{ "cells": [ { "cell_type": "markdown", "id": "b6d1e3ec", "metadata": {}, "source": [ "---\n", "title: Dissociation PES curves with Qunova HiVQE\n", "description: Use Qunova HiVQE to compute dissociation potential energy surface (PES) curves.\n", "---\n", "\n", "{/* cspell:ignore fontsize labelsize DMRG hivqe mcscf CASCI */}\n", "\n", "# Dissociation PES curves with Qunova HiVQE\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a6f69b77", "metadata": {}, "source": [ "\n", " Qiskit Functions are an experimental feature available only to IBM Quantum® Premium Plan, Flex Plan, and On-Prem (via IBM Quantum Platform API) Plan users. They are in preview release status and subject to change.\n", "\n", "\n", "*Usage estimate (NOTE: This is an estimate only. Your runtime might vary.)*\n", "\n", "* Li2S: Five minutes QPU time on a Heron r2 processor\n", "* FeP-NO: Five minutes QPU time on a Heron r2 processor\n", "\n" ] }, { "cell_type": "markdown", "id": "8bf80006", "metadata": {}, "source": [ "## Background\n", "\n", "Accurately calculating chemical reaction energies is crucial for scientific advancements in materials science, chemical engineering, drug discovery, and other fields. Among various chemical systems, the Li-S system has garnered significant interest for understanding and developing new battery compositions. This tutorial provides hands-on experience in calculating the Li-S bond dissociation potential energy surface (PES) of a $Li_2S$ system by removing one lithium atom using HiVQE calculations. The results can be compared with reference calculations (CASCI) as well as classical methods like Hartree-Fock (HF) for a 20-qubit problem.\n", "\n" ] }, { "cell_type": "markdown", "id": "55b94021", "metadata": {}, "source": [ "## Requirements\n", "\n", "Install the following dependencies to run the code in this tutorial.\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": [ "## Setup\n", "\n", "To run this tutorial, import `qunova/hivqe-chemistry` function via `QiskitFunctionCatalog`. You need an IBM Quantum Premium Plan, Flex Plan, or On-Prem (IBM Quantum Platform API) Plan account with a license from Qunova to run this function.\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", " token=\"YOUR_API_KEY\", # Use the 44-character API_KEY you created and saved from the IBM Quantum Platform Home dashboard\n", ")\n", "\n", "hivqe = catalog.load(\"qunova/hivqe-chemistry\")" ] }, { "attachments": {}, "cell_type": "markdown", "id": "988ee237", "metadata": {}, "source": [ "## Part 1: Li2S (20Q)\n", "\n", "### Step 1: Map classical inputs to a quantum problem\n", "\n", "Define $Li_2S$ geometries in dictionary format for different bond distance of Li-S to calculate PES curve. These geometries are optimized using B3LYP/631g calculations.\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 calculations will be performed with the options defined below. Using sto3g basis for $Li_2S$, there are 19 spatial orbitals with 22 electrons. To run (10o,10e) case with HiVQE calculation, you can define 10 active orbitals and six frozen orbitals. At each iteration, 100 shots will be used to sample electron configuration generated by the ExcitationPreserving quantum circuit (`epa`) with `circular` entanglement and two repetitions (`reps`). The maximum number of iteration is set to be 30 to ensure termination of iteration with energy convergence.\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": [ "### Step 2 and 3: Optimize problem for quantum hardware execution and execute using the HiVQE Chemistry function\n", "\n", "Set up the `for` loop to run HiVQE calculations with geometries with options defined below. Jobs are submitted in the `for` loop. In this tutorial, you will submit six geometries and retrieve results when they are all completed. In the main function run, you need to define the `max_states` and `max_expansion_states` to control the maximum size of the subspace matrix and to control how many states can be generated using classical CI expansion methods per iteration. The function job ids will be stored in the dictionary with each geometry label to further track and process the ouptut.\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": [ "Let's check whether all jobs are still running or completed.\n", "\n" ] }, { "cell_type": "code", "execution_count": 40, "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, Running or Queued {running_jobs_num} job\"\n", ")" ] }, { "cell_type": "markdown", "id": "fb4264d5", "metadata": {}, "source": [ "Once all jobs are completed, let's retrieve all calculation results.\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": [ "The entire QPU runtime used in the job can be tracked by logging in to [IBM Quantum Platform](/) and viewing submitted jobs with the `qunova-chemistry-hivqe` tag.\n", "\n" ] }, { "cell_type": "markdown", "id": "75fc5cf6", "metadata": {}, "source": [ "### Step 4: Post-process and compare with classical methods\n", "\n", "Classical reference calculation (CASCI) can be conducted for (10o,10e) to validate HiVQE results.\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}, CASCI Energy: {casci_solver.e_tot:14.10}\"\n", " )" ] }, { "cell_type": "markdown", "id": "e1900a94", "metadata": {}, "source": [ "### Plotting the dissociation curve for Li\\_2S\n", "\n", "Let's plot and compare HiVQE results with HF and CASCI.\n", "You can observe that all HiVQE calculations are well-matched with the classical reference result (CASCI).\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "2db64a7d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "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": [ "## Part 2: FeP-NO (44Q)\n", "\n", "Note that to run the function on the FeP-NO system with the settings shown in this example, you need a license that permits using the function with at least 44 qubits. Email [qiskit.support@qunovacomputing.com](mailto:qiskit.support@qunovacomputing.com) to inquire about obtaining a license.\n", "\n", "### Step 1: Map classical inputs to a quantum problem\n", "\n", "Define the options for HiVQE calculations\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": [ "Define FeP-NO geometries in dictionary format for different bond distances of Fe-N to calculate PES curve.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "8c93344d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'5.0': '\\nFe 9.918629 31.289202 1.717339\\nN 10.542914 31.832173 -0.080685\\nN 11.795572 31.199413 2.341831\\nN 9.294593 30.741247 3.513929\\nN 8.042689 31.359481 1.087282\\nC 9.775254 32.111817 -1.200449\\nC 10.600219 32.479101 -2.319680\\nC 11.891090 32.425876 -1.887580\\nC 11.847694 32.024341 -0.507342\\nC 12.945734 31.464689 1.611366\\nC 14.116395 31.289997 2.423572\\nC 13.685777 30.915122 3.663719\\nC 12.252381 30.861042 3.608186\\nC 10.062170 30.463021 4.634102\\nC 9.236749 30.104333 5.755782\\nC 7.945687 30.161198 5.324720\\nC 7.989641 30.552269 3.941498\\nC 6.892881 31.087489 1.815829\\nC 5.722676 31.253502 1.001149\\nC 6.153153 31.631057 -0.238233\\nC 7.586010 31.695401 -0.179773\\nC 8.390724 32.047572 -1.247553\\nH 7.903308 32.291586 -2.187969\\nC 12.973334 31.849872 0.283741\\nH 13.944682 32.031190 -0.169145\\nC 11.447158 30.518591 4.678739\\nH 11.934423 30.277429 5.619969\\nC 6.864795 30.711643 3.146118\\nH 5.893357 30.532078 3.599511\\nH 12.800139 32.636412 -2.439296\\nH 10.224017 32.743662 -3.301293\\nH 15.131785 31.441247 2.076257\\nH 14.273933 30.694315 4.546802\\nH 9.612512 29.848040 6.739754\\nH 7.036117 29.960530 5.879248\\nH 4.707408 31.099933 1.347803\\nH 5.564992 31.851940 -1.121294\\nN 9.666041 36.091609 3.085945\\nO 9.598728 37.226756 3.411299\\n'}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "geometry_1_75 = \"\"\"\n", "Fe 9.910596 31.534095 1.798088\n", "N 10.557481 31.888419 -0.055204\n", "N 11.823496 31.255002 2.384659\n", "N 9.292831 30.783362 3.568730\n", "N 8.036805 31.418327 1.124265\n", "C 9.784765 32.177349 -1.158798\n", "C 10.612656 32.501029 -2.296868\n", "C 11.903375 32.404043 -1.876832\n", "C 11.859093 32.028943 -0.483750\n", "C 12.965737 31.464698 1.641427\n", "C 14.146517 31.236323 2.440231\n", "C 13.713061 30.885870 3.681911\n", "C 12.268752 30.896411 3.634891\n", "C 10.067717 30.486167 4.664747\n", "C 9.246224 30.053411 5.772052\n", "C 7.957075 30.082846 5.336488\n", "C 7.995710 30.538421 3.967046\n", "C 6.900258 31.104497 1.836595\n", "C 5.722470 31.251707 1.015333\n", "C 6.148430 31.668586 -0.207993\n", "C 7.587039 31.767438 -0.130483\n", "C 8.399453 32.134197 -1.192329\n", "H 7.912872 32.388031 -2.131079\n", "C 12.984883 31.836053 0.306093\n", "H 13.955948 31.977044 -0.162626\n", "C 11.453768 30.560663 4.708020\n", "H 11.940677 30.298823 5.644352\n", "C 6.877071 30.697580 3.164102\n", "H 5.907240 30.476797 3.603674\n", "H 12.813946 32.569160 -2.441577\n", "H 10.236332 32.758110 -3.280309\n", "H 15.164312 31.335191 2.080201\n", "H 14.299625 30.629109 4.556760\n", "H 9.626524 29.758225 6.743433\n", "H 7.053076 29.823583 5.875809\n", "H 4.709768 31.058315 1.350561\n", "H 5.561898 31.886355 -1.093106\n", "N 9.832739 33.209042 2.298783\n", "O 9.346337 34.075996 1.606023\n", "\"\"\"\n", "\n", "geometry_2_00 = \"\"\"\n", "Fe 9.917990 31.445558 1.778346\n", "N 10.556809 31.866188 -0.055498\n", "N 11.814089 31.227003 2.372666\n", "N 9.297875 30.758246 3.550104\n", "N 8.043584 31.397768 1.120485\n", "C 9.784831 32.164652 -1.160219\n", "C 10.611624 32.501801 -2.293514\n", "C 11.902858 32.406547 -1.875160\n", "C 11.859552 32.017818 -0.486307\n", "C 12.960503 31.454432 1.636717\n", "C 14.140770 31.242960 2.439615\n", "C 13.708543 30.884151 3.678983\n", "C 12.266351 30.874173 3.627468\n", "C 10.070264 30.465070 4.655102\n", "C 9.247247 30.053101 5.766681\n", "C 7.958085 30.091201 5.332866\n", "C 7.998432 30.529979 3.958727\n", "C 6.901428 31.093932 1.833807\n", "C 5.723289 31.255057 1.016540\n", "C 6.151314 31.670649 -0.206350\n", "C 7.589736 31.755538 -0.133074\n", "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": "code", "execution_count": null, "id": "52b55a07", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'5.0': '\\nFe 9.918629 31.289202 1.717339\\nN 10.542914 31.832173 -0.080685\\nN 11.795572 31.199413 2.341831\\nN 9.294593 30.741247 3.513929\\nN 8.042689 31.359481 1.087282\\nC 9.775254 32.111817 -1.200449\\nC 10.600219 32.479101 -2.319680\\nC 11.891090 32.425876 -1.887580\\nC 11.847694 32.024341 -0.507342\\nC 12.945734 31.464689 1.611366\\nC 14.116395 31.289997 2.423572\\nC 13.685777 30.915122 3.663719\\nC 12.252381 30.861042 3.608186\\nC 10.062170 30.463021 4.634102\\nC 9.236749 30.104333 5.755782\\nC 7.945687 30.161198 5.324720\\nC 7.989641 30.552269 3.941498\\nC 6.892881 31.087489 1.815829\\nC 5.722676 31.253502 1.001149\\nC 6.153153 31.631057 -0.238233\\nC 7.586010 31.695401 -0.179773\\nC 8.390724 32.047572 -1.247553\\nH 7.903308 32.291586 -2.187969\\nC 12.973334 31.849872 0.283741\\nH 13.944682 32.031190 -0.169145\\nC 11.447158 30.518591 4.678739\\nH 11.934423 30.277429 5.619969\\nC 6.864795 30.711643 3.146118\\nH 5.893357 30.532078 3.599511\\nH 12.800139 32.636412 -2.439296\\nH 10.224017 32.743662 -3.301293\\nH 15.131785 31.441247 2.076257\\nH 14.273933 30.694315 4.546802\\nH 9.612512 29.848040 6.739754\\nH 7.036117 29.960530 5.879248\\nH 4.707408 31.099933 1.347803\\nH 5.564992 31.851940 -1.121294\\nN 9.666041 36.091609 3.085945\\nO 9.598728 37.226756 3.411299\\n'}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "geometry_1_75 = \"\"\"\n", "Fe 9.910596 31.534095 1.798088\n", "N 10.557481 31.888419 -0.055204\n", "N 11.823496 31.255002 2.384659\n", "N 9.292831 30.783362 3.568730\n", "N 8.036805 31.418327 1.124265\n", "C 9.784765 32.177349 -1.158798\n", "C 10.612656 32.501029 -2.296868\n", "C 11.903375 32.404043 -1.876832\n", "C 11.859093 32.028943 -0.483750\n", "C 12.965737 31.464698 1.641427\n", "C 14.146517 31.236323 2.440231\n", "C 13.713061 30.885870 3.681911\n", "C 12.268752 30.896411 3.634891\n", "C 10.067717 30.486167 4.664747\n", "C 9.246224 30.053411 5.772052\n", "C 7.957075 30.082846 5.336488\n", "C 7.995710 30.538421 3.967046\n", "C 6.900258 31.104497 1.836595\n", "C 5.722470 31.251707 1.015333\n", "C 6.148430 31.668586 -0.207993\n", "C 7.587039 31.767438 -0.130483\n", "C 8.399453 32.134197 -1.192329\n", "H 7.912872 32.388031 -2.131079\n", "C 12.984883 31.836053 0.306093\n", "H 13.955948 31.977044 -0.162626\n", "C 11.453768 30.560663 4.708020\n", "H 11.940677 30.298823 5.644352\n", "C 6.877071 30.697580 3.164102\n", "H 5.907240 30.476797 3.603674\n", "H 12.813946 32.569160 -2.441577\n", "H 10.236332 32.758110 -3.280309\n", "H 15.164312 31.335191 2.080201\n", "H 14.299625 30.629109 4.556760\n", "H 9.626524 29.758225 6.743433\n", "H 7.053076 29.823583 5.875809\n", "H 4.709768 31.058315 1.350561\n", "H 5.561898 31.886355 -1.093106\n", "N 9.832739 33.209042 2.298783\n", "O 9.346337 34.075996 1.606023\n", "\"\"\"\n", "\n", "geometry_2_00 = \"\"\"\n", "Fe 9.917990 31.445558 1.778346\n", "N 10.556809 31.866188 -0.055498\n", "N 11.814089 31.227003 2.372666\n", "N 9.297875 30.758246 3.550104\n", "N 8.043584 31.397768 1.120485\n", "C 9.784831 32.164652 -1.160219\n", "C 10.611624 32.501801 -2.293514\n", "C 11.902858 32.406547 -1.875160\n", "C 11.859552 32.017818 -0.486307\n", "C 12.960503 31.454432 1.636717\n", "C 14.140770 31.242960 2.439615\n", "C 13.708543 30.884151 3.678983\n", "C 12.266351 30.874173 3.627468\n", "C 10.070264 30.465070 4.655102\n", "C 9.247247 30.053101 5.766681\n", "C 7.958085 30.091201 5.332866\n", "C 7.998432 30.529979 3.958727\n", "C 6.901428 31.093932 1.833807\n", "C 5.723289 31.255057 1.016540\n", "C 6.151314 31.670649 -0.206350\n", "C 7.589736 31.755538 -0.133074\n", "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": [ "### Step 2 and 3: Optimize problem for quantum hardware execution and execute using the HiVQE Chemistry function\n", "\n", "Based on the setup of HiVQE and geometries, obtain results sequentially.\n", "\n" ] }, { "cell_type": "markdown", "id": "316f26d8", "metadata": {}, "source": [ "#### Submit d(Fe-N) = 1.75 $\\AA$ calculation.\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": [ "Track the job and retrieve the result for d(Fe-N) = 1.75 $\\AA$ calculation.\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": [ "#### Submit d(Fe-N) = 2.00 $\\AA$ calculation.\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": [ "Track the job and retrieve the result for d(Fe-N) = 2.00 $\\AA$ calculation.\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": [ "#### Submit d(Fe-N) = 5.00 $\\AA$ calculation.\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": [ "Track the job and retrieve the result for d(Fe-N) = 5.00 $\\AA$ calculation.\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": [ "### Step 4: Post-process and compare with classical methods\n", "\n", "Classical reference calculation (CASCI-DMRG, maxM=800) results are provided for (22o,22e) to validate HiVQE results.\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": [ "\"Output" ] }, "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": [ "## Tutorial survey\n", "\n", "Please take this short survey to provide feedback on this tutorial. Your insights will help us improve our content offerings and user experience.\n", "\n", "[Link to survey](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" } }, "nbformat": 4, "nbformat_minor": 5 }