{
"cells": [
{
"cell_type": "markdown",
"id": "b6d1e3ec",
"metadata": {},
"source": [
"---\n",
"title: \"Dissoziations-PES-Kurven mit Qunova HiVQE\"\n",
"description: \"Verwenden Sie Qunova HiVQE, um Dissoziationspotentialenergie-Oberflächenkurven (PES) zu berechnen.\"\n",
"---\n",
"\n",
"{/* cspell:ignore fontsize labelsize DMRG hivqe mcscf CASCI */}\n",
"\n",
"\n",
"\n",
"# Dissoziations-PES-Kurven mit Qunova HiVQE\n",
"\n"
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "a6f69b77",
"metadata": {},
"source": [
"\n",
" Qiskit-Funktionen sind eine experimentelle Funktion, die nur für Benutzer des IBM Quantum® Premium Plan, Flex Plan und On-Prem (über IBM Quantum Platform API) Plan verfügbar ist. Sie befinden sich im Status einer Vorabversion und können sich noch ändern.\n",
"\n",
"\n",
"*Schätzung des Verbrauchs (HINWEIS: Dies ist nur eine Schätzung. Ihre Laufzeit kann variieren.)*\n",
"\n",
"* Li2S: Fünf Minuten QPU-Zeit auf einem Heron r2 Prozessor\n",
"* FeP-NO: Fünf Minuten QPU-Zeit auf einem Heron r2 Prozessor\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "8bf80006",
"metadata": {},
"source": [
"\n",
"\n",
"## Hintergrund\n",
"\n",
"Die genaue Berechnung chemischer Reaktionsenergien ist von entscheidender Bedeutung für wissenschaftliche Fortschritte in der Materialwissenschaft, der chemischen Technik, der Arzneimittelforschung und anderen Bereichen. Unter den verschiedenen chemischen Systemen hat das Li-S-System großes Interesse für das Verständnis und die Entwicklung neuer Batteriezusammensetzungen geweckt. Dieses Tutorial vermittelt praktische Erfahrungen bei der Berechnung der potentiellen Energieoberfläche der Li-S-Bindung (PES) eines $Li_2S$ Systems durch Entfernen eines Lithiumatoms mit Hilfe von HiVQE Berechnungen. Die Ergebnisse können sowohl mit Referenzrechnungen (CASCI) als auch mit klassischen Methoden wie Hartree-Fock (HF) für ein 20-Qubit-Problem verglichen werden.\n",
"\n",
"Das Beispiel der Lithium-Schwefel-Batterie verbindet diesen Arbeitsablauf mit der Forschung an Batterien der nächsten Generation für die Energiespeicherung. Die Berechnung der Energieveränderungen beim Aufbrechen einer Li–S-Bindung liefert Erkenntnisse auf molekularer Ebene, die für das Verständnis der chemischen Umwandlungen in diesen Systemen von Bedeutung sind. Allgemeiner gesagt sind potentielle Energieoberflächen Werkzeuge zur Untersuchung von Reaktionswegen und Katalysatoren für ressourceneffizientere chemische Prozesse.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "55b94021",
"metadata": {},
"source": [
"\n",
"\n",
"## Anforderungen\n",
"\n",
"Installieren Sie die folgenden Abhängigkeiten, um den Code in diesem Lernprogramm auszuführen.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0a778d85",
"metadata": {},
"outputs": [],
"source": [
"!pip install --upgrade pip\n",
"!pip install -U qiskit-ibm-catalog \"qiskit_ibm_runtime<0.42.0\" pyscf numpy matplotlib typing_extensions"
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "7db2e559",
"metadata": {},
"source": [
"\n",
"\n",
"## Einrichtung\n",
"\n",
"Um dieses Lernprogramm auszuführen, importieren Sie die Funktion `qunova/hivqe-chemistry` über `QiskitFunctionCatalog`. Sie benötigen ein IBM Quantum Premium Plan-, Flex Plan- oder On-Prem ( IBM Quantum Platform API) Plan-Konto mit einer Lizenz von Qunova, um diese Funktion auszuführen.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bc380c46",
"metadata": {},
"outputs": [],
"source": [
"from qiskit_ibm_catalog import QiskitFunctionsCatalog\n",
"from pyscf import gto, scf, mcscf\n",
"import matplotlib.pyplot as plt\n",
"import pprint\n",
"\n",
"catalog = QiskitFunctionsCatalog(\n",
" channel=\"ibm_quantum_platform\",\n",
" instance=\"INSTANCE_CRN\",\n",
" # For `token`, use the 44-character API_KEY you created\n",
" # and saved from the IBM Quantum Platform Home dashboard\n",
" token=\"YOUR_API_KEY\",\n",
")\n",
"\n",
"hivqe = catalog.load(\"qunova/hivqe-chemistry\")"
]
},
{
"attachments": {},
"cell_type": "markdown",
"id": "988ee237",
"metadata": {},
"source": [
"\n",
"\n",
"## Teil 1: Li2S ( 20Q )\n",
"\n",
"\n",
"\n",
"### Schritt 1: Klassische Eingaben einem Quantenproblem zuordnen\n",
"\n",
"Definieren Sie $Li_2S$ Geometrien im Wörterbuchformat für verschiedene Bindungsabstände von Li-S, um die PES-Kurve zu berechnen. Diese Geometrien werden mit Hilfe von B3LYP/631g Berechnungen optimiert.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "14dcfa48",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'1.51': 'S -1.239044 0.671232 -0.030374; Li -1.506327 0.432403 -1.498949; Li -0.899996 0.973348 1.826768',\n",
" '1.91': 'S -1.215858 0.692272 0.099232; Li -1.553305 0.390283 -1.758043; Li -0.876205 0.994426 1.956257',\n",
" '2.40': 'S -1.741432 0.680397 0.346702; Li -0.529307 0.488006 -1.729343; Li -1.284307 0.989409 2.177209',\n",
" '3.10': 'S -2.347450 0.657089 0.566194; Li -0.199353 0.527517 -1.665148; Li -1.008243 0.973206 1.893522',\n",
" '3.80': 'S -2.707255 0.674298 0.909161; Li 0.079218 0.552012 -1.671656; Li -0.927010 0.931502 1.557063',\n",
" '4.50': 'S -2.913363 0.709175 1.276987; Li 0.368656 0.559989 -1.798088; Li -1.010340 0.888647 1.315670'}"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"str_geometries = {\n",
" \"1.51\": \"S -1.239044 0.671232 -0.030374; Li -1.506327 0.432403 -1.498949; Li -0.899996 0.973348 1.826768\",\n",
" \"1.91\": \"S -1.215858 0.692272 0.099232; Li -1.553305 0.390283 -1.758043; Li -0.876205 0.994426 1.956257\",\n",
" \"2.40\": \"S -1.741432 0.680397 0.346702; Li -0.529307 0.488006 -1.729343; Li -1.284307 0.989409 2.177209\",\n",
" \"3.10\": \"S -2.347450 0.657089 0.566194; Li -0.199353 0.527517 -1.665148; Li -1.008243 0.973206 1.893522\",\n",
" \"3.80\": \"S -2.707255 0.674298 0.909161; Li 0.079218 0.552012 -1.671656; Li -0.927010 0.931502 1.557063\",\n",
" \"4.50\": \"S -2.913363 0.709175 1.276987; Li 0.368656 0.559989 -1.798088; Li -1.010340 0.888647 1.315670\",\n",
"}\n",
"str_geometries"
]
},
{
"cell_type": "markdown",
"id": "3cd2cc70",
"metadata": {},
"source": [
"HiVQE die Berechnungen werden mit den unten definierten Optionen durchgeführt. Unter Verwendung der sto3g Basis für $Li_2S$ gibt es 19 räumliche Orbitale mit 22 Elektronen. Um den Fall ( 10o,10e ) mit HiVQE zu berechnen, können Sie 10 aktive Orbitale und sechs eingefrorene Orbitale definieren. Bei jeder Iteration werden 100 Schüsse verwendet, um die Elektronenkonfiguration zu testen, die von der Quantenschaltung ExcitationPreserving (`epa`) mit `circular` Verschränkung und zwei Wiederholungen (`reps`) erzeugt wird. Die maximale Anzahl der Iterationen wird auf 30 festgelegt, um die Beendigung der Iteration mit Energiekonvergenz sicherzustellen.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "52833c26",
"metadata": {},
"outputs": [],
"source": [
"molecule_options = {\n",
" \"basis\": \"sto3g\",\n",
" \"active_orbitals\": list(range(5, 15)),\n",
" \"frozen_orbitals\": list(range(5)),\n",
"}\n",
"\n",
"hivqe_options = {\n",
" \"shots\": 100,\n",
" \"max_iter\": 30,\n",
" \"ansatz\": \"epa\",\n",
" \"ansatz_entanglement\": \"circular\",\n",
" \"ansatz_reps\": 2,\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "3ee5ec4c",
"metadata": {},
"source": [
"\n",
"\n",
"### Schritt 2 und 3: Optimieren Sie das Problem für die Ausführung auf Quantenhardware und führen Sie es mit der Funktion „ HiVQE Chemistry” aus\n",
"\n",
"Richten Sie die Schleife `for` ein, um HiVQE Berechnungen mit Geometrien mit den unten definierten Optionen durchzuführen. Die Aufträge werden in der Schleife `for` übermittelt. In diesem Lernprogramm werden Sie sechs Geometrien einreichen und die Ergebnisse abrufen, wenn sie alle fertig sind. Im Hauptfunktionslauf müssen Sie `max_states` und `max_expansion_states` definieren, um die maximale Größe der Unterraummatrix zu steuern und um zu kontrollieren, wie viele Zustände mit klassischen CI-Expansionsmethoden pro Iteration erzeugt werden können. Die Auftragskennungen der Funktionen werden im Wörterbuch mit jeder Geometriebezeichnung gespeichert, um das Ergebnis weiter zu verfolgen und zu verarbeiten.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "39109638",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'1.51': 'de3b8818-c9db-4fa3-a3c2-d51551c2dfaf', '1.91': '55d9467a-fc85-49a8-9bc6-8f6990e421e5', '2.40': '415112b3-69ff-4d53-8b10-cb4e3be68c9e', '3.10': 'ef67b600-3887-4225-b872-e354dfdf8454', '3.80': 'b16d3502-a9e4-4560-9775-852e9d07e70f', '4.50': '0c0bffc7-af77-4a56-a656-2a2610c991d6'}\n"
]
}
],
"source": [
"info_jobid = {}\n",
"for dis, geom in str_geometries.items():\n",
" hivqe_run = hivqe.run(\n",
" geometry=geom,\n",
" backend_name=\"\",\n",
" max_states=40000,\n",
" max_expansion_states=100,\n",
" molecule_options=molecule_options,\n",
" hivqe_options=hivqe_options,\n",
" )\n",
" status = hivqe_run.status()\n",
" info_jobid[dis] = hivqe_run.job_id\n",
"print(info_jobid)"
]
},
{
"cell_type": "markdown",
"id": "5f48bee4",
"metadata": {},
"source": [
"Lassen Sie uns prüfen, ob alle Aufträge noch laufen oder abgeschlossen sind.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f3be3b7b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.51 de3b8818-c9db-4fa3-a3c2-d51551c2dfaf DONE\n",
"1.91 55d9467a-fc85-49a8-9bc6-8f6990e421e5 DONE\n",
"2.40 415112b3-69ff-4d53-8b10-cb4e3be68c9e DONE\n",
"3.10 ef67b600-3887-4225-b872-e354dfdf8454 DONE\n",
"3.80 b16d3502-a9e4-4560-9775-852e9d07e70f DONE\n",
"4.50 0c0bffc7-af77-4a56-a656-2a2610c991d6 DONE\n",
"Completed 6 job, Running or Queued 0 job\n"
]
}
],
"source": [
"completed_jobs_num = 0\n",
"running_jobs_num = 0\n",
"completed_jobs = {}\n",
"for i, info in enumerate(info_jobid.items()):\n",
" dis, job_id = info\n",
" submitted_job = catalog.get_job_by_id(job_id)\n",
" stat = submitted_job.status()\n",
" print(dis, submitted_job.job_id, stat)\n",
" if stat == \"DONE\":\n",
" completed_jobs_num += 1\n",
" completed_jobs[dis] = submitted_job\n",
" if (stat == \"RUNNING\") or (stat == \"QUEUED\"):\n",
" running_jobs_num += 1\n",
"\n",
"print(\n",
" f\"Completed {completed_jobs_num} job, \"\n",
" f\"Running or Queued {running_jobs_num} job\"\n",
")"
]
},
{
"cell_type": "markdown",
"id": "fb4264d5",
"metadata": {},
"source": [
"Sobald alle Aufträge abgeschlossen sind, können wir alle Berechnungsergebnisse abrufen.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7e7adaba",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"All jobs are completed\n",
"1.51 -407.8944801731773\n",
"1.91 -407.9800570932916\n",
"2.40 -407.9372992999806\n",
"3.10 -407.86278336000134\n",
"3.80 -407.83092972296157\n",
"4.50 -407.82971011225766\n"
]
}
],
"source": [
"hivqe_result = {}\n",
"if len(info_jobid) == completed_jobs_num:\n",
" print(\"All jobs are completed\")\n",
" for i, job in enumerate(completed_jobs.items()):\n",
" dis, cal = job\n",
" print(dis, cal.result()[\"energy\"])\n",
" hivqe_result[str(dis)] = cal.result()[\"energy\"]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dc9982c5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'1.51': -407.8944801731773,\n",
" '1.91': -407.9800570932916,\n",
" '2.40': -407.9372992999806,\n",
" '3.10': -407.86278336000134,\n",
" '3.80': -407.83092972296157,\n",
" '4.50': -407.82971011225766}\n"
]
}
],
"source": [
"pprint.pprint(hivqe_result)"
]
},
{
"cell_type": "markdown",
"id": "cc7c2793",
"metadata": {},
"source": [
"Die gesamte QPU-Laufzeit, die für den Auftrag verwendet wurde, kann nachverfolgt werden, indem man sich bei [IBM Quantum Platform](/) anmeldet und eingereichte Aufträge mit dem Tag `qunova-chemistry-hivqe` anzeigt.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "75fc5cf6",
"metadata": {},
"source": [
"\n",
"\n",
"### Schritt 4: Nachbearbeitung und Vergleich mit klassischen Methoden\n",
"\n",
"Die klassische Referenzberechnung (CASCI) kann für ( 10o,10e ) durchgeführt werden, um die Ergebnisse von HiVQE zu validieren.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3310e3b8",
"metadata": {},
"outputs": [],
"source": [
"str_geometries = {\n",
" \"1.31\": \"S -1.250686 0.660708 -0.095168; Li -1.482812 0.453464 -1.369406; Li -0.911870 0.962810 1.762020\",\n",
" \"1.41\": \"S -1.244856 0.665971 -0.062773; Li -1.494574 0.442933 -1.434177; Li -0.905937 0.968078 1.794395\",\n",
" \"1.51\": \"S -1.239044 0.671232 -0.030374; Li -1.506327 0.432403 -1.498949; Li -0.899996 0.973348 1.826768\",\n",
" \"1.61\": \"S -1.233245 0.676492 0.002027; Li -1.518073 0.421873 -1.563722; Li -0.894049 0.978617 1.859141\",\n",
" \"1.71\": \"S -1.227453 0.681752 0.034429; Li -1.529816 0.411343 -1.628496; Li -0.888099 0.983887 1.891513\",\n",
" \"1.81\": \"S -1.221659 0.687012 0.066831; Li -1.541558 0.400813 -1.693270; Li -0.882150 0.989157 1.923885\",\n",
" \"1.91\": \"S -1.215858 0.692272 0.099232; Li -1.553305 0.390283 -1.758043; Li -0.876205 0.994426 1.956257\",\n",
" \"2.01\": \"S -1.209887 0.697544 0.131599; Li -1.565136 0.379748 -1.822800; Li -0.870344 0.999691 1.988646\",\n",
" \"2.11\": \"S -1.203945 0.702813 0.163973; Li -1.576953 0.369214 -1.887560; Li -0.864469 1.004956 2.021033\",\n",
" \"2.21\": \"S -1.198023 0.708081 0.196350; Li -1.588760 0.358680 -1.952322; Li -0.858584 1.010221 2.053417\",\n",
" \"2.30\": \"S -1.365426 0.717714 0.367060; Li -0.689401 0.458925 -1.828368; Li -1.500219 0.981173 2.255876\",\n",
" \"2.31\": \"S -1.192118 0.713348 0.228731; Li -1.600559 0.348146 -2.017085; Li -0.852690 1.015488 2.085800\",\n",
" \"2.40\": \"S -1.741432 0.680397 0.346702; Li -0.529307 0.488006 -1.729343; Li -1.284307 0.989409 2.177209\",\n",
" \"2.50\": \"S -1.885961 0.669986 0.365815; Li -0.461563 0.499084 -1.695846; Li -1.207523 0.988741 2.124599\",\n",
" \"2.60\": \"S -1.977163 0.665155 0.389784; Li -0.416654 0.504966 -1.683655; Li -1.161229 0.987690 2.088439\",\n",
" \"2.70\": \"S -2.063642 0.661518 0.418977; Li -0.367600 0.510505 -1.676408; Li -1.123804 0.985788 2.051998\",\n",
" \"2.80\": \"S -2.141072 0.659218 0.451663; Li -0.323153 0.515056 -1.673046; Li -1.090821 0.983538 2.015951\",\n",
" \"2.90\": \"S -2.212097 0.657968 0.487535; Li -0.281989 0.518909 -1.672407; Li -1.060960 0.980935 1.979440\",\n",
" \"3.00\": \"S -2.281477 0.657123 0.525155; Li -0.239607 0.523326 -1.668669; Li -1.033963 0.977363 1.938081\",\n",
" \"3.10\": \"S -2.347450 0.657089 0.566194; Li -0.199353 0.527517 -1.665148; Li -1.008243 0.973206 1.893522\",\n",
" \"3.20\": \"S -2.410882 0.657532 0.608912; Li -0.157788 0.532069 -1.659971; Li -0.986376 0.968211 1.845627\",\n",
" \"3.30\": \"S -2.470306 0.658818 0.654893; Li -0.118007 0.536237 -1.656311; Li -0.966733 0.962757 1.795986\",\n",
" \"3.40\": \"S -2.525776 0.660762 0.702910; Li -0.078312 0.540189 -1.654076; Li -0.950958 0.956861 1.745734\",\n",
" \"3.50\": \"S -2.576885 0.663376 0.752788; Li -0.039076 0.543706 -1.654536; Li -0.939085 0.950730 1.696316\",\n",
" \"3.60\": \"S -2.623930 0.666534 0.803853; Li 0.000274 0.546839 -1.657697; Li -0.931390 0.944439 1.648412\",\n",
" \"3.70\": \"S -2.667364 0.670217 0.856250; Li 0.039572 0.549616 -1.663265; Li -0.927254 0.937980 1.601583\",\n",
" \"3.80\": \"S -2.707255 0.674298 0.909161; Li 0.079218 0.552012 -1.671656; Li -0.927010 0.931502 1.557063\",\n",
" \"3.90\": \"S -2.744005 0.678718 0.962425; Li 0.119268 0.554073 -1.682595; Li -0.930310 0.925021 1.514738\",\n",
" \"4.00\": \"S -2.777891 0.683415 1.015798; Li 0.159751 0.555810 -1.696024; Li -0.936907 0.918587 1.474794\",\n",
" \"4.10\": \"S -2.809179 0.688333 1.069057; Li 0.200678 0.557234 -1.711873; Li -0.946546 0.912245 1.437385\",\n",
" \"4.20\": \"S -2.838194 0.693443 1.122205; Li 0.242066 0.558401 -1.729770; Li -0.958918 0.905968 1.402134\",\n",
" \"4.30\": \"S -2.864984 0.698619 1.174415; Li 0.283858 0.559186 -1.750539; Li -0.973920 0.900007 1.370693\",\n",
" \"4.40\": \"S -2.889984 0.703887 1.226140; Li 0.326068 0.559728 -1.773231; Li -0.991131 0.894196 1.341660\",\n",
" \"4.50\": \"S -2.913363 0.709175 1.276987; Li 0.368656 0.559989 -1.798088; Li -1.010340 0.888647 1.315670\",\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "95e7040f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"d=1.3 RHF Energy: -407.7137006, CASCI Energy: -407.7193917\n",
"d=1.4 RHF Energy: -407.8183196, CASCI Energy: -407.8245211\n",
"d=1.5 RHF Energy: -407.8878013, CASCI Energy: -407.8944802\n",
"d=1.6 RHF Energy: -407.9315356, CASCI Energy: -407.9385663\n",
"d=1.7 RHF Energy: -407.9569034, CASCI Energy: -407.9641258\n",
"d=1.8 RHF Energy: -407.9693681, CASCI Energy: -407.9766313\n",
"d=1.9 RHF Energy: -407.9728592, CASCI Energy: -407.9800572\n",
"d=2.0 RHF Energy: -407.9701684, CASCI Energy: -407.9772549\n",
"d=2.1 RHF Energy: -407.9632701, CASCI Energy: -407.9702381\n",
"d=2.2 RHF Energy: -407.9535584, CASCI Energy: -407.9604007\n",
"d=2.3 RHF Energy: -407.9420173, CASCI Energy: -407.9487043\n",
"d=2.3 RHF Energy: -407.9420156, CASCI Energy: -407.9487024\n",
"d=2.4 RHF Energy: -407.9297216, CASCI Energy: -407.9372993\n",
"d=2.5 RHF Energy: -407.9172, CASCI Energy: -407.9261859\n",
"d=2.6 RHF Energy: -407.9061139, CASCI Energy: -407.915961\n",
"d=2.7 RHF Energy: -407.8937118, CASCI Energy: -407.904259\n",
"d=2.8 RHF Energy: -407.8816389, CASCI Energy: -407.8928292\n",
"d=2.9 RHF Energy: -407.8700448, CASCI Energy: -407.8819574\n",
"d=3.0 RHF Energy: -407.859054, CASCI Energy: -407.8719092\n",
"d=3.1 RHF Energy: -407.8487619, CASCI Energy: -407.8628304\n",
"d=3.2 RHF Energy: -407.8392304, CASCI Energy: -407.8548482\n",
"d=3.3 RHF Energy: -407.8304842, CASCI Energy: -407.8480217\n",
"d=3.4 RHF Energy: -407.8225124, CASCI Energy: -407.8423743\n",
"d=3.5 RHF Energy: -407.8152758, CASCI Energy: -407.8378892\n",
"d=3.6 RHF Energy: -407.8087161, CASCI Energy: -407.8345331\n",
"d=3.7 RHF Energy: -407.802764, CASCI Energy: -407.8322563\n",
"d=3.8 RHF Energy: -407.7973458, CASCI Energy: -407.83093\n",
"d=3.9 RHF Energy: -407.7923883, CASCI Energy: -407.8303555\n",
"d=4.0 RHF Energy: -407.7878216, CASCI Energy: -407.83025\n",
"d=4.1 RHF Energy: -407.783582, CASCI Energy: -407.8303243\n",
"d=4.2 RHF Energy: -407.7796124, CASCI Energy: -407.8303791\n",
"d=4.3 RHF Energy: -407.7758633, CASCI Energy: -407.8302885\n",
"d=4.4 RHF Energy: -407.7722923, CASCI Energy: -407.8300614\n",
"d=4.5 RHF Energy: -407.7688641, CASCI Energy: -407.829711\n"
]
}
],
"source": [
"rhf_result = {}\n",
"casci_result = {}\n",
"\n",
"cas_list = molecule_options[\"active_orbitals\"]\n",
"distance_ref = []\n",
"for dis, geom in str_geometries.items():\n",
" distance_ref.append(dis)\n",
" mole = gto.M(atom=geom, basis=molecule_options[\"basis\"])\n",
" mole.verbose = 0\n",
" # RHF energy\n",
" mf = scf.RHF(mole).run()\n",
" mo_occ = mf.mo_occ\n",
" num_elecs_as = int(sum([mo_occ[idx] for idx in cas_list]))\n",
"\n",
" rhf_result[str(dis)] = mf.e_tot\n",
" # CASCI energy\n",
" casci_solver = mcscf.CASCI(mf, len(cas_list), num_elecs_as)\n",
" orbs = mcscf.addons.sort_mo(casci_solver, mf.mo_coeff, cas_list, base=0)\n",
" casci_solver.kernel(orbs)\n",
" casci_result[str(dis)] = casci_solver.e_tot\n",
" print(\n",
" f\"d={dis:4.3} RHF Energy: {mf.e_tot:14.10}, \"\n",
" f\"CASCI Energy: {casci_solver.e_tot:14.10}\"\n",
" )"
]
},
{
"cell_type": "markdown",
"id": "e1900a94",
"metadata": {},
"source": [
"\n",
"\n",
"### Aufzeichnen der Dissoziationskurve für Li\\_2S\n",
"\n",
"Wir stellen die Ergebnisse von HiVQE dar und vergleichen sie mit HF und CASCI.\n",
"Sie können feststellen, dass alle HiVQE Berechnungen gut mit dem klassischen Referenzergebnis (CASCI) übereinstimmen.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2db64a7d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"hf_energy = [v for key, v in rhf_result.items()]\n",
"casci_energy = [v for key, v in casci_result.items()]\n",
"hivqe_energy = [v for key, v in hivqe_result.items()]\n",
"distance_ref = [float(key) for key, v in rhf_result.items()]\n",
"distance = [float(key) for key, v in hivqe_result.items()]\n",
"\n",
"ax.plot(distance_ref, hf_energy, \"-o\", label=\"RHF\", c=\"blue\")\n",
"ax.plot(distance_ref, casci_energy, \"-o\", label=\"CASCI\", c=\"green\")\n",
"ax.plot(distance, hivqe_energy, \"x\", label=\"HiVQE\", c=\"red\", markersize=20)\n",
"ax.legend(fontsize=20)\n",
"ax.tick_params(\"both\", labelsize=16)\n",
"ax.set_xlabel(\"Bond distance (angstrom)\", size=20)\n",
"ax.set_ylabel(\"Energy (Ha)\", size=20)\n",
"ax.set_title(\"Li2S PES curve\", size=20)\n",
"fig.set_size_inches(14, 8)"
]
},
{
"cell_type": "markdown",
"id": "46379f8a",
"metadata": {},
"source": [
"\n",
"\n",
"## Teil 2: FeP-NO ( 44Q )\n",
"\n",
"Beachten Sie, dass Sie für die Ausführung der Funktion auf dem System „ FeP-NO “ mit den in diesem Beispiel gezeigten Einstellungen eine Lizenz benötigen, die die Verwendung der Funktion mit mindestens 44 Qubits erlaubt. Senden Sie eine E-Mail an [qiskit.support @ qunovacomputing.com,](mailto:qiskit.support@qunovacomputing.com) um Informationen zum Erwerb einer Lizenz zu erhalten.\n",
"\n",
"\n",
"\n",
"### Schritt 1: Klassische Eingaben einem Quantenproblem zuordnen\n",
"\n",
"Definieren Sie die Optionen für HiVQE Berechnungen\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "39bce095",
"metadata": {},
"outputs": [],
"source": [
"molecule_options = {\n",
" \"basis\": \"631g*\",\n",
" \"active_orbitals\": list(range(90, 112, 1)),\n",
" \"frozen_orbitals\": list(range(0, 90, 1)),\n",
" \"charge\": -1,\n",
"}\n",
"\n",
"hivqe_options = {\n",
" \"shots\": 2000,\n",
" \"max_iter\": 40,\n",
" \"ansatz\": \"epa\",\n",
" \"ansatz_entanglement\": \"linear\",\n",
" \"ansatz_reps\": 2,\n",
" \"amplitude_screening_tolerance\": 1e-6,\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "e7c29d79",
"metadata": {},
"source": [
"Definieren Sie FeP-NO Geometrien im Wörterbuchformat für verschiedene Bindungsabstände von Fe-N zur Berechnung der PES-Kurve.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8c93344d",
"metadata": {},
"outputs": [
{
"data": {
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"metadata": {},
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"\"\"\"\n",
"\n",
"str_geometries = {\n",
" \"1.75\": geometry_1_75,\n",
" \"2.00\": geometry_2_00,\n",
" \"5.00\": geometry_5_00,\n",
"}\n",
"\n",
"\n",
"hivqe_result = {}"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "52b55a07",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
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"metadata": {},
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}
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"C 8.400230 32.124963 -1.194447\n",
"H 7.913264 32.386655 -2.130914\n",
"C 12.983905 31.827747 0.302415\n",
"H 13.955696 31.979687 -0.161365\n",
"C 11.454251 30.533644 4.698234\n",
"H 11.941002 30.276716 5.636156\n",
"C 6.877444 30.689985 3.159940\n",
"H 5.907605 30.480118 3.604825\n",
"H 12.813105 32.581608 -2.437367\n",
"H 10.233725 32.768337 -3.273979\n",
"H 15.157796 31.357524 2.082132\n",
"H 14.295001 30.638320 4.557047\n",
"H 9.626721 29.768762 6.741623\n",
"H 7.051752 29.847502 5.875478\n",
"H 4.709710 31.071712 1.354640\n",
"H 5.565103 31.898376 -1.089333\n",
"N 9.840508 33.353531 2.373019\n",
"O 9.344561 34.158205 1.637232\n",
"\"\"\"\n",
"\n",
"geometry_5_00 = \"\"\"\n",
"Fe 9.918629 31.289202 1.717339\n",
"N 10.542914 31.832173 -0.080685\n",
"N 11.795572 31.199413 2.341831\n",
"N 9.294593 30.741247 3.513929\n",
"N 8.042689 31.359481 1.087282\n",
"C 9.775254 32.111817 -1.200449\n",
"C 10.600219 32.479101 -2.319680\n",
"C 11.891090 32.425876 -1.887580\n",
"C 11.847694 32.024341 -0.507342\n",
"C 12.945734 31.464689 1.611366\n",
"C 14.116395 31.289997 2.423572\n",
"C 13.685777 30.915122 3.663719\n",
"C 12.252381 30.861042 3.608186\n",
"C 10.062170 30.463021 4.634102\n",
"C 9.236749 30.104333 5.755782\n",
"C 7.945687 30.161198 5.324720\n",
"C 7.989641 30.552269 3.941498\n",
"C 6.892881 31.087489 1.815829\n",
"C 5.722676 31.253502 1.001149\n",
"C 6.153153 31.631057 -0.238233\n",
"C 7.586010 31.695401 -0.179773\n",
"C 8.390724 32.047572 -1.247553\n",
"H 7.903308 32.291586 -2.187969\n",
"C 12.973334 31.849872 0.283741\n",
"H 13.944682 32.031190 -0.169145\n",
"C 11.447158 30.518591 4.678739\n",
"H 11.934423 30.277429 5.619969\n",
"C 6.864795 30.711643 3.146118\n",
"H 5.893357 30.532078 3.599511\n",
"H 12.800139 32.636412 -2.439296\n",
"H 10.224017 32.743662 -3.301293\n",
"H 15.131785 31.441247 2.076257\n",
"H 14.273933 30.694315 4.546802\n",
"H 9.612512 29.848040 6.739754\n",
"H 7.036117 29.960530 5.879248\n",
"H 4.707408 31.099933 1.347803\n",
"H 5.564992 31.851940 -1.121294\n",
"N 9.666041 36.091609 3.085945\n",
"O 9.598728 37.226756 3.411299\n",
"\"\"\"\n",
"\n",
"str_geometries = {\n",
" \"1.75\": geometry_1_75,\n",
" \"2.00\": geometry_2_00,\n",
" \"5.00\": geometry_5_00,\n",
"}\n",
"\n",
"\n",
"hivqe_result = {}"
]
},
{
"cell_type": "markdown",
"id": "5ed92d44",
"metadata": {},
"source": [
"\n",
"\n",
"### Schritt 2 und 3: Optimieren Sie das Problem für die Ausführung auf Quantenhardware und führen Sie es mit der Funktion „ HiVQE Chemistry” aus\n",
"\n",
"Auf der Grundlage der Einrichtung von HiVQE und der Geometrien erhalten Sie nacheinander Ergebnisse.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "316f26d8",
"metadata": {},
"source": [
"\n",
"\n",
"#### Reichen Sie die Berechnung von d(Fe-N) = 1.75 $\\AA$ ein.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5e103316",
"metadata": {},
"outputs": [],
"source": [
"hivqe_run_1_75 = hivqe.run(\n",
" geometry=str_geometries[\"1.75\"],\n",
" backend_name=\"\",\n",
" max_states=400000000,\n",
" max_expansion_states=100,\n",
" molecule_options=molecule_options,\n",
" hivqe_options=hivqe_options,\n",
")\n",
"info_jobid_1_75 = hivqe_run_1_75.job_id"
]
},
{
"cell_type": "markdown",
"id": "49a1ff1c",
"metadata": {},
"source": [
"Verfolgen Sie den Auftrag und rufen Sie das Ergebnis der Berechnung von d(Fe-N) = 1.75 $\\AA$ ab.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2e1b231f",
"metadata": {},
"outputs": [],
"source": [
"submitted_job_1_75 = catalog.get_job_by_id(info_jobid_1_75)\n",
"stat = submitted_job_1_75.status()\n",
"print(submitted_job_1_75.job_id, stat)\n",
"if stat == \"DONE\":\n",
" hivqe_run_1_75_energy = submitted_job_1_75.result()[\"energy\"]\n",
" print(f\"Completed HiVQE calculation, Energy {hivqe_run_1_75_energy}\")\n",
" hivqe_result[\"1.75\"] = hivqe_run_1_75_energy"
]
},
{
"cell_type": "markdown",
"id": "b30a0145",
"metadata": {},
"source": [
"\n",
"\n",
"#### Reichen Sie die Berechnung von d(Fe-N) = 2.00 $\\AA$ ein.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "66eaaa38",
"metadata": {},
"outputs": [],
"source": [
"hivqe_run_2_00 = hivqe.run(\n",
" geometry=str_geometries[\"2.00\"],\n",
" backend_name=\"\",\n",
" max_states=400000000,\n",
" max_expansion_states=100,\n",
" molecule_options=molecule_options,\n",
" hivqe_options=hivqe_options,\n",
")\n",
"info_jobid_2_00 = hivqe_run_2_00.job_id"
]
},
{
"cell_type": "markdown",
"id": "1cce86be",
"metadata": {},
"source": [
"Verfolgen Sie den Auftrag und rufen Sie das Ergebnis der Berechnung von d(Fe-N) = 2.00 $\\AA$ ab.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7a1ea72d",
"metadata": {},
"outputs": [],
"source": [
"submitted_job_2_00 = catalog.get_job_by_id(info_jobid_2_00)\n",
"stat = submitted_job_2_00.status()\n",
"print(submitted_job_2_00.job_id, stat)\n",
"if stat == \"DONE\":\n",
" hivqe_run_2_00_energy = submitted_job_2_00.result()[\"energy\"]\n",
" print(f\"Completed HiVQE calculation, Energy {hivqe_run_2_00_energy}\")\n",
" hivqe_result[\"2.00\"] = hivqe_run_2_00_energy"
]
},
{
"cell_type": "markdown",
"id": "ec081701",
"metadata": {},
"source": [
"\n",
"\n",
"#### Reichen Sie die Berechnung von d(Fe-N) = 5.00 $\\AA$ ein.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e72c0730",
"metadata": {},
"outputs": [],
"source": [
"hivqe_run_5_00 = hivqe.run(\n",
" geometry=str_geometries[\"5.00\"],\n",
" backend_name=\"\",\n",
" max_states=400000000,\n",
" max_expansion_states=100,\n",
" molecule_options=molecule_options,\n",
" hivqe_options=hivqe_options,\n",
")\n",
"info_jobid_5_00 = hivqe_run_5_00.job_id"
]
},
{
"cell_type": "markdown",
"id": "1b0bcce6",
"metadata": {},
"source": [
"Verfolgen Sie den Auftrag und rufen Sie das Ergebnis der Berechnung von d(Fe-N) = 5.00 $\\AA$ ab.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2758dfba",
"metadata": {},
"outputs": [],
"source": [
"submitted_job_5_00 = catalog.get_job_by_id(info_jobid_5_00)\n",
"stat = submitted_job_5_00.status()\n",
"print(submitted_job_5_00.job_id, stat)\n",
"if stat == \"DONE\":\n",
" hivqe_run_5_00_energy = submitted_job_5_00.result()[\"energy\"]\n",
" print(f\"Completed HiVQE calculation, Energy {hivqe_run_5_00_energy}\")\n",
" hivqe_result[\"5.00\"] = hivqe_run_5_00_energy"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a7793eea",
"metadata": {},
"outputs": [],
"source": [
"hivqe_result = {\n",
" \"1.75\": -2373.681781,\n",
" \"2.00\": -2373.694128,\n",
" \"5.00\": -2373.637807,\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "e6c08de7",
"metadata": {},
"source": [
"\n",
"\n",
"### Schritt 4: Nachbearbeitung und Vergleich mit klassischen Methoden\n",
"\n",
"Die Ergebnisse der klassischen Referenzberechnung (CASCI-DMRG, maxM=800 ) werden für ( 22o,22e ) bereitgestellt, um die Ergebnisse von HiVQE zu validieren.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "62937d55",
"metadata": {},
"outputs": [],
"source": [
"rhf_result = {\n",
" \"1.75\": -2373.59331683504,\n",
" \"2.00\": -2373.60640773065,\n",
" \"5.00\": -2373.50214278007,\n",
"}\n",
"casci_result = {\"1.75\": -2373.6827, \"2.00\": -2373.6948, \"5.00\": -2373.6393}"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "49a9bf81",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": []
},
{
"data": {
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1)\n",
"hf_energy = [v for key, v in rhf_result.items()]\n",
"casci_energy = [v for key, v in casci_result.items()]\n",
"hivqe_energy = [v for key, v in hivqe_result.items()]\n",
"distance_ref = [float(key) for key, v in rhf_result.items()]\n",
"distance = [float(key) for key, v in hivqe_result.items()]\n",
"\n",
"ax.plot(distance_ref, hf_energy, \"-o\", label=\"RHF\", c=\"blue\")\n",
"ax.plot(distance_ref, casci_energy, \"-o\", label=\"CASCI\", c=\"green\")\n",
"ax.plot(distance, hivqe_energy, \"x\", label=\"HiVQE\", c=\"red\", markersize=20)\n",
"ax.legend(fontsize=20)\n",
"ax.tick_params(\"both\", labelsize=16)\n",
"ax.set_xlabel(\"Fe-N bond distance ($\\AA$)\", size=20)\n",
"ax.set_ylabel(\"Energy (Ha)\", size=20)\n",
"ax.set_title(\"FeP-NO PES curve\", size=20)\n",
"fig.set_size_inches(14, 8)"
]
},
{
"cell_type": "markdown",
"id": "a5124358",
"metadata": {},
"source": [
"\n",
"\n",
"## Tutorial-Umfrage\n",
"\n",
"Bitte nehmen Sie an dieser kurzen Umfrage teil, um uns Ihr Feedback zu diesem Lernprogramm zu geben. Ihre Erkenntnisse helfen uns, unser Inhaltsangebot und unsere Nutzererfahrung zu verbessern.\n",
"\n",
"[Link zur Umfrage](https://your.feedback.ibm.com/jfe/form/SV_9AizRyKFHEGzVs2)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"id": "a1b8767d",
"source": "© IBM Corp., 2017-2026"
}
],
"metadata": {
"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"
},
"hours": 1.5,
"qpuSeconds": 300
},
"nbformat": 4,
"nbformat_minor": 5
}