{
"cells": [
{
"cell_type": "markdown",
"id": "1682996d",
"metadata": {},
"source": [
"---\n",
"title: Implicit solvent calculations using Qiskit Serverless\n",
"description: Learn to compute implicit solvent effects on quantum hardware using SQD and IEF-PCM.\n",
"---\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "d2c31ae8",
"metadata": {},
"source": [
"# Implicit solvent calculations using Qiskit Serverless\n",
"\n",
"*Usage estimate: 2 minutes on a Heron r2 processor (NOTE: This is an estimate only. Your runtime may vary.)*\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": [
"## Learning outcomes\n",
"\n",
"After going through this tutorial, users should understand:\n",
"\n",
"* How to configure and run a remote workflow using [Qiskit Serverless](/docs/guides/serverless)\n",
"* How to compute implicit solvent effects using a quantum computer\n",
"\n",
"## Prerequisites\n",
"\n",
"We suggest that users are familiar with the following topic before going through this tutorial:\n",
"\n",
"* [Sample-based quantum diagonalization](/learning/courses/quantum-diagonalization-algorithms/sqd-overview)\n",
"\n",
"## Background\n",
"\n",
"Implicit solvent calculations are frequently used in computational biophysics. These models describe how a solute compound interacts with a solvent, without modeling the solvent system directly. Instead, an approximation is made wherein the solute system model is wrapped in a mathematical representation of a dielectric medium characterized empirically. This dielectric approximation then interacts with the solute, which is itself modeled directly. The dielectric medium influences characteristics of the solute system, such as its ground state energy, by interacting with its electron field. This is important to biophysical models used, say, in drug discovery, because compounds behave differently in various dielectric environments. Modeling a compound in the air (in vacuo) will describe different behavior than modeling it in water. Since pharmaceutical compounds must enter into the human body, which itself is composed mostly of water, it is helpful to model a compound in a solution like water instead of in vacuo. With implicit solvent models, we can achieve this behavior cheaply, although the end result will generally be more approximate than the counterpart: more computationally costly explicit solvent models that create direct representations of both solute and solvent molecules.\n",
"\n",
"In this tutorial, we demonstrate how a quantum algorithm, Sample-based Quantum Diagonalization (SQD), can be worked into a relatively computationally cheap implicit solvent model. In the example, we describe how methylamine behaves when it dissolves in water. We compare the quantum algorithm to a classical state-of-the-art comparison method called CASCI and demonstrate close agreement between these computations. We showcase a quantum-centric supercomputing architecture in miniature, offloading the computationally expensive classical post-processing of the quantum sampling portion of the routine into a cloud-based environment within Qiskit Serverless. The code also demonstrates parallelization across the remotely available CPU cores to improve computation time.\n",
"\n",
"Qiskit Serverless is a framework for running distributed quantum and classical workloads without managing infrastructure. There is no server provisioning (no spinning up EC2s, clusters, Docker containers), no orchestration tools (Kubernetes, Docker Swarm) and no monitoring/maintenance. Each Serverless job runs in a clean container, executes your code, and then shuts down. There is no memory between jobs. You simply write your code then submit your job. Within a Serverless job, a program can seamlessly access IBM Quantum® backends and classically post-process results therein. With Qiskit Serverless, users can access always-on remote CPU cores and memory, which provides for the distribution of certain classical workloads across remote resources. Users also gain some advantage in parallel processing of programs while avoiding common headaches from device shutdown mid-execution. For more information on Qiskit Serverless, see its [documentation](/docs/guides/serverless), as well as additional material on [GitHub](https://qiskit.github.io/qiskit-serverless/index.html).\n",
"\n",
"This tutorial shows a relevant application of the following:\n",
"\n",
"* Sample-based quantum diagonalization\n",
"* Client-server computational models for quantum computing\n",
"\n",
"This tutorial is inspired by and based upon research conducted at Cleveland Clinic, as described in [Kaliakin, Danil, et al. \"Implicit solvent sample-based quantum diagonalization.\" The Journal of Physical Chemistry B 129.23 (2025): 5788-5796](https://pubs.acs.org/doi/10.1021/acs.jpcb.5c01030), exposing the full workflow for implicit solvent calculations and extending it with iterative solvent self-consistency (\"The Heartwood Algorithm\", M. Motta, T. Pellegrini, 2025), geometry optimization, and automatic qubit layout selection. Please refer to the [SQD IEF-PCM Qiskit Function template](/docs/guides/function-template-chemistry-workflow), jointly developed by Cleveland Clinic and IBM® based on Cleveland Clinic research, for a streamlined, black-box interface for running implicit solvent calculations.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "55b94021",
"metadata": {},
"source": [
"## Requirements\n",
"\n",
"Before starting this tutorial, be sure you have the following installed:\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "9456ea67",
"metadata": {},
"source": [
"* Qiskit SDK v2.0 or later with [visualization](/docs/api/qiskit/visualization) support\n",
"* Qiskit Runtime v0.40 or later (`pip install qiskit-ibm-runtime`)\n",
"* Qiskit SDK v2.0 or later with visualization support `pip install qiskit[visualization]`\n",
"* Qiskit Runtime v0.40 or later `pip install qiskit_ibm_runtime`\n",
"* Qiskit IBM Catalog `pip install qiskit_ibm_catalog`\n",
"* Qiskit IBM Serverless `pip install qiskit_serverless`\n",
"* Qiskit addon: Sample-based quantum diagonalization (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",
"* Geometric `pip install geometric`\n",
"\n"
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "7db2e559",
"metadata": {},
"source": [
"## Setup\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": [
"Create a directory exactly next to the main notebook program called `source_files`. You will put Python files into this directory that you intend to share with the remote compute environment. You must create two files:\n",
"\n",
"* `source_files\\diagonalization_engine.py`\n",
"* `source_files\\classical_simulation.py`\n",
"\n",
"Click to expand the text for each script below, then copy and paste the content into a local file with these path names.\n",
"\n",
"\n",
" \n",
" \n",
" \n",
"\n",
" \n",
" \n",
" \n",
"\n",
"\n",
"\n",
" For more information, please see the [SQD IEF-PCM Qiskit Function template guide](/docs/guides/function-template-chemistry-workflow) (jointly developed by Cleveland Clinic and IBM) referenced above. See also the [`qiskit_addon_sqd`](/docs/guides/qiskit-addons-sqd) library.\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": [
"We need to share the program intended to run in the cloud environment, and re-upload it any time we change its source code:\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": [
"## Small-scale simulator example\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "b0db693d",
"metadata": {},
"source": [
"This tutorial does not make use of a small-scale simulator because the intent is to demonstrate a scalable quantum application that extends beyond the regime of simulator exploration. Instead, we show later on how this method can be implemented using a classical state-of-the-art comparison method called CASCI.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "431a5bd2-e6ed-471b-ad9e-c4edd27784a8",
"metadata": {},
"source": [
"## Large-scale hardware example\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": [
"## Step 1: Map classical inputs to a quantum problem\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "cf4bbd59",
"metadata": {},
"source": [
"### 1.1: Initialize molecule object using known $\\textit{a priori}$ molecular geometry\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": [
"### 1.2: Define solvation effects using the Polarizable Continuum Model (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": [
"### 1.3: Geometry optimization using 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": [
"### 1.4: Prepare continuum model and mean field object with relevant variables\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": [
"## Step 2: Optimize problem for quantum hardware execution\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "52506835",
"metadata": {},
"source": [
"For more information on the helper functions demonstrated here, see the [Sample-based quantum diagonalization of a chemistry Hamiltonian](/docs/tutorials/sample-based-quantum-diagonalization) tutorial.\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": [
"## Steps 3 & 4: Execute using Qiskit and post-process using Qiskit Serverless\n",
"\n",
"Here, we combine Step 3 (Execute) and Step 4 (Post-process) because the application context of the implicit solvent model requires an iterative feedback loop that executes several cycles of execution and post-processing to improve the end computation.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "8715bb6b",
"metadata": {},
"source": [
"### 3.1 Compute the restricted Hartree-Fock energy\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": [
"### 3.2: Establish classical reference energy with 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": [
"## Configure application parameters\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": [
"## Next steps\n",
"\n",
"\n",
" If you found this work interesting, you might be interested in the following resources:\n",
"\n",
" * The [Quantum Resource Management Interface (QRMI)](https://github.com/qiskit-community/qrmi) — integrate quantum and classical resources into HPC workload managers like Slurm, extending the distributed computing pattern demonstrated in this tutorial\n",
" * [Guide to Qiskit Serverless](/docs/guides/serverless)\n",
" * [Qiskit Serverless GitHub](https://qiskit.github.io/qiskit-serverless/index.html)\n",
" * [Sample-based quantum diagonalization of a chemistry Hamiltonian](/docs/tutorials/sample-based-quantum-diagonalization) tutorial\n",
" * [Sample-based quantum diagonalization (SQD) overview](/docs/guides/qiskit-addons-sqd)\n",
" * [Deploy and run a template for electronic structure simulation with an implicit solvent model](/docs/guides/function-template-chemistry-workflow) (SQD IEF-PCM Qiskit Function template, jointly developed by Cleveland Clinic and IBM)\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"id": "a1b8767d",
"source": "© IBM Corp., 2017-2026"
}
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