Serverless e executar uma carga de trabalho de exemplo. O template é estruturado como um padrão Qiskit com quatro etapas:

1. Coletar entradas e mapear o problema

Esta etapa recebe como entrada a geometria da molécula, o espaço ativo selecionado, o modelo de solvatação, as opções LUCJ e as opções SQD. Em seguida, produz o arquivo Checkpoint do PySCF, que contém os dados IEF-PCM de Hartree-Fock (HF). Esses dados serão usados na parte SQD do fluxo de trabalho. Para a parte LUCJ, a seção de entrada também gera os dados HF em fase gasosa, armazenados internamente no formato FCIDUMP do PySCF.

As informações da simulação HF em fase gasosa e a definição do espaço ativo são usadas como entrada. Importante: também são utilizadas as informações definidas pelo usuário na seção de entrada referentes à supressão de erros, número de shots, nível de otimização do transpilador de circuito e o layout dos qubits.

Essa etapa gera integrais de um elétron e de dois elétrons dentro do espaço ativo definido. As integrais são então usadas para realizar os cálculos clássicos de CCSD, que retornam amplitudes t2 usadas para parametrizar o circuito LUCJ.

2. Otimizar o circuito

O circuito LUCJ é então transpilado para um circuito ISA compatível com o hardware alvo. Um primitivo Sampler é instanciado com um conjunto padrão de opções de mitigação de erros para gerenciar a execução.

3. Executar o circuito

Os cálculos LUCJ retornam as bitstrings para cada medição, onde essas bitstrings correspondem às configurações eletrônicas do sistema estudado. As bitstrings são então usadas como entrada para o pós-processamento.

4. Pós-processar usando SQD

Esta etapa final recebe como entrada o arquivo Checkpoint do PySCF contendo as informações HF IEF-PCM, as bitstrings representando as configurações eletrônicas previstas pelo LUCJ e as opções SQD definidas pelo usuário na seção de entrada. Como saída, ela produz a energia total SQD IEF-PCM do lote de menor energia e a energia livre de solvatação correspondente.

Opções

Para este template, você precisa especificar opções para gerar o circuito LUCJ e os parâmetros de execução do SQD.

Opções LUCJ

Quando o circuito quântico LUCJ é executado, um conjunto de amostras representando os estados da base computacional da distribuição de probabilidade do sistema molecular é produzido. Para equilibrar a profundidade do circuito LUCJ e sua expressividade, os qubits correspondentes aos spin-orbitais de spin oposto têm as gates de dois qubits aplicadas entre eles quando esses qubits são vizinhos através de um único qubit ancilla. Para implementar essa abordagem no hardware da IBM com topologia heavy-hex, qubits que representam spin-orbitais do mesmo spin são conectados por uma topologia em linha onde cada linha assume um formato em zigue-zague devido à conectividade heavy-hex do hardware alvo, enquanto os qubits que representam spin-orbitais de spin oposto têm conexão apenas a cada quatro qubits.

Clique para mais detalhes sobre as opções obrigatórias:

O usuário precisa fornecer o array initial_layout correspondente aos qubits que satisfazem esse padrão zig-zag na seção lucj_options da função SQD IEF-PCM. No caso de simulações SQD IEF-PCM (14e,12o)/cc-pvdz do metanol, escolhemos o layout inicial de qubits correspondente à diagonal principal do QPU Eagle R3. Aqui, os primeiros 12 elementos do array initial_layout [0, 14, 18, 19, 20, 33, 39, 40, 41, 53, 60, 61, ...] correspondem aos spin-orbitais alfa. Os últimos 12 elementos [... 2, 3, 4, 15, 22, 23, 24, 34, 43, 44, 45, 54] correspondem aos spin-orbitais beta.

É importante que o usuário determine o number_of_shots, que corresponde ao número de medições no circuito LUCJ. O número de shots precisa ser suficientemente grande porque o primeiro passo do procedimento S-CORE depende das amostras no setor de partículas correto para obter a aproximação inicial da distribuição do número de ocupação do estado fundamental.

O número de shots é altamente dependente do sistema e do hardware, mas estudos SQD não-covalentes, baseados em fragmentos e de solvente implícito sugerem que a precisão química pode ser alcançada seguindo estas diretrizes:

  • 20.000 - 200.000 shots para sistemas com menos de 16 orbitais moleculares (32 spin-orbitais)
  • 200.000 shots para sistemas com 16 - 18 orbitais moleculares
  • 200.000 - 2.000.000 shots para sistemas com mais de 18 orbitais moleculares

O número necessário de shots é afetado pelo número de spin-orbitais no sistema estudado e pelo tamanho do espaço de Hilbert correspondente ao espaço ativo selecionado dentro do sistema estudado. Em geral, instâncias com espaços de Hilbert menores requerem menos shots. Outras opções LUCJ disponíveis são o nível de otimização do transpilador de circuito e as opções de supressão de erros. Observe que essas opções também afetam o número necessário de shots e a precisão resultante.

Opções SQD

As opções importantes nas simulações SQD incluem sqd_iterations, number_of_batches e samples_per_batch. Em geral, um número menor de amostras por lote pode ser compensado com mais lotes (number_of_batches) e mais iterações de S-CORE (sqd_iterations). Com mais lotes, podemos amostrar mais variações dos subespaços configuracionais. Como o lote de menor energia é tomado como solução para a energia do estado fundamental do sistema, mais lotes podem melhorar os resultados por meio de melhores estatísticas. Iterações adicionais de S-CORE permitem que mais configurações sejam recuperadas da distribuição LUCJ original caso o número de amostras no setor de partículas correto seja baixo. Isso pode permitir a redução do número de amostras por lote.

Clique para mais informações sobre como configurar as opções SQD:

Uma estratégia alternativa é usar mais amostras por lote, o que garante que a maior parte das amostras LUCJ iniciais no espaço de partículas correto seja usada durante o procedimento S-CORE, e que os subespaços individuais contemplem uma variedade suficiente de configurações eletrônicas. Isso reduz o número de etapas S-CORE necessárias, onde apenas duas ou três iterações de SQD são suficientes se o número de amostras por lote for grande o suficiente. No entanto, mais amostras por lote resulta em um custo computacional mais alto de cada etapa de diagonalização. Portanto, o equilíbrio entre precisão e custo computacional nas simulações SQD pode ser alcançado escolhendo sqd_iterations, number_of_batches e samples_per_batch de forma otimizada.

O estudo SQD IEF-PCM mostra que quando três iterações de S-CORE são usadas, a precisão química pode ser alcançada seguindo estas diretrizes:

  • 600 amostras por lote em simulações SQD IEF-PCM (14e,12o) de metanol
  • 1500 amostras por lote em simulações SQD IEF-PCM (14e,13o) de metilamina
  • 6000 amostras por lote em simulações SQD IEF-PCM (8e,23o) de água
  • 16000 amostras por lote em simulações SQD IEF-PCM (20e,18o) de etanol

Assim como o número necessário de shots no LUCJ, o número necessário de amostras por lote usado no procedimento S-CORE é altamente dependente do sistema e do hardware. Os exemplos acima podem ser usados para estimar o ponto inicial para o benchmark do número necessário de amostras por lote. O tutorial sobre o benchmark sistemático do número necessário de amostras por lote pode ser encontrado aqui.

Implante e execute a função template 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

Autenticação

Use qiskit-ibm-catalog para autenticar no QiskitServerless com sua chave de API (token), que pode ser encontrada no painel do IBM Quantum Platform. Isso permite a instanciação do cliente serverless para fazer o upload ou executar a função selecionada:

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
)

Opcionalmente, use save_account() para salvar suas credenciais em um ambiente local (consulte o guia Configure sua conta IBM Cloud). Observe que isso grava suas credenciais no mesmo arquivo que QiskitRuntimeService.save_account():

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

Se a conta já estiver salva, não é necessário fornecer o token para autenticar:

from qiskit_ibm_catalog import QiskitServerless

serverless = QiskitServerless()

Fazer upload do template

Para fazer o upload de uma Qiskit Function personalizada, você precisa primeiro instanciar um objeto QiskitFunction que define o código-fonte da função. O título permitirá identificar a função assim que ela estiver no cluster remoto. O ponto de entrada principal é o arquivo que contém if __name__ == "__main__". Se o seu fluxo de trabalho precisar de arquivos-fonte adicionais, você pode definir um diretório de trabalho que será enviado junto com o ponto de entrada.

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)

Assim que a instância estiver pronta, faça o upload para o serverless:

serverless.upload(template)
QiskitFunction(sqd_pcm_template)

Para verificar se o programa foi enviado com sucesso, use serverless.list():

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

Carregar e executar o template remotamente

O template de função foi enviado, então você pode executá-lo remotamente com o Qiskit Serverless. Primeiro, carregue o template pelo nome:

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

Em seguida, execute o template com as entradas de nível de domínio para SQD-IEF PCM. Este exemplo especifica uma carga de trabalho baseada em metanol.

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

Verifique o status detalhado do job:

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

Enquanto o job está em execução, você pode buscar os logs criados a partir das saídas de logger.info. Eles podem fornecer informações úteis sobre o progresso do fluxo de trabalho SQD IEF-PCM. Por exemplo, as conexões entre os spin-orbitais do mesmo spin ou a profundidade de gates de dois qubits do circuito ISA final destinado à execução no hardware.

print(job.logs())

Chamar o resultado do job bloqueia o restante do programa até que um resultado esteja disponível. Após a conclusão do job, você pode recuperar os resultados. Eles incluem a energia livre de solvatação, bem como informações sobre o lote de menor energia, o valor de menor energia e outras informações úteis, como a duração total do 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}}

Observe que os metadados do resultado incluem um resumo do uso de recursos que permite estimar melhor o tempo de QPU e CPU necessário para cada carga de trabalho (este exemplo foi executado em um dispositivo fictício, então os tempos reais de uso de recursos podem ser diferentes). Após a conclusão do job, toda a saída de log estará disponível.

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

Próximos passos

Recomendações

Referências

[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/")