{
"cells": [
{
"cell_type": "markdown",
"id": "1682996d",
"metadata": {},
"source": [
"---\n",
"title: \"Cálculos de solvente implícito utilizando o programa “ Qiskit Serverless ”\"\n",
"description: \"Aprenda a calcular os efeitos do solvente implícito em hardware quântico utilizando SQD e IEF-PCM.\"\n",
"---\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "d2c31ae8",
"metadata": {},
"source": [
"\n",
"\n",
"# Cálculos de solvente implícito utilizando o programa “ Qiskit Serverless ”\n",
"\n",
"*Estimativa de tempo de execução: 2 minutos em um processador Heron r2 (NOTA: Trata-se apenas de uma estimativa. (O tempo de execução pode variar.)*\n",
"\n",
"{/* cspell:ignore avas AVAS hcore textit TRIC dmas mocore ncore ncas mocas fermilevel ecore orbts iiter IITER edup textcoords xytext fontsize fontweight frameon */}\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "8bf80006",
"metadata": {},
"source": [
"\n",
"\n",
"## Resultados do aprendizado\n",
"\n",
"Após concluir este tutorial, os usuários deverão compreender:\n",
"\n",
"* Como configurar e executar um fluxo de trabalho remoto usando o [Qiskit Serverless](/docs/guides/serverless)\n",
"* Como calcular os efeitos do solvente implícito usando um computador quântico\n",
"\n",
"\n",
"\n",
"## Pré-requisitos\n",
"\n",
"Recomendamos que os usuários estejam familiarizados com o seguinte tópico antes de seguir com este tutorial:\n",
"\n",
"* [Diagonalização quântica baseada em amostras](/learning/courses/quantum-diagonalization-algorithms/sqd-overview)\n",
"\n",
"\n",
"\n",
"## Segundo plano\n",
"\n",
"Os cálculos com solvente implícito são frequentemente utilizados na biofísica computacional. Esses modelos descrevem como um composto soluto interage com um solvente, sem modelar diretamente o sistema solvente. Em vez disso, é feita uma aproximação na qual o modelo do sistema de solutos é incorporado a uma representação matemática de um meio dielétrico caracterizado empiricamente. Essa aproximação dielétrica interage então com o soluto, que é modelado diretamente. O meio dielétrico influencia as características do sistema de solutos, tais como sua energia do estado fundamental, ao interagir com seu campo eletrônico. Isso é importante para os modelos biofísicos utilizados, por exemplo, na descoberta de medicamentos, pois os compostos se comportam de maneira diferente em diversos ambientes dielétricos. A simulação de um composto no ar (no vácuo) resultará em um comportamento diferente daquele obtido ao simular o mesmo composto na água. Como os compostos farmacêuticos precisam entrar no corpo humano, que por sua vez é composto principalmente de água, é útil simular um composto em uma solução como a água, em vez de no vácuo. Com modelos de solvente implícito, podemos obter esse comportamento com menor custo computacional, embora o resultado final seja, em geral, mais aproximado do que o obtido com os modelos de solvente explícito, que são mais onerosos em termos computacionais e criam representações diretas tanto das moléculas do soluto quanto das do solvente.\n",
"\n",
"Neste tutorial, demonstramos como um algoritmo quântico, a Diagonalização Quântica Baseada em Amostras (SQD), pode ser integrado a um modelo de solvente implícito relativamente pouco dispendioso em termos computacionais. No exemplo, descrevemos como a metilamina se comporta quando se dissolve na água. Comparamos o algoritmo quântico com um método clássico de comparação de última geração chamado CASCI e demonstramos uma estreita concordância entre esses cálculos. Apresentamos uma arquitetura de supercomputação centrada na computação quântica em miniatura, transferindo o pós-processamento clássico — que exige grande capacidade computacional — da parte de amostragem quântica da rotina para um ambiente baseado em nuvem dentro do Qiskit Serverless. O código também demonstra a paralelização entre os núcleos de CPU disponíveis remotamente para reduzir o tempo de computação.\n",
"\n",
"Qiskit Serverless é uma estrutura para executar cargas de trabalho quânticas e clássicas distribuídas sem a necessidade de gerenciar a infraestrutura. Não há provisionamento de servidores (não é necessário iniciar EC2s, clusters, Docker contêineres), nem ferramentas de orquestração ( Kubernetes, Docker Swarm) e nem monitoramento/manutenção. Cada tarefa do Serverless é executada em um contêiner limpo, executa seu código e, em seguida, é encerrada. Não há memória entre tarefas. Basta escrever seu código e enviar sua tarefa. Dentro de uma tarefa sem servidor, um programa pode acessar facilmente back-ends d IBM Quantum® e e, tradicionalmente, realizar o pós-processamento dos resultados nesses back-ends. Com o serviço \" Qiskit Serverless \", os usuários podem acessar núcleos de CPU e memória remotos sempre disponíveis, o que permite a distribuição de determinadas cargas de trabalho tradicionais entre recursos remotos. Os usuários também obtêm algumas vantagens no processamento paralelo de programas, evitando ao mesmo tempo os problemas comuns decorrentes do desligamento do dispositivo no meio da execução. Para obter mais informações sobre o Qiskit Serverless, consulte [a documentação](/docs/guides/serverless) do site, bem como o material adicional disponível em [GitHub](https://qiskit.github.io/qiskit-serverless/index.html).\n",
"\n",
"Este tutorial mostra uma aplicação relevante do seguinte:\n",
"\n",
"* Diagonalização quântica baseada em amostras\n",
"* Modelos computacionais cliente-servidor para computação quântica\n",
"\n",
"Este tutorial é inspirado e baseado em pesquisas realizadas na Cleveland Clinic, conforme descrito em [Kaliakin, Danil, et al. \"Diagonalização quântica implícita baseada em amostras de solvente.\" The Journal of Physical Chemistry B 129.23 (2025): 5788-5796](https://pubs.acs.org/doi/10.1021/acs.jpcb.5c01030), apresentando o fluxo de trabalho completo para cálculos de solvente implícito e ampliando-o com a autoconsistência iterativa do solvente (“The Heartwood Algorithm”, M. Motta, T. Pellegrini (2025), otimização geométrica e seleção automática do layout dos qubits. Consulte [o modelo de função SQD IEF-PCM do Qiskit](/docs/guides/function-template-chemistry-workflow), desenvolvido em conjunto pela Cleveland Clinic e pelo Instituto de Pesquisa em Engenharia de Computação ( IBM® ) com base em pesquisas da Cleveland Clinic, para obter uma interface simplificada do tipo “caixa preta” para a execução de cálculos com solvente implícito.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "55b94021",
"metadata": {},
"source": [
"\n",
"\n",
"## Requisitos\n",
"\n",
"Antes de iniciar este tutorial, certifique-se de que os seguintes itens estejam instalados:\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "9456ea67",
"metadata": {},
"source": [
"* Qiskit SDK v2.0 ou versões posteriores com suporte [à visualização](/docs/api/qiskit/visualization)\n",
"* Qiskit Runtime v0.40 ou posterior (`pip install qiskit-ibm-runtime`)\n",
"* Qiskit SDK v2.0 ou versões posteriores com suporte à visualização `pip install qiskit[visualization]`\n",
"* Qiskit Runtime v0.40 ou posterior `pip install qiskit_ibm_runtime`\n",
"* Catálogo do Qiskit no IBM `pip install qiskit_ibm_catalog`\n",
"* Qiskit IBM : sem servidor `pip install qiskit_serverless`\n",
"* Complemento do Qiskit: Diagonalização quântica baseada em amostras (SQD) v0.12.0 `pip install qiskit_addon_sqd`\n",
"* PySCF `pip install pyscf`\n",
"* FFSIM `pip install ffsim`\n",
"* Matplotlib `pip install matplotlib`\n",
"* Geométrico `pip install geometric`\n",
"\n"
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "7db2e559",
"metadata": {},
"source": [
"\n",
"\n",
"## Instalação\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2c88b910",
"metadata": {},
"outputs": [],
"source": [
"# Establish Quantum Resource connection\n",
"from qiskit_ibm_runtime import QiskitRuntimeService\n",
"\n",
"service = QiskitRuntimeService()\n",
"\n",
"backend = service.least_busy()\n",
"print(f\"Using backend {backend.name}\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "af9286cf",
"metadata": {},
"outputs": [],
"source": [
"# Establish Classical HPC Resource connection\n",
"from qiskit_ibm_catalog import QiskitFunction, QiskitServerless\n",
"\n",
"client = QiskitServerless()"
]
},
{
"cell_type": "markdown",
"id": "aee647af",
"metadata": {},
"source": [
"Crie uma pasta exatamente ao lado do programa principal do notebook chamada `source_files`. Você colocará os arquivos d Python m neste diretório para compartilhá-los com o ambiente de computação remoto. Você deve criar dois arquivos:\n",
"\n",
"* `source_files\\diagonalization_engine.py`\n",
"* `source_files\\classical_simulation.py`\n",
"\n",
"Clique para expandir o texto de cada script abaixo e, em seguida, copie e cole o conteúdo em um arquivo local com esses nomes de caminho.\n",
"\n",
"\n",
" \n",
" \n",
" \n",
"\n",
" \n",
" \n",
" \n",
"\n",
"\n",
"\n",
" Para obter mais informações, consulte o [guia do modelo de função SQD IEF-PCM Qiskit](/docs/guides/function-template-chemistry-workflow) (desenvolvido em conjunto pela Cleveland Clinic e pelo IBM ) mencionado acima. Veja também a [`qiskit_addon_sqd`](/docs/addons/qiskit-addon-sqd) biblioteca.\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7347c7e5",
"metadata": {
"tags": [
"id-diagonalization"
]
},
"outputs": [],
"source": [
"#!/usr/bin/env python3\n",
"import numpy as np\n",
"from json.encoder import JSONEncoder\n",
"from json.decoder import JSONDecoder\n",
"from functools import partial\n",
"import os\n",
"\n",
"from qiskit_ibm_runtime import QiskitRuntimeService\n",
"from qiskit_serverless import distribute_task, get_arguments, get, save_result\n",
"from qiskit_addon_sqd.fermion import (\n",
" SCIResult,\n",
" diagonalize_fermionic_hamiltonian,\n",
" solve_sci,\n",
")\n",
"\n",
"\n",
"### Argument retrieval\n",
"args = get_arguments()\n",
"\n",
"data = args[\"data\"] # Chemistry Data\n",
"energy_tol = args[\"energy_tol\"] # SQD option\n",
"occupancies_tol = args[\"occupancies_tol\"] # SQD option\n",
"max_iterations = args[\"max_iterations\"] # SQD option\n",
"symmetrize_spin = args[\"symmetrize_spin\"] # Eigenstate solver option\n",
"carryover_threshold = args[\"carryover_threshold\"] # Eigenstate solver option\n",
"num_batches = args[\"num_batches\"] # Eigenstate solver option\n",
"samples_per_batch = args[\"samples_per_batch\"] # Eigenstate solver option\n",
"max_cycle = args[\"max_cycle\"] # Eigenstate solver option\n",
"mem = args[\"mem\"] # Memory per Worker\n",
"\n",
"\n",
"# --- fan‑out target: 1 CPU + mem GB RAM per call -------------\n",
"@distribute_task(target={\"cpu\": 1, \"mem\": mem * 1024**3})\n",
"def _solve_sci_worker(\n",
" ix, ci_strs, one_body_tensor, two_body_tensor, norb, nelec, spin_sq\n",
"):\n",
" print(f\">>>>> WORKER {ix} INITIATED\")\n",
" res = solve_sci(\n",
" ci_strs,\n",
" one_body_tensor,\n",
" two_body_tensor,\n",
" norb=norb,\n",
" nelec=nelec,\n",
" spin_sq=spin_sq,\n",
" )\n",
"\n",
" print(f\">>>>> WORKER {ix} COMPLETE\")\n",
" return res\n",
"\n",
"\n",
"def distribute_solve_sci_batch(\n",
" ci_strings: list[tuple[np.ndarray, np.ndarray]],\n",
" one_body_tensor: np.ndarray,\n",
" two_body_tensor: np.ndarray,\n",
" norb: int,\n",
" nelec: tuple[int, int],\n",
" *,\n",
" spin_sq: float | None = None,\n",
" **kwargs,\n",
") -> list[SCIResult]:\n",
" \"\"\"Diagonalize Hamiltonian in subspaces, parallelizing across\n",
" vCPUs in the Serverless environment.\n",
"\n",
" Args:\n",
" ci_strings: List of pairs (strings_a, strings_b) of arrays of\n",
" spin-alpha CI strings and spin-beta CI strings whose Cartesian\n",
" product gives the basis of the subspace in which to perform a\n",
" diagonalization.\n",
" one_body_tensor: The one-body tensor of the Hamiltonian.\n",
" two_body_tensor: The two-body tensor of the Hamiltonian.\n",
" norb: The number of spatial orbitals.\n",
" nelec: The numbers of alpha and beta electrons.\n",
" spin_sq: Target value for the total spin squared for the ground state.\n",
" If ``None``, no spin will be imposed.\n",
" **kwargs: Keyword arguments to pass to\n",
" `pyscf.fci.selected_ci.kernel_fixed_space`\n",
" (https://pyscf.org/pyscf_api_docs/pyscf.fci.html#pyscf.fci.selected_ci.kernel_fixed_space\n",
"\n",
" Returns:\n",
" The results of the diagonalizations in the subspaces given by ci_strings.\n",
" \"\"\"\n",
" inputs = [\n",
" (ix, ci_strs, one_body_tensor, two_body_tensor, norb, nelec, spin_sq)\n",
" for ix, ci_strs in enumerate(ci_strings)\n",
" ]\n",
"\n",
" # fan‑out: spawn one worker per input tuple\n",
" print(\">>>>> ENTERING WORKER FAN-OUT\")\n",
" refs = [_solve_sci_worker(*input_) for input_ in inputs]\n",
" print(\">>>>> WAITING ON WORKERS TO FINISH TASKS\")\n",
"\n",
" # fan‑in: block until every worker finishes\n",
" results = get(refs)\n",
" print(\">>>>> DISTRIBUTED JOBS COMPLETED\")\n",
"\n",
" return results\n",
"\n",
"\n",
"# A caveat of executing a Python program remotely is\n",
"# that the inputs to the remote program must be passed\n",
"# over an internet network. Similarly, the outputs\n",
"# must be passed back to the local program via the same\n",
"# structure. Python objects are not always able to be\n",
"# passed over a network, and must be encoded in a\n",
"# JSON serializable format.\n",
"i_data = JSONDecoder().decode(data)\n",
"\n",
"# i_data has all of the information needed from the\n",
"# local program to pick up where the computation left off\n",
"# after its submission to the remote environment.\n",
"[\n",
" job_id,\n",
" hcore,\n",
" eri,\n",
" num_orbitals,\n",
" nuclear_repulsion_energy,\n",
" num_elec_a,\n",
" num_elec_b,\n",
"] = i_data\n",
"\n",
"# Re-convert data back into numpy format, after serialization\n",
"hcore = np.array(hcore)\n",
"eri = np.array(eri)\n",
"nuclear_repulsion_energy = np.float64(nuclear_repulsion_energy)\n",
"\n",
"# Instantiate Runtime Service to retrieve the\n",
"# bitstrings from the QPU job. We provided these\n",
"# credentials upon Serverless setup.\n",
"service = QiskitRuntimeService(\n",
" channel=os.environ.get(\"QISKIT_IBM_CHANNEL\"),\n",
" token=os.environ.get(\"QISKIT_IBM_TOKEN\"),\n",
" instance=os.environ.get(\"QISKIT_IBM_INSTANCE\"),\n",
")\n",
"\n",
"# retrieving the QPU job data from the Serverless side\n",
"job = service.job(job_id)\n",
"primitive_result = job.result()\n",
"pub_result = primitive_result[0]\n",
"bit_array = pub_result.data.meas # Getting the bitstrings\n",
"\n",
"# Pass options to the built-in eigensolver\n",
"sci_solver = partial(\n",
" distribute_solve_sci_batch, spin_sq=0.0, max_cycle=max_cycle\n",
")\n",
"\n",
"# List to capture intermediate results\n",
"result_history = []\n",
"\n",
"\n",
"def callback(results: list[SCIResult]):\n",
" result_history.append(results)\n",
" iteration = len(result_history)\n",
" print(f\">>>>> SQD ITERATION {iteration}\")\n",
" for i, result in enumerate(results):\n",
" print(f\">>>>> SUBSAMPLE {i}\")\n",
" print(f\">>>>> \\tENERGY: {result.energy + nuclear_repulsion_energy}\")\n",
" print(\n",
" f\">>>>> \\tSUBSPACE DIMENSION: {np.prod(result.sci_state.amplitudes.shape)}\"\n",
" )\n",
"\n",
"\n",
"result = diagonalize_fermionic_hamiltonian(\n",
" hcore,\n",
" eri,\n",
" bit_array,\n",
" samples_per_batch=samples_per_batch,\n",
" norb=num_orbitals,\n",
" nelec=(num_elec_a, num_elec_b),\n",
" num_batches=num_batches,\n",
" energy_tol=energy_tol,\n",
" occupancies_tol=occupancies_tol,\n",
" max_iterations=max_iterations,\n",
" sci_solver=sci_solver,\n",
" symmetrize_spin=symmetrize_spin,\n",
" carryover_threshold=carryover_threshold,\n",
" callback=callback,\n",
" seed=12345,\n",
")\n",
"\n",
"print(\">>>>> EXACT DIAGONALIZATION COMPLETE. CLEANING UP, SERIALIZING DATA.\")\n",
"# Numpy arrays are not JSON serializable.\n",
"# Convert them to List objects before using the JSONEncoder\n",
"o_data = JSONEncoder().encode(\n",
" [\n",
" result.energy + nuclear_repulsion_energy,\n",
" result.energy,\n",
" result.rdm1.tolist(),\n",
" result.rdm2.tolist(),\n",
" [x.tolist() for x in result.orbital_occupancies],\n",
" [\n",
" result.sci_state.nelec,\n",
" result.sci_state.norb,\n",
" [x.tolist() for x in result.sci_state.orbital_occupancies()],\n",
" [x.tolist() for x in result.sci_state.rdm()],\n",
" ],\n",
" ]\n",
")\n",
"\n",
"# JSON-safe package\n",
"save_result({\"outputs\": o_data}) # single JSON blob returned to client"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "41807b3a",
"metadata": {
"tags": [
"id-classical"
]
},
"outputs": [],
"source": [
"#!/usr/bin/env python3\n",
"from json.encoder import JSONEncoder\n",
"from json.decoder import JSONDecoder\n",
"\n",
"from qiskit_serverless import get_arguments, save_result\n",
"\n",
"import pyscf\n",
"from pyscf import gto, scf\n",
"from pyscf.solvent import pcm\n",
"from pyscf.mcscf import avas\n",
"\n",
"import psutil\n",
"\n",
"mem_info = (\n",
" psutil.virtual_memory()\n",
") # Get information about virtual memory (RAM)\n",
"total_ram_gb = mem_info.total / (1024**3) # Convert bytes to GB\n",
"print(f\">>>>> SERVERLESS TOTAL RAM: {total_ram_gb:.2f} GB\")\n",
"\n",
"### Argument retrieval\n",
"args = get_arguments()\n",
"data = args[\"data\"] # Chemistry Data\n",
"\n",
"i_data = JSONDecoder().decode(data)\n",
"[mol_geo, eps, ao_labels] = i_data\n",
"\n",
"print(\">>>>> DEFINING MOLECULE\")\n",
"mol = gto.M()\n",
"mol.atom = mol_geo\n",
"mol.basis = \"cc-pVDZ\"\n",
"mol.unit = \"Ang\"\n",
"mol.charge = 0\n",
"mol.spin = 0\n",
"mol.verbose = 0\n",
"\n",
"print(\">>>>> BUILDING MOLECULE\")\n",
"mol.build()\n",
"\n",
"print(\">>>>> DEFINING PCM\")\n",
"cm = pcm.PCM(mol)\n",
"cm.eps = eps # for water\n",
"cm.method = \"IEF-PCM\"\n",
"\n",
"print(\">>>>> BUILDING RESTRICTED HARTREE FOCK\")\n",
"mf = scf.RHF(mol).PCM(cm) # This is the Final SCF object\n",
"mf.kernel(verbose=0)\n",
"\n",
"print(\">>>>> RUNNING AVAS\")\n",
"avas_ = avas.AVAS(mf, ao_labels, with_iao=True, canonicalize=True, verbose=0)\n",
"avas_.kernel()\n",
"norb, ne_act, mo_avas = avas_.ncas, avas_.nelecas, avas_.mo_coeff\n",
"\n",
"print(\">>>>> STARTING CASCI\")\n",
"mc_pcm = pyscf.mcscf.CASCI(mf, norb, ne_act).PCM(\n",
" cm\n",
") # Make sure to decorate the CASCI object with PCM\n",
"mc_pcm.mo_coeff = mo_avas\n",
"# mc_pcm.max_memory = 140000\n",
"\n",
"(CASCI_E, _, _, _, _) = mc_pcm.kernel(verbose=0)\n",
"\n",
"print(f\">>>>> CASCI_E: {CASCI_E}\")\n",
"o_data = JSONEncoder().encode([float(CASCI_E)])\n",
"\n",
"# JSON-safe package\n",
"save_result({\"outputs\": o_data}) # single JSON blob returned to client"
]
},
{
"cell_type": "markdown",
"id": "c94aebd8",
"metadata": {},
"source": [
"Precisamos compartilhar o programa destinado a ser executado no ambiente de nuvem e reenviá-lo sempre que alterarmos seu código-fonte:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "cc00669f",
"metadata": {},
"outputs": [],
"source": [
"client.upload(\n",
" QiskitFunction(\n",
" title=\"diagonalization_engine\",\n",
" entrypoint=\"diagonalization_engine.py\", # lives in ./source_files\n",
" working_dir=\"source_files\",\n",
" )\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ef726eee",
"metadata": {},
"outputs": [],
"source": [
"client.upload(\n",
" QiskitFunction(\n",
" title=\"classical_simulation\",\n",
" entrypoint=\"classical_simulation.py\", # lives in ./source_files\n",
" working_dir=\"source_files\",\n",
" )\n",
")"
]
},
{
"cell_type": "markdown",
"id": "0cd9185e",
"metadata": {},
"source": [
"\n",
"\n",
"## Exemplo de simulador em pequena escala\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "b0db693d",
"metadata": {},
"source": [
"Este tutorial não utiliza um simulador de pequena escala, pois o objetivo é demonstrar uma aplicação quântica escalável que vai além do âmbito da exploração por meio de simuladores. Em vez disso, mostramos mais adiante como esse método pode ser implementado utilizando um método clássico de comparação de última geração chamado CASCI.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "431a5bd2-e6ed-471b-ad9e-c4edd27784a8",
"metadata": {},
"source": [
"\n",
"\n",
"## Exemplo de hardware em grande escala\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5df67bda",
"metadata": {},
"outputs": [],
"source": [
"# This is a useful helper function that displays\n",
"# remote job execution details to the user's local machine\n",
"def feedback_serverless(serverless_job):\n",
" import time\n",
"\n",
" # Wait for the job to execute\n",
" print(f\">>>>> Serverless status: {serverless_job.job_id}\")\n",
" timer = 0\n",
" while timer < 10000:\n",
" if (\n",
" serverless_job.status() == \"QUEUED\"\n",
" or serverless_job.status() == \"INITIALIZING\"\n",
" or serverless_job.status() == \"RUNNING\"\n",
" ):\n",
" print(f\">>>>> [{timer}s] Serverless job {serverless_job.job_id}: \\\n",
" {serverless_job.status()}\")\n",
" time.sleep(10)\n",
" timer += 10\n",
"\n",
" elif serverless_job.status() == \"ERROR\":\n",
" print(\n",
" f\">>>>> Serverless job {serverless_job.job_id}: {serverless_job.status()}\"\n",
" )\n",
" print(\">>>>> Logs:\")\n",
" print(serverless_job.logs())\n",
" break\n",
"\n",
" elif serverless_job.status() == \"DONE\":\n",
" print(\n",
" f\">>>>> Serverless job {serverless_job.job_id}: {serverless_job.status()}\"\n",
" )\n",
" break\n",
"\n",
" else:\n",
" break\n",
"\n",
" return"
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "988ee237",
"metadata": {},
"source": [
"\n",
"\n",
"## Passo 1: Mapeie entradas clássicas para um problema quântico\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "cf4bbd59",
"metadata": {},
"source": [
"\n",
"\n",
"### 1.1: Inicializar o objeto molécula utilizando a geometria molecular conhecida do $\\textit{a priori}$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "566e06b4",
"metadata": {},
"outputs": [],
"source": [
"# Reference guide for building molecule structures:\n",
"# https://pyscf.org/user/gto.html\n",
"# Video tutorial on building molecular objects in PySCF:\n",
"# https://www.youtube.com/watch?v=cNC2cY9E9j0\n",
"\n",
"molecule_name = \"Methylamine\"\n",
"\n",
"methylamine_geo = \"\"\"\n",
" N -0.7154 0.0000 0.0000;\n",
" C 0.7154 0.0000 0.0000;\n",
" H 1.1069 0.0916 1.0174;\n",
" H 1.0996 0.8349 -0.5930;\n",
" H 1.0996 -0.9274 -0.4345;\n",
" H -1.0625 0.8564 0.4294;\n",
" H -1.0625 -0.7661 0.5753;\n",
"\"\"\""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4a7aec02",
"metadata": {},
"outputs": [],
"source": [
"# Imports\n",
"import pyscf\n",
"from pyscf import gto # Deals with molecular initialization\n",
"from pyscf import scf # Solvation methods\n",
"\n",
"# Explicitly defining the Methylamine molecule\n",
"mol = gto.M()\n",
"mol.atom = methylamine_geo\n",
"mol.basis = \"cc-pVDZ\"\n",
"mol.unit = \"Ang\"\n",
"mol.charge = 0\n",
"mol.spin = 0\n",
"mol.verbose = 0\n",
"\n",
"mol.build()"
]
},
{
"cell_type": "markdown",
"id": "99359d80",
"metadata": {},
"source": [
"\n",
"\n",
"### 1.2: Definir os efeitos de solvatação utilizando o Modelo de Continuum Polarizável (PCM)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9294b528",
"metadata": {},
"outputs": [],
"source": [
"# You can explore other solvents (such as methanol) by\n",
"# retrieving other dielectric parameters from:\n",
"# https://gaussian.com/scrf/\n",
"from pyscf.solvent import pcm\n",
"\n",
"eps_water = 78.3553 # If solvating in a different medium,\n",
"# set this constant appropriately using a known value"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ffccfb92",
"metadata": {},
"outputs": [],
"source": [
"cm = pcm.PCM(mol)\n",
"cm.eps = eps_water # PySCF defaults to water solvation,\n",
"# but here we show this solvation parameter explicitly\n",
"\n",
"cm.method = (\n",
" \"IEF-PCM\" # Alternative solvation models include C-PCM, SS(V)PE, COSMO\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bfef3c9b",
"metadata": {},
"outputs": [],
"source": [
"# Create a \"Restricted Hartree-Fock\" object for the solute,\n",
"# then wrap the SCF object with a Polarizable Continuum Model\n",
"mf_pcm0 = scf.RHF(mol).PCM(\n",
" cm\n",
") # Restricted Hartree-Fock misses instantaneous correlations,\n",
"# post-HF methods like CCSD, CI, MP2 might be worth exploring"
]
},
{
"cell_type": "markdown",
"id": "b5e6c20a",
"metadata": {},
"source": [
"\n",
"\n",
"### 1.3: Otimização geométrica utilizando o TRIC\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "493402b3",
"metadata": {},
"outputs": [],
"source": [
"# Geometry optimization with geomeTRIC\n",
"from pyscf.geomopt.geometric_solver import (\n",
" optimize,\n",
") # GeomeTRIC under the hood, for geometry optimization\n",
"\n",
"mol_opt = optimize(\n",
" mf_pcm0, tol_grad=3e-4, verbose=0\n",
") # Use geomeTRIC/TRIC under the hood"
]
},
{
"cell_type": "markdown",
"id": "58c168bf",
"metadata": {},
"source": [
"\n",
"\n",
"### 1.4: Prepare o modelo contínuo e o objeto de campo médio com as variáveis relevantes\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1834cb22",
"metadata": {},
"outputs": [],
"source": [
"from pyscf.mcscf import avas\n",
"\n",
"# Re-define PCM\n",
"cm = pcm.PCM(mol_opt)\n",
"cm.eps = eps_water # for water\n",
"cm.method = \"IEF-PCM\"\n",
"\n",
"# Re-build Restricted Hartree Fock object\n",
"mf_opt = scf.RHF(mol_opt).PCM(cm)\n",
"mf_opt.kernel(verbose=0)\n",
"\n",
"# Run AVAS\n",
"ao_labels = [\"C 2s\", \"C 2p\", \"N 2s\", \"N 2p\", \"H 1s\"]\n",
"avas_ = avas.AVAS(\n",
" mf_opt, ao_labels, with_iao=True, canonicalize=True, verbose=0\n",
")\n",
"avas_.kernel()\n",
"norb, ne_act, mo_avas = avas_.ncas, avas_.nelecas, avas_.mo_coeff\n",
"\n",
"num_elec_a = (ne_act + mol_opt.spin) // 2\n",
"num_elec_b = (ne_act - mol_opt.spin) // 2"
]
},
{
"cell_type": "markdown",
"id": "ac6f36e3",
"metadata": {},
"source": [
"\n",
"\n",
"## Passo 2: Otimizar o problema para execução em hardware quântico\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "52506835",
"metadata": {},
"source": [
"Para obter mais informações sobre as funções auxiliares demonstradas aqui, consulte o tutorial “[Diagonalização quântica baseada em amostras de um hamiltoniano químico](/docs/tutorials/sample-based-quantum-diagonalization) ”.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dc27c42e",
"metadata": {},
"outputs": [],
"source": [
"# Standard SQD helper functions (From SQD Tutorial)\n",
"\n",
"from typing import Sequence\n",
"import rustworkx\n",
"from qiskit.providers import BackendV2\n",
"from qiskit import QuantumCircuit, QuantumRegister\n",
"\n",
"from rustworkx import NoEdgeBetweenNodes, PyGraph\n",
"\n",
"IBM_TWO_Q_GATES = {\"cx\", \"ecr\", \"cz\"}\n",
"\n",
"\n",
"def create_linear_chains(num_orbitals: int) -> PyGraph:\n",
" \"\"\"In zig-zag layout, there are two linear chains (with connecting\n",
" qubits between the chains). This function creates those two linear\n",
" chains: a rustworkx PyGraph with two disconnected linear chains.\n",
" Each chain contains `num_orbitals` number of nodes, that is, in the\n",
" final graph there are `2 * num_orbitals` number of nodes.\n",
"\n",
" Args:\n",
" num_orbitals (int): Number orbitals or nodes in each linear chain.\n",
" They are also known as alpha-alpha interaction qubits.\n",
"\n",
" Returns:\n",
" A rustworkx.PyGraph with two disconnected linear chains each with\n",
" `num_orbitals` number of nodes.\n",
" \"\"\"\n",
" G = rustworkx.PyGraph()\n",
"\n",
" for n in range(num_orbitals):\n",
" G.add_node(n)\n",
"\n",
" for n in range(num_orbitals - 1):\n",
" G.add_edge(n, n + 1, None)\n",
"\n",
" for n in range(num_orbitals, 2 * num_orbitals):\n",
" G.add_node(n)\n",
"\n",
" for n in range(num_orbitals, 2 * num_orbitals - 1):\n",
" G.add_edge(n, n + 1, None)\n",
"\n",
" return G\n",
"\n",
"\n",
"def create_lucj_zigzag_layout(\n",
" num_orbitals: int, backend_coupling_graph: PyGraph\n",
") -> tuple[PyGraph, int]:\n",
" \"\"\"This function creates the complete zigzag graph that 'can be mapped'\n",
" to an IBM QPU with heavy-hex connectivity (the zigzag must be an\n",
" isomorphic sub-graph to the QPU/backend coupling graph for it to be\n",
" mapped). The zigzag pattern includes both linear chains (alpha-alpha\n",
" interactions) and connecting qubits between the linear chains\n",
" (alpha-beta interactions).\n",
"\n",
" Args:\n",
" num_orbitals (int): Number of orbitals, that is, number of nodes in\n",
" each alpha-alpha linear chain.\n",
" backend_coupling_graph (PyGraph): The coupling graph of the backend\n",
" on which the LUCJ ansatz will be mapped and run. This function takes\n",
" the coupling graph as a undirected `rustworkx.PyGraph` where there\n",
" is only one 'undirected' edge between two nodes, that is, qubits.\n",
" Usually, the coupling graph of a IBM backend is directed (for\n",
" example, Eagle devices such as ibm_brisbane) or may have two edges\n",
" between two nodes (for example, Heron `ibm_torino`). A user\n",
" needs to make such graphs undirected or remove duplicate edges\n",
" (or do both) to make them compatible with this function.\n",
"\n",
" Returns:\n",
" G_new (PyGraph): The graph with IBM backend compliant zigzag pattern.\n",
" num_alpha_beta_qubits (int): Number of connecting qubits between the\n",
" linear chains in the zigzag pattern. While we want as many\n",
" connecting (alpha-beta) qubits between the linear (alpha-alpha)\n",
" chains, we cannot accommodate all due to qubit and connectivity\n",
" constraints of backends. This is the maximum number of connecting\n",
" qubits the zigzag pattern can have while being backend compliant\n",
" (that is, isomorphic to backend coupling graph).\n",
" \"\"\"\n",
" isomorphic = False\n",
" G = create_linear_chains(num_orbitals=num_orbitals)\n",
"\n",
" num_iters = num_orbitals\n",
" while not isomorphic:\n",
" G_new = G.copy()\n",
" num_alpha_beta_qubits = 0\n",
" for n in range(num_iters):\n",
" if n % 4 == 0:\n",
" new_node = 2 * num_orbitals + num_alpha_beta_qubits\n",
" G_new.add_node(new_node)\n",
" G_new.add_edge(n, new_node, None)\n",
" G_new.add_edge(new_node, n + num_orbitals, None)\n",
" num_alpha_beta_qubits = num_alpha_beta_qubits + 1\n",
" isomorphic = rustworkx.is_subgraph_isomorphic(\n",
" backend_coupling_graph, G_new\n",
" )\n",
" num_iters -= 1\n",
"\n",
" return G_new, num_alpha_beta_qubits\n",
"\n",
"\n",
"def lightweight_layout_error_scoring(\n",
" backend: BackendV2,\n",
" virtual_edges: Sequence[Sequence[int]],\n",
" physical_layouts: Sequence[int],\n",
" two_q_gate_name: str,\n",
") -> list[list[list[int], float]]:\n",
" \"\"\"Lightweight and heuristic function to score isomorphic layouts. There\n",
" can be many zigzag patterns, each with different set of physical qubits,\n",
" that can be mapped to a backend. Some of them might include fewer noise\n",
" qubits and couplings than others. This function computes a simple error\n",
" score for each such layout. It sums up 2Q gate error for all couplings\n",
" in the zigzag pattern (layout) and measurement of errors of physical\n",
" qubits in the layout to compute the error score.\n",
"\n",
" Note:\n",
" This lightweight scoring can be refined using concepts such as\n",
" mapomatic.\n",
"\n",
" Args:\n",
" backend (BackendV2): A backend.\n",
" virtual_edges (Sequence[Sequence[int]]): Edges in the device-\n",
" compliant zigzag pattern where nodes are numbered from 0 to (2 *\n",
" num_orbitals + num_alpha_beta_qubits).\n",
" physical_layouts (Sequence[int]): All physical layouts of the zigzag\n",
" pattern that are isomorphic to each other and to the larger backend\n",
" coupling map.\n",
" two_q_gate_name (str): The name of the two-qubit gate of the\n",
" backend. The name is used for fetching two-qubit gate error from\n",
" backend properties.\n",
"\n",
" Returns:\n",
" scores (list): A list of lists where each sublist contains two\n",
" items. First item is the layout, and second item is a float\n",
" representing error score of the layout. The layouts in the `scores`\n",
" are sorted in the ascending order of error score.\n",
" \"\"\"\n",
" props = backend.properties()\n",
" scores = []\n",
" for layout in physical_layouts:\n",
" total_2q_error = 0\n",
" for edge in virtual_edges:\n",
" physical_edge = (layout[edge[0]], layout[edge[1]])\n",
" try:\n",
" ge = props.gate_error(two_q_gate_name, physical_edge)\n",
" except Exception:\n",
" ge = props.gate_error(two_q_gate_name, physical_edge[::-1])\n",
" total_2q_error += ge\n",
" total_measurement_error = 0\n",
" for qubit in layout:\n",
" meas_error = props.readout_error(qubit)\n",
" total_measurement_error += meas_error\n",
" scores.append([layout, total_2q_error + total_measurement_error])\n",
" return sorted(scores, key=lambda x: x[1])\n",
"\n",
"\n",
"def _make_backend_cmap_pygraph(backend: BackendV2) -> PyGraph:\n",
" graph = backend.coupling_map.graph\n",
" if not graph.is_symmetric():\n",
" graph.make_symmetric()\n",
" backend_coupling_graph = graph.to_undirected()\n",
"\n",
" edge_list = backend_coupling_graph.edge_list()\n",
" removed_edge = []\n",
" for edge in edge_list:\n",
" if set(edge) in removed_edge:\n",
" continue\n",
" try:\n",
" backend_coupling_graph.remove_edge(edge[0], edge[1])\n",
" removed_edge.append(set(edge))\n",
" except NoEdgeBetweenNodes:\n",
" pass\n",
"\n",
" return backend_coupling_graph\n",
"\n",
"\n",
"def get_zigzag_physical_layout(\n",
" num_orbitals: int, backend: BackendV2, score_layouts: bool = True\n",
") -> tuple[list[int], int]:\n",
" \"\"\"The main function that generates the zigzag pattern\n",
" with physical qubits that can be used as an `intial_layout` in a\n",
" preset passmanager/transpiler.\n",
"\n",
" Args:\n",
" num_orbitals (int): Number of orbitals.\n",
" backend (BackendV2): A backend.\n",
" score_layouts (bool): Optional. If `True`, it uses the\n",
" `lightweight_layout_error_scoring` function to score the\n",
" isomorphic layouts and returns the layout with\n",
" fewer erroneous qubits.\n",
" If `False`, returns the first isomorphic subgraph.\n",
"\n",
" Returns:\n",
" A tuple of device compliant layout (list[int]) with zigzag pattern\n",
" and an int representing number of alpha-beta-interactions.\n",
" \"\"\"\n",
" backend_coupling_graph = _make_backend_cmap_pygraph(backend=backend)\n",
"\n",
" G, num_alpha_beta_qubits = create_lucj_zigzag_layout(\n",
" num_orbitals=num_orbitals,\n",
" backend_coupling_graph=backend_coupling_graph,\n",
" )\n",
"\n",
" isomorphic_mappings = rustworkx.vf2_mapping(\n",
" backend_coupling_graph, G, subgraph=True\n",
" )\n",
" isomorphic_mappings = list(isomorphic_mappings)\n",
"\n",
" edges = list(G.edge_list())\n",
"\n",
" layouts = []\n",
" for mapping in isomorphic_mappings:\n",
" initial_layout = [None] * (2 * num_orbitals + num_alpha_beta_qubits)\n",
" for key, value in mapping.items():\n",
" initial_layout[value] = key\n",
" layouts.append(initial_layout)\n",
"\n",
" two_q_gate_name = IBM_TWO_Q_GATES.intersection(\n",
" backend.configuration().basis_gates\n",
" ).pop()\n",
"\n",
" if score_layouts:\n",
" scores = lightweight_layout_error_scoring(\n",
" backend=backend,\n",
" virtual_edges=edges,\n",
" physical_layouts=layouts,\n",
" two_q_gate_name=two_q_gate_name,\n",
" )\n",
"\n",
" return scores[0][0][:-num_alpha_beta_qubits], num_alpha_beta_qubits\n",
"\n",
" return layouts[0][:-num_alpha_beta_qubits], num_alpha_beta_qubits"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "87f8e3ec",
"metadata": {},
"outputs": [],
"source": [
"from qiskit.transpiler import generate_preset_pass_manager\n",
"import ffsim\n",
"\n",
"# Initial LUCJ ansatz layout\n",
"initial_layout, _ = get_zigzag_physical_layout(norb, backend=backend)\n",
"\n",
"# Initialize a pass manager\n",
"pass_manager = generate_preset_pass_manager(\n",
" optimization_level=3, backend=backend, initial_layout=initial_layout\n",
")\n",
"\n",
"pass_manager.pre_init = ffsim.qiskit.PRE_INIT"
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "b4d480b3",
"metadata": {},
"source": [
"\n",
"\n",
"## Etapas 3 e 4: Executar usando o Qiskit e realizar o pós-processamento usando o Qiskit Serverless\n",
"\n",
"Aqui, combinamos a Etapa 3 (Execução) e a Etapa 4 (Pós-processamento), pois o contexto de aplicação do modelo de solvente implícito requer um ciclo de retroalimentação iterativo que executa vários ciclos de execução e pós-processamento para melhorar o resultado final do cálculo.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "8715bb6b",
"metadata": {},
"source": [
"\n",
"\n",
"### 3.1 Calcular a energia de Hartree-Fock restrita\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3aa879ad",
"metadata": {},
"outputs": [],
"source": [
"# Run the kernel to get the RHF energy\n",
"mf_opt = scf.RHF(mol_opt).PCM(cm)\n",
"hf_e = float(mf_opt.kernel())"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "480dd476",
"metadata": {},
"outputs": [],
"source": [
"print(f\"Restricted Hartree-Fock Energy: {hf_e}\")"
]
},
{
"cell_type": "markdown",
"id": "fd0145c6",
"metadata": {},
"source": [
"\n",
"\n",
"### 3.2: Estabelecer a energia de referência clássica com o CASCI\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f629119d",
"metadata": {},
"outputs": [],
"source": [
"# Setup a Serverless Client\n",
"worker = client.load(\"classical_simulation\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bb9d2407",
"metadata": {},
"outputs": [],
"source": [
"from json.encoder import JSONEncoder\n",
"\n",
"ao_labels = [\"C 2s\", \"C 2p\", \"N 2s\", \"N 2p\", \"H 1s\"]\n",
"data_e = JSONEncoder().encode([mol_opt.tostring(), eps_water, ao_labels])"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "93874c58",
"metadata": {},
"outputs": [],
"source": [
"serverless_job = worker.run(data=data_e)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "756f0fdf",
"metadata": {},
"outputs": [],
"source": [
"# Optionally, check the Serverless status feedback\n",
"# Don't sit here and stare at the feedback unless debugging.\n",
"# You can go develop something else while the Serverless job runs.\n",
"_ = feedback_serverless(serverless_job)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d3ede43c",
"metadata": {},
"outputs": [],
"source": [
"# If you make a mistake and need to cancel something\n",
"\n",
"# for job in client.jobs():\n",
"# job.cancel()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7379c49f",
"metadata": {},
"outputs": [],
"source": [
"from json.decoder import JSONDecoder\n",
"\n",
"CASCI_E = JSONDecoder().decode(serverless_job.result()[\"outputs\"])[0]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0a5f4b88",
"metadata": {},
"outputs": [],
"source": [
"# We have approximated the red, classical baseline from\n",
"# Figure 1 for Methanol (North-West panel)\n",
"print(f\"CASCI/IEF-PCM(cc-pVDZ): E={CASCI_E}\")"
]
},
{
"cell_type": "markdown",
"id": "b22a1b00",
"metadata": {},
"source": [
"\n",
"\n",
"## Configurar parâmetros do aplicativo\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "618375af",
"metadata": {},
"outputs": [],
"source": [
"# Systematically vary these parameters to improve hardware results\n",
"\n",
"# Set to \"True\" to run on real hardware\n",
"use_hardware = True\n",
"\n",
"# Error suppression/mitigation options\n",
"# >> Configure within Sampler primitive\n",
"\n",
"# Transpiler Options\n",
"optimization_level = 3\n",
"\n",
"# Heartwood algorithm options\n",
"n_iter = 15 # How many update loops to run\n",
"resample = 1 # (resample=1 -> resample the QPU after every\n",
"# update loop; resample=n_iter -> sample QPU only once)\n",
"shots = 10000\n",
"\n",
"# SQD options\n",
"energy_tol = 1e-4\n",
"occupancies_tol = 1e-3\n",
"max_iterations = 12\n",
"\n",
"# Eigenstate solver options\n",
"num_batches = 5\n",
"samples_per_batch = 300\n",
"symmetrize_spin = True\n",
"carryover_threshold = 1e-5\n",
"max_cycle = 200\n",
"\n",
"# Classical post-processing options\n",
"local = (\n",
" False # Remote, Serverless (False) versus Local Post-Processing (True)\n",
")\n",
"mem = 16 # Memory allocated to each diagonalization worker (Gb)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ce75a126",
"metadata": {},
"outputs": [],
"source": [
"# Heartwood algorithm subroutines\n",
"import os\n",
"import numpy as np\n",
"import pyscf\n",
"from pyscf import ao2mo, cc\n",
"from functools import reduce\n",
"import ffsim\n",
"\n",
"from json.encoder import JSONEncoder\n",
"from json.decoder import JSONDecoder\n",
"import time\n",
"\n",
"from functools import partial\n",
"from qiskit_addon_sqd.fermion import (\n",
" SCIResult,\n",
" diagonalize_fermionic_hamiltonian,\n",
" solve_sci_batch,\n",
")\n",
"\n",
"\n",
"def update_rdm(casci_object, dmas):\n",
" \"\"\"\n",
" Inputs:\n",
" mc -> CASCI object\n",
" dmas -> Spin-summed 1-particle reduced density matrix\n",
"\n",
" This function returns the CASCI/SQD one-body density matrix in\n",
" the full basis of atomic orbitals, written as the sum (last line)\n",
" of two terms:\n",
" - a contribution from the core orbitals,\n",
" np.dot(mocore, mocore.conj().T) * 2, (core = inactive and doubly-occupied)\n",
" - a contribution from the active-space orbitals and electrons (dmas)\n",
" rotated from the active-space to the AO basis (the reduce operation)\n",
"\n",
" Outputs:\n",
" rho_approximation: The CASCI/SQD one-body density matrix\n",
" in the full basis of atomic orbitals\n",
"\n",
" \"\"\"\n",
" mo_coeff = casci_object.mo_coeff\n",
" ncore = casci_object.ncore\n",
" ncas = casci_object.ncas\n",
" mocore = mo_coeff[:, :ncore]\n",
" mocas = mo_coeff[:, ncore : ncore + ncas]\n",
" dm1 = np.dot(mocore, mocore.conj().T) * 2\n",
"\n",
" rho_approximation = dm1 + reduce(np.dot, (mocas, dmas, mocas.conj().T))\n",
" return rho_approximation\n",
"\n",
"\n",
"def run_active_space_calculation(\n",
" h1e_cas, h2e_cas, norb, ne_act, orbs, fermilevel, ecore\n",
"):\n",
" # ----- perform an HF and a CCSD calculation in the active space\n",
" from pyscf import tools\n",
" from datetime import datetime\n",
"\n",
" now = datetime.now().strftime(\"%H:%M:%S\")\n",
" print(\">>>>> ACTIVE SPACE CALCULATIONS \")\n",
" tools.fcidump.from_integrals(\n",
" f\"as_fcidump_{now}.txt\",\n",
" h1e_cas,\n",
" h2e_cas,\n",
" norb,\n",
" ne_act,\n",
" ms=0,\n",
" nuc=ecore,\n",
" ) # Forcefully represents the active space in the correct structure\n",
" mf_as = tools.fcidump.to_scf(f\"as_fcidump_{now}.txt\")\n",
" os.remove(f\"as_fcidump_{now}.txt\")\n",
" mf_as.kernel()\n",
" print(\">>>>> RUNNING CCSD\")\n",
"\n",
" mf_cc = cc.CCSD(mf_as)\n",
" mf_cc.kernel()\n",
" orbts = mf_as.mo_coeff\n",
" t1, t2 = mf_cc.t1, mf_cc.t2\n",
" print(\">>>>> UPDATED t1, t2 PARAMETERS\")\n",
"\n",
" # ----- update the HF orbitals\n",
" active = list(\n",
" range(fermilevel - ne_act // 2, fermilevel - ne_act // 2 + norb)\n",
" )\n",
" orbs[:, active] = np.dot(orbs[:, active], orbts)\n",
" return orbs, t1, t2\n",
"\n",
"\n",
"def get_lucj(norb, num_elec_a, num_elec_b, t1, t2, n_reps=1):\n",
" print(\">>>>> CONSTRUCTING LUCJ CIRCUIT\")\n",
"\n",
" alpha_alpha_indices = [(p, p + 1) for p in range(norb - 1)]\n",
" alpha_beta_indices = [(p, p) for p in range(0, norb, 4)]\n",
"\n",
" ucj_op = ffsim.UCJOpSpinBalanced.from_t_amplitudes(\n",
" t1=t1, # <---- Update t1 each loop\n",
" t2=t2, # <---- Update t2 each loop\n",
" n_reps=n_reps,\n",
" interaction_pairs=(alpha_alpha_indices, alpha_beta_indices),\n",
" )\n",
" nelec = (num_elec_a, num_elec_b)\n",
"\n",
" # create an empty quantum circuit\n",
" qubits = QuantumRegister(2 * norb, name=\"q\")\n",
" circuit = QuantumCircuit(qubits)\n",
"\n",
" # prepare Hartree-Fock state as the reference state\n",
" # and append it to the quantum circuit\n",
" circuit.append(ffsim.qiskit.PrepareHartreeFockJW(norb, nelec), qubits)\n",
"\n",
" # apply the UCJ operator to the reference state\n",
" circuit.append(ffsim.qiskit.UCJOpSpinBalancedJW(ucj_op), qubits)\n",
" circuit.measure_all()\n",
"\n",
" return circuit\n",
"\n",
"\n",
"# Classical diagonalization engine sent to HPC\n",
"def classically_diagonalize(\n",
" bit_array=None, # Bit string array (only needed if locally processing data)\n",
" nuclear_repulsion_energy=None, # Electronic energy from the core orbitals\n",
" hcore=None, # 1-electron hamiltonian integrals\n",
" eri=None, # 2-electron hamiltonian integrals\n",
" num_orbitals=None, # Number of spatial orbitals\n",
" nelec=None, # Number of electrons\n",
" num_elec_a=None, # Alpha orbitals\n",
" num_elec_b=None, # Beta orbitals\n",
" job_id=None, # QPU bitstring Job ID\n",
" client=None, # Diagonalization engine worker\n",
" energy_tol=1e-4, # SQD option\n",
" occupancies_tol=1e-3, # SQD option\n",
" max_iterations=12, # SQD option\n",
" num_batches=8, # Eigenstate solver option\n",
" samples_per_batch=300, # Eigenstate solver option\n",
" symmetrize_spin=False, # Eigenstate solver option\n",
" carryover_threshold=1e-5, # Eigenstate solver option\n",
" max_cycle=200, # Eigenstate solver option\n",
" local=True, # Remote vs Local Diagonalization\n",
" mem=16.0, # Memory per Serverless Worker (Gb)\n",
"):\n",
" print(\">>>>> STARTING DIAGONALIZATION ENGINE \")\n",
" # Pass options to the built-in eigensolver. If you just want to use\n",
" # the defaults, you can omit this step, in which case you would not\n",
" # specify the sci_solver argument in the call to\n",
" # diagonalize_fermionic_hamiltonian below.\n",
" if local:\n",
" sci_solver = partial(\n",
" solve_sci_batch, spin_sq=0.0, max_cycle=max_cycle\n",
" )\n",
"\n",
" # List to capture intermediate results\n",
" result_history = []\n",
"\n",
" def callback(results: list[SCIResult]):\n",
" result_history.append(results)\n",
" iteration = len(result_history)\n",
" print(f\">>>>> SQD ITERATION {iteration}\")\n",
" for i, result in enumerate(results):\n",
" print(f\">>>>> SUBSAMPLE {i}\")\n",
" print(\n",
" f\">>>>> \\tENERGY: {result.energy + nuclear_repulsion_energy}\"\n",
" )\n",
" print(\n",
" f\">>>>> \\tSUBSPACE DIMENSION: {np.prod(result.sci_state.amplitudes.shape)}\"\n",
" )\n",
"\n",
" result = diagonalize_fermionic_hamiltonian(\n",
" hcore,\n",
" eri,\n",
" bit_array,\n",
" samples_per_batch=samples_per_batch,\n",
" norb=num_orbitals,\n",
" nelec=(nelec // 2, nelec // 2),\n",
" num_batches=num_batches,\n",
" energy_tol=energy_tol,\n",
" occupancies_tol=occupancies_tol,\n",
" max_iterations=max_iterations,\n",
" sci_solver=sci_solver,\n",
" symmetrize_spin=symmetrize_spin,\n",
" carryover_threshold=carryover_threshold,\n",
" callback=callback,\n",
" seed=12345,\n",
" )\n",
"\n",
" result = (result.energy, result.rdm1, result.rdm2)\n",
"\n",
" else:\n",
" # Serverless Logic\n",
" print(\n",
" f\">>>>> SENDING QISKIT RUNTIME JOB {job_id} TO QISKIT SERVERLESS\"\n",
" )\n",
"\n",
" data = [\n",
" job_id,\n",
" hcore.tolist(),\n",
" eri.tolist(),\n",
" int(num_orbitals),\n",
" float(nuclear_repulsion_energy),\n",
" int(num_elec_a),\n",
" int(num_elec_b),\n",
" ]\n",
"\n",
" # Encode the execution dependencies with the JSONEncoder\n",
" data_e = JSONEncoder().encode(data)\n",
"\n",
" # Send to Serverless\n",
" worker = client.load(\"diagonalization_engine\")\n",
" serverless_job = worker.run(\n",
" data=data_e,\n",
" energy_tol=energy_tol, # SQD option\n",
" occupancies_tol=occupancies_tol, # SQD option\n",
" max_iterations=max_iterations, # SQD option\n",
" symmetrize_spin=symmetrize_spin, # Eigenstate solver option\n",
" carryover_threshold=carryover_threshold, # Eigenstate solver option\n",
" num_batches=num_batches, # Eigenstate solver option\n",
" samples_per_batch=samples_per_batch, # Eigenstate solver option\n",
" max_cycle=max_cycle, # Eigenstate solver option\n",
" mem=mem, # Memory per Worker (Gb)\n",
" )\n",
"\n",
" # Wait for the job to execute\n",
" _ = feedback_serverless(serverless_job)\n",
"\n",
" o_data = JSONDecoder().decode(serverless_job.result()[\"outputs\"])\n",
" result = (o_data[1], np.array(o_data[2]), np.array(o_data[3]))\n",
"\n",
" print(f\">>>>>>>>>> Active Space Energy: {o_data[1]}\")\n",
" print(f\">>>>>>>>>> rdm1: {o_data[2]}\")\n",
" print(f\">>>>>>>>>> rdm2: {o_data[3]}\")\n",
"\n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d1e23956",
"metadata": {},
"outputs": [],
"source": [
"# The Heartwood algorithm\n",
"import numpy as np\n",
"\n",
"from qiskit_ibm_runtime import SamplerV2 as Sampler\n",
"from qiskit_addon_sqd.counts import generate_bit_array_uniform\n",
"\n",
"mc = pyscf.mcscf.CASCI(mf_opt, ncas=norb, nelecas=ne_act).PCM(cm)\n",
"mc.with_solvent.method = mf_opt.with_solvent.method # Here we make sure\n",
"# that mc is also using the same solvent method defined earlier (IEF-PCM)\n",
"mc.with_solvent.eps = mf_opt.with_solvent.eps # Set the dielectric parameters\n",
"mc.mo_coeff = mo_avas.copy() # Update the molecular orbitals to include\n",
"# those computed in the presence of the solvent\n",
"\n",
"h1e_cas, ecore = (\n",
" mc.get_h1eff()\n",
") # <-- h1eff is the 1-electron hamiltonian integrals. h1e_cas is\n",
"# a common alias. ecore is the electronic energy from the core orbitals.\n",
"h2e_cas = ao2mo.restore(\n",
" 1, mc.get_h2eff(), norb\n",
") # <-- get the 2-electron hamiltonian integrals\n",
"\n",
"mc.mo_coeff, t1, t2 = run_active_space_calculation(\n",
" h1e_cas,\n",
" h2e_cas,\n",
" norb,\n",
" ne_act,\n",
" mo_avas.copy(),\n",
" mf_opt.mol.nelectron // 2,\n",
" ecore,\n",
")\n",
"\n",
"# Sampler primitive options\n",
"sampler = Sampler(mode=backend)\n",
"\n",
"# Explore error suppression techniques and see if they can improve result quality\n",
"sampler.options.dynamical_decoupling.enable = True\n",
"sampler.options.dynamical_decoupling.sequence_type = \"XY4\"\n",
"sampler.options.twirling.enable_measure = True\n",
"sampler.options.environment.job_tags = [\"TUT_ISC\"]\n",
"# sampler.options.twirling.enable_gates = False\n",
"# sampler.options.twirling.num_randomizations = 10\n",
"# sampler.options.twirling.shots_per_randomization = 1024\n",
"\n",
"# initial approximation for rdm1\n",
"with_solvent_e, with_solvent_v = None, None # Don't touch\n",
"data = []\n",
"for iiter in range(n_iter):\n",
" print(f\">>>>> IMPLICIT SOLVENT ITERATION {iiter+1}/{n_iter}\")\n",
" if with_solvent_v is not None:\n",
" # Subsequent update loops enter here\n",
" mc.get_hcore = lambda *args: mc._scf.get_hcore() + with_solvent_v\n",
" else:\n",
" # First update loop starts here\n",
" # hcore is the CAS space (classically computed) 1-electron\n",
" # hamiltonian, which we default to at the start of the routine.\n",
" mc.get_hcore = (\n",
" lambda *args: mc._scf.get_hcore()\n",
" ) # REF: https://pyscf.org/pyscf_api_docs/pyscf.mcscf.html#pyscf.scf.hf.CASBase.get_h1cas\n",
"\n",
" # Alias mapping\n",
" # hcore : h1e_cas : h1e_eff\n",
" # nuclear_repulsion_energy : ecore\n",
" # eri : h2e_cas : h2e_eff\n",
"\n",
" h1e_cas, ecore = (\n",
" mc.get_h1eff()\n",
" ) # <-- h1eff is the 1-electron hamiltonian integrals. h1e_cas is a\n",
" # common alias. ecore is the electronic energy from the core orbitals.\n",
" h2e_cas = ao2mo.restore(\n",
" 1, mc.get_h2eff(), norb\n",
" ) # <-- get the 2-electron hamiltonian integrals\n",
"\n",
" mc.mo_coeff, t1, t2 = run_active_space_calculation(\n",
" h1e_cas,\n",
" h2e_cas,\n",
" norb,\n",
" ne_act,\n",
" mo_avas.copy(),\n",
" mf_opt.mol.nelectron // 2,\n",
" ecore,\n",
" )\n",
"\n",
" if use_hardware:\n",
" if (\n",
" iiter % resample == 0\n",
" ): # <-- Toggle how often you refresh your bitstrings here. The\n",
" # developer suggests that you do it every time, but benevolently\n",
" # provides the freedom to disagree with him via the resample\n",
" # control variable.\n",
" # The \"Quantum-Centric\" part\n",
" print(\">>>>> GENERATING BITSTRINGS USING QUANTUM HARDWARE\")\n",
" # LUCJ Ansatz construction\n",
" circuit = get_lucj(norb, num_elec_a, num_elec_b, t1, t2, n_reps=1)\n",
"\n",
" print(f\">>>>> TRANSPILING LUCJ TO {backend.name}\")\n",
" isa_circuit = pass_manager.run(circuit)\n",
" print(f\">>>>> SUBMITTING ISA_CIRCUIT TO {backend.name}\")\n",
" job = sampler.run(\n",
" [isa_circuit], shots=shots\n",
" ) # <----- Error Suppression/Mitigation configured performed upstream\n",
" job_id = str(job.job_id())\n",
"\n",
" timer = 0\n",
" while job.status() != \"DONE\":\n",
" timer += 10\n",
" print(\n",
" f\">>>>> [{timer}s] RUNTIME JOB {job_id}: {job.status()}\"\n",
" )\n",
" time.sleep(10)\n",
"\n",
" primitive_result = job.result()\n",
" print(f\">>>>> RETRIEVED {job_id} FROM {backend.name}\")\n",
"\n",
" pub_result = primitive_result[0]\n",
" bit_array = pub_result.data.meas\n",
"\n",
" else:\n",
" print(\">>>>> GENERATING BITSTRINGS CLASSICALLY\")\n",
" rng = np.random.default_rng(24)\n",
" bit_array = generate_bit_array_uniform(\n",
" 100_000, 2 * norb, rand_seed=rng\n",
" ) # <-- Sample bitstrings from a uniform distribution. This is\n",
" # useful for debug, but runs out of steam on large systems\n",
" job_id = float(\n",
" \"nan\"\n",
" ) # <-- we will check that valid job_id's were passed during grading\n",
" local = True\n",
"\n",
" # The \"Classical Post-processing\" part\n",
" result = classically_diagonalize(\n",
" bit_array=bit_array,\n",
" nuclear_repulsion_energy=ecore, # Electronic energy from the core orbitals\n",
" hcore=h1e_cas, # 1-electron hamiltonian integrals\n",
" eri=h2e_cas, # 2-electron hamiltonian integrals\n",
" num_orbitals=norb, # Number of spatial orbitals\n",
" nelec=ne_act, # Number of electrons\n",
" num_elec_a=ne_act // 2, # Alpha orbitals\n",
" num_elec_b=ne_act // 2, # Beta orbitals\n",
" job_id=job_id, # QPU bitstring Job ID\n",
" client=client, # Diagonalization engine worker\n",
" energy_tol=energy_tol, # SQD option\n",
" occupancies_tol=occupancies_tol, # SQD option\n",
" max_iterations=max_iterations, # SQD option\n",
" num_batches=num_batches, # Eigenstate solver option\n",
" samples_per_batch=samples_per_batch, # Eigenstate solver option\n",
" symmetrize_spin=symmetrize_spin, # Eigenstate solver option\n",
" carryover_threshold=carryover_threshold, # Eigenstate solver option\n",
" max_cycle=max_cycle, # Eigenstate solver option\n",
" local=local, # Remote vs Local Diagonalization\n",
" mem=mem, # Memory per Worker (Gb)\n",
" )\n",
"\n",
" # e : SQD-based estimate of the energy\n",
" # rdm1: Spin-summed 1-particle reduced density matrix\n",
" e, rdm1 = result[0], result[1]\n",
" rho_approximation = update_rdm(\n",
" mc, rdm1\n",
" ).copy() # <--- Reconstruct the one-body density matrix in the\n",
" # atomic orbital basis to update the external potential due to\n",
" # the solvent\n",
"\n",
" if with_solvent_e is not None:\n",
" # Subsequent update loops enter here\n",
" edup = np.einsum(\n",
" \"ij,ji->\", with_solvent_v, rho_approximation\n",
" ) # <-- edup: Incrementing the energy calculation with\n",
" # subsequent iterations\n",
" e += ecore + with_solvent_e - edup\n",
"\n",
" else:\n",
" # First update loop enters here\n",
" e += (\n",
" ecore # Pulled from the CAS space object (molecule's core energy)\n",
" )\n",
"\n",
" # Outputs:\n",
" # with_solvent_e : scalar energy correction due to solvent polarization\n",
" # with_solvent_v : Fock-like matrix to be added to the core Hamiltonian in SCF\n",
" with_solvent_e, with_solvent_v = mc.with_solvent._get_vind(\n",
" rho_approximation\n",
" )\n",
" data.append((iiter, float(e), job_id))\n",
" print(f\">>>>> END IITER {iiter}\")\n",
" print(f\">>>>> TOTAL ENERGY: {e}\\n\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3905922f",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"from matplotlib.ticker import ScalarFormatter\n",
"\n",
"\n",
"def plot_data(data, baseline=0, name=None, save=False):\n",
" x_vals, y_vals, job_ids = zip(*data)\n",
" fig, ax = plt.subplots(figsize=(10, 6))\n",
"\n",
" # Plot line + markers\n",
" ax.plot(\n",
" x_vals,\n",
" y_vals,\n",
" color=\"navy\",\n",
" linewidth=2,\n",
" marker=\"o\",\n",
" markersize=5,\n",
" label=\"Energy trajectory\",\n",
" )\n",
" ax.axhline(\n",
" baseline,\n",
" color=\"red\",\n",
" linestyle=\"--\",\n",
" linewidth=1.5,\n",
" label=\"Reference energy\",\n",
" )\n",
"\n",
" # Force plain formatting\n",
" ax.yaxis.set_major_formatter(ScalarFormatter(useMathText=True))\n",
" ax.ticklabel_format(style=\"plain\", axis=\"y\")\n",
"\n",
" # Annotate each point with its exact value\n",
" for x, y, job_id in zip(x_vals, y_vals, job_ids):\n",
" ax.annotate(\n",
" f\"{y:.8f}, ID: {job_id}\",\n",
" (x, y),\n",
" textcoords=\"offset points\",\n",
" xytext=(0, 8), # vertical offset\n",
" ha=\"center\",\n",
" fontsize=8,\n",
" rotation=25,\n",
" color=\"navy\",\n",
" )\n",
"\n",
" # Annotate the Classical Reference line\n",
" for x, y in zip([0.5], [baseline]):\n",
" ax.annotate(\n",
" f\"{y:.5f}\",\n",
" (x, y),\n",
" textcoords=\"offset points\",\n",
" xytext=(0, 8), # vertical offset\n",
" ha=\"center\",\n",
" fontsize=8,\n",
" rotation=25,\n",
" color=\"red\",\n",
" )\n",
"\n",
" # Titles, labels, etc\n",
" ax.set_title(\n",
" f\"SQD/IEF-PCM(cc-pVDZ) - {name}\\nEnergy Convergence\",\n",
" fontsize=14,\n",
" fontweight=\"bold\",\n",
" pad=15,\n",
" )\n",
" ax.set_xlabel(\"Update Iterations\", fontsize=12)\n",
" ax.set_ylabel(\"Total Energy (Hartrees)\", fontsize=12)\n",
" ax.grid(True, linestyle=\"--\", linewidth=0.6, alpha=0.7)\n",
" ax.legend(frameon=True, loc=\"best\")\n",
" plt.tight_layout()\n",
"\n",
" if save:\n",
" plt.savefig(f\"./results/{name}_energy_convergence.png\")\n",
" return fig, ax"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6fdb639b",
"metadata": {},
"outputs": [],
"source": [
"# Plot your data\n",
"\n",
"fig, ax = plot_data(data, baseline=CASCI_E, name=molecule_name, save=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "75f48e6a-c7e4-46f3-9d39-a7a877427a04",
"metadata": {},
"source": [
"\n",
"\n",
"## Próximas etapas\n",
"\n",
"\n",
" Se você achou este trabalho interessante, talvez se interesse pelos seguintes recursos:\n",
"\n",
" * [A Interface de Gerenciamento de Recursos Quânticos (QRMI)](https://github.com/qiskit-community/qrmi) — integra recursos quânticos e clássicos a gerenciadores de cargas de trabalho de HPC, como o Slurm, ampliando o padrão de computação distribuída demonstrado neste tutorial\n",
" * [Guia para o site Qiskit Serverless](/docs/guides/serverless)\n",
" * [Qiskit Serverless GitHub](https://qiskit.github.io/qiskit-serverless/index.html)\n",
" * Tutorial [sobre diagonalização quântica baseada em amostras de um hamiltoniano químico](/docs/tutorials/sample-based-quantum-diagonalization)\n",
" * [Visão geral da diagonalização quântica baseada em amostras (SQD)](/docs/addons/qiskit-addon-sqd)\n",
" * [Implemente e execute um modelo para simulação de estrutura eletrônica com um modelo de solvente implícito](/docs/guides/function-template-chemistry-workflow) (modelo de função SQD IEF-PCM do Qiskit, desenvolvido em conjunto pela Cleveland Clinic e pelo IBM )\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
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"id": "a1b8767d",
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