{ "cells": [ { "cell_type": "markdown", "id": "1682996d", "metadata": {}, "source": [ "---\n", "title: \"Berechnungen mit implizitem Lösungsmittel unter Verwendung von „ Qiskit Serverless “\"\n", "description: \"Lernen Sie, wie man implizite Lösungsmitteleffekte auf Quantenhardware mithilfe von SQD und IEF-PCM berechnet.\"\n", "---\n", "\n" ] }, { "cell_type": "markdown", "id": "d2c31ae8", "metadata": {}, "source": [ "\n", "\n", "# Berechnungen mit implizitem Lösungsmittel unter Verwendung von „ Qiskit Serverless “\n", "\n", "*Geschätzte Laufzeit: 2 Minuten auf einem Heron- r2 -Prozessor (HINWEIS: Dies ist lediglich eine Schätzung. (Die Laufzeit kann variieren.)*\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 electrocatalysis */}\n", "\n" ] }, { "cell_type": "markdown", "id": "8bf80006", "metadata": {}, "source": [ "\n", "\n", "## Lernziele\n", "\n", "* So konfigurieren und führen Sie einen Remote-Workflow mit „ [Qiskit Serverless](/docs/guides/serverless) “ aus\n", "* Wie man implizite Lösungsmitteleffekte mit einem Quantencomputer berechnet\n", "\n", "\n", "\n", "## Voraussetzungen\n", "\n", "* [Probenbasierte Quantendiagonalisierung](/learning/courses/quantum-diagonalization-algorithms/sqd-overview)\n", "\n", "\n", "\n", "## Hintergrund\n", "\n", "Berechnungen mit implizitem Lösungsmittel finden in der computergestützten Biophysik häufige Anwendung. Diese Modelle beschreiben, wie eine gelöste Verbindung mit einem Lösungsmittel interagiert, ohne das Lösungsmittelsystem direkt zu modellieren. Stattdessen wird eine Näherung vorgenommen, bei der das Modell des gelösten Stoffes in eine mathematische Darstellung eines empirisch charakterisierten dielektrischen Mediums eingebettet wird. Diese dielektrische Näherung steht dann in Wechselwirkung mit dem gelösten Stoff, der seinerseits direkt modelliert wird. Das dielektrische Medium beeinflusst Eigenschaften des gelösten Stoffsystems, wie beispielsweise dessen Grundzustandsenergie, indem es mit dessen Elektronenfeld in Wechselwirkung tritt. Dies ist für biophysikalische Modelle wichtig, die beispielsweise in der Wirkstoffforschung zum Einsatz kommen, da sich Verbindungen in verschiedenen dielektrischen Umgebungen unterschiedlich verhalten. Die Modellierung einer Verbindung in der Luft (im Vakuum) führt zu einem anderen Verhalten als die Modellierung in Wasser. Da pharmazeutische Wirkstoffe in den menschlichen Körper gelangen müssen, der selbst größtenteils aus Wasser besteht, ist es sinnvoll, einen Wirkstoff in einer Lösung wie Wasser zu modellieren, anstatt im Vakuum. Mit Modellen mit implizitem Lösungsmittel lässt sich dieses Verhalten mit geringem Rechenaufwand erzielen, auch wenn das Endergebnis in der Regel weniger genau ist als bei den rechenintensiveren Modellen mit explizitem Lösungsmittel, die direkte Darstellungen sowohl der gelösten Stoffe als auch der Lösungsmittelmoleküle erzeugen.\n", "\n", "In diesem Tutorial zeigen wir, wie ein Quantenalgorithmus, die Sample-based Quantum Diagonalization (SQD), in ein relativ rechenintensitätsarmes implizites Lösungsmittelmodell integriert werden kann. In diesem Beispiel beschreiben wir, wie sich Methylamin verhält, wenn es sich in Wasser löst. Wir vergleichen den Quantenalgorithmus mit einer klassischen, auf dem neuesten Stand der Technik befindlichen Vergleichsmethode namens CASCI und zeigen, dass diese Berechnungen weitgehend übereinstimmen. Wir präsentieren eine quantenzentrierte Supercomputing-Architektur im Miniaturformat, bei der die rechenintensive klassische Nachbearbeitung des Quanten-Sampling-Teils der Routine in eine cloudbasierte Umgebung innerhalb von „ Qiskit Serverless “ ausgelagert wird. Der Code demonstriert zudem die Parallelisierung über die remote verfügbaren CPU-Kerne hinweg, um die Rechenzeit zu verkürzen.\n", "\n", "Das Verständnis darüber, wie Lösungsmittel die molekularen Eigenschaften beeinflussen, ist für die Nachhaltigkeitsforschung von Bedeutung, unter anderem in den Bereichen Kohlenstoffabscheidung, Elektrokatalyse und der Entwicklung von Batterieelektrolyten. Das Beispiel „Methylamin in Wasser“ stellt einen Arbeitsablauf vor, bei dem quantenmechanische Elektronenstrukturberechnungen mit einem impliziten Lösungsmittelmodell kombiniert werden, und bietet damit einen Ausgangspunkt für die Untersuchung des molekularen Verhaltens in diesen weiter gefassten Anwendungsbereichen.\n", "\n", "Qiskit Serverless ist ein Framework zur Ausführung verteilter quanten- und klassischer Workloads, ohne dass die Infrastruktur verwaltet werden muss. Es gibt keine Serverbereitstellung (kein Hochfahren von EC2s, Clustern, Docker -Containern), keine Orchestrierungstools ( Kubernetes, Docker Swarm) und keine Überwachung/Wartung. Jeder Serverless-Job wird in einem sauberen Container ausgeführt, führt Ihren Code aus und wird anschließend beendet. Zwischen den Aufträgen gibt es keinen Speicher. Sie schreiben einfach Ihren Code und reichen dann Ihren Auftrag ein. Innerhalb eines serverlosen Jobs kann ein Programm nahtlos auf Backends unter IBM Quantum® zugreifen und die Ergebnisse dort klassisch nachbearbeiten. Mit „ Qiskit Serverless “ können Nutzer auf ständig verfügbare Remote-CPU-Kerne und -Speicher zugreifen, was die Verteilung bestimmter klassischer Workloads auf Remote-Ressourcen ermöglicht. Benutzer profitieren zudem von Vorteilen bei der parallelen Ausführung von Programmen und vermeiden gleichzeitig die üblichen Probleme, die durch das Herunterfahren von Geräten während der Ausführung entstehen. Weitere Informationen zu „ Qiskit Serverless “ finden Sie in [der Dokumentation](/docs/guides/serverless) sowie in zusätzlichen Materialien auf [GitHub](https://qiskit.github.io/qiskit-serverless/index.html).\n", "\n", "Dieses Tutorial zeigt eine relevante Anwendung der folgenden Punkte:\n", "\n", "* Probenbasierte Quantendiagonalisierung\n", "* Client-Server-Rechenmodelle für das Quantencomputing\n", "\n", "Dieses Tutorial ist inspiriert von und basiert auf Forschungsarbeiten der Cleveland Clinic, wie sie in [Kaliakin, Danil et al. „Implicit solvent sample-based quantum diagonalization“ beschrieben sind The Journal of Physical Chemistry B 129.23 (2025): 5788–5796](https://pubs.acs.org/doi/10.1021/acs.jpcb.5c01030), in dem der gesamte Arbeitsablauf für Berechnungen mit implizitem Lösungsmittel dargelegt und durch iterative Selbstkonsistenz des Lösungsmittels erweitert wird („The Heartwood Algorithm“, M. Motta, T. Pellegrini (2025), Geometrieoptimierung und automatische Auswahl des Qubit-Layouts. Bitte beachten Sie [die Vorlage](/docs/guides/function-template-chemistry-workflow) „SQD IEF-PCM Qiskit Function“, die gemeinsam von der Cleveland Clinic und IBM® auf der Grundlage von Forschungsergebnissen der Cleveland Clinic entwickelt wurde und eine optimierte Black-Box-Schnittstelle für die Durchführung impliziter Lösungsmittelberechnungen bietet.\n", "\n" ] }, { "cell_type": "markdown", "id": "55b94021", "metadata": {}, "source": [ "\n", "\n", "## Anforderungen\n", "\n", "Bevor Sie mit diesem Tutorial beginnen, stellen Sie bitte sicher, dass Folgendes installiert ist:\n", "\n" ] }, { "cell_type": "markdown", "id": "9456ea67", "metadata": {}, "source": [ "* Qiskit SDK v2.0 oder später mit [Visual](/docs/api/qiskit/visualization) isierungsunterstützung\n", "* Qiskit Runtime v0.40 oder später (`pip install qiskit-ibm-runtime`)\n", "* Qiskit- IBM -Katalog `pip install qiskit_ibm_catalog`\n", "* Qiskit- IBM -Serverless `pip install qiskit_serverless`\n", "* Qiskit-Add-on: 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", "* Geometrisch `pip install geometric`\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7db2e559", "metadata": {}, "source": [ "\n", "\n", "## Einrichtung\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": [ "Erstellen Sie direkt neben dem Hauptprogramm des Notebooks ein Verzeichnis mit dem Namen `source_files`. In diesem Verzeichnis speichern Sie die Dateien unter „ Python “, die Sie für die Remote-Rechenumgebung freigeben möchten. Sie müssen zwei Dateien erstellen:\n", "\n", "* `source_files\\diagonalization_engine.py`\n", "* `source_files\\classical_simulation.py`\n", "\n", "Klicken Sie unten auf die einzelnen Skripte, um den Text anzuzeigen, und kopieren Sie den Inhalt anschließend in eine lokale Datei mit diesen Pfadnamen.\n", "\n", "\n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " Weitere Informationen finden Sie in der oben genannten [Anleitung zur](/docs/guides/function-template-chemistry-workflow) SQD-IEF-PCM-Qiskit-Funktionsvorlage (gemeinsam entwickelt von der Cleveland Clinic und IBM ). Siehe auch die [`qiskit_addon_sqd`](/docs/addons/qiskit-addon-sqd) Bibliothek.\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_serverless import (\n", " distribute_task,\n", " get_arguments,\n", " get,\n", " save_result,\n", " get_runtime_service,\n", ")\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 = get_runtime_service()\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": [ "Wir müssen das Programm, das in der Cloud-Umgebung ausgeführt werden soll, freigeben und es jedes Mal neu hochladen, wenn wir seinen Quellcode ändern:\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", "## Beispiel für einen Simulator im kleinen Maßstab\n", "\n" ] }, { "cell_type": "markdown", "id": "b0db693d", "metadata": {}, "source": [ "In diesem Tutorial wird kein Simulator im kleinen Maßstab verwendet, da das Ziel darin besteht, eine skalierbare Quantenanwendung zu demonstrieren, die über den Rahmen der Simulatoruntersuchung hinausgeht. Stattdessen zeigen wir später, wie diese Methode mithilfe einer klassischen, auf dem neuesten Stand der Technik befindlichen Vergleichsmethode namens CASCI umgesetzt werden kann.\n", "\n" ] }, { "cell_type": "markdown", "id": "431a5bd2-e6ed-471b-ad9e-c4edd27784a8", "metadata": {}, "source": [ "\n", "\n", "## Beispiel für groß angelegte Hardware\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", "## Schritt 1: Klassische Eingaben auf ein Quantenproblem abbilden\n", "\n" ] }, { "cell_type": "markdown", "id": "cf4bbd59", "metadata": {}, "source": [ "\n", "\n", "### 1.1: Molekülobjekt anhand der bekannten Molekülgeometrie unter $\\textit{a priori}$ initialisieren\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: Bestimme Solvatisierungseffekte unter Verwendung des 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": [ "\n", "\n", "### 1.3: Geometrieoptimierung mit 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: Erstellen Sie ein Kontinuumsmodell und ein Mean-Field-Objekt mit den entsprechenden Variablen\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", "## Schritt 2: Optimierung des Problems für die Ausführung auf Quantenhardware\n", "\n" ] }, { "cell_type": "markdown", "id": "52506835", "metadata": {}, "source": [ "Weitere Informationen zu den hier vorgestellten Hilfsfunktionen finden Sie im Tutorial [„Sample-based quantum diagonalization of a chemistry Hamiltonian“](/docs/tutorials/sample-based-quantum-diagonalization) (Quanten-Diagonalisierung eines chemischen Hamilton-Operators auf Basis von Stichproben).\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 an 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", "## Schritte 3 und 4: Ausführung mit Qiskit und Nachbearbeitung mit Qiskit Serverless\n", "\n", "Hier fassen wir Schritt 3 (Ausführung) und Schritt 4 (Nachbearbeitung) zusammen, da der Anwendungskontext des Modells mit implizitem Lösungsmittel eine iterative Rückkopplungsschleife erfordert, die mehrere Zyklen aus Ausführung und Nachbearbeitung durchläuft, um das Endergebnis zu verbessern.\n", "\n" ] }, { "cell_type": "markdown", "id": "8715bb6b", "metadata": {}, "source": [ "\n", "\n", "### 3.1 Berechne die eingeschränkte Hartree-Fock-Energie\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: Ermittlung klassischer Referenzenergie mit 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", "## Anwendungsparameter konfigurieren\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 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", "## Nächste Schritte\n", "\n", "\n", " Wenn Sie diese Arbeit interessant fanden, könnten Sie auch an den folgenden Ressourcen interessiert sein:\n", "\n", " * Die [Quantum Resource Management Interface (QRMI)](https://github.com/qiskit-community/qrmi) – integriert Quanten- und klassische Ressourcen in HPC-Workload-Manager wie Slurm und erweitert damit das in diesem Tutorial vorgestellte Modell des verteilten Rechnens\n", " * [Leitfaden zu „ Qiskit Serverless “](/docs/guides/serverless)\n", " * [Qiskit Serverless GitHub](https://qiskit.github.io/qiskit-serverless/index.html)\n", " * Tutorial [zur samplebasierten Quantendiagonalisierung eines chemischen Hamilton-Operators](/docs/tutorials/sample-based-quantum-diagonalization)\n", " * [Überblick über die samplebasierte Quantendiagonalisierung (SQD)](/docs/addons/qiskit-addon-sqd)\n", " * [Eine Vorlage für die Simulation der elektronischen Struktur mit einem impliziten Lösungsmittelmodell bereitstellen und ausführen](/docs/guides/function-template-chemistry-workflow) (SQD-IEF-PCM-Qiskit-Funktionsvorlage, gemeinsam entwickelt von der Cleveland Clinic und IBM )\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "id": "a1b8767d", "source": "© IBM Corp., 2017-2026" } ], "metadata": { "hours": 1.5, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3" }, "qpuSeconds": 120 }, "nbformat": 4, "nbformat_minor": 5 }