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* Add 3 notebooks outlining how to use the QCQMC code and interpret zenodo data.
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# Analyzing the Experimentally Reconstructed Wavefunctions\n", | ||
| "\n", | ||
| "The experimentally reconstructe wavefunctions from the \n", | ||
| "[QCQMC](https://www.nature.com/articles/s41586-021-04351-z) paper are available\n", | ||
| "for download from [zenodo](https://zenodo.org/records/10141262)." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import urllib.request\n", | ||
| "import tarfile\n", | ||
| "\n", | ||
| "stream = urllib.request.urlopen(\"https://zenodo.org/records/10141262/files/qcqmc_data.tar.gz\")\n", | ||
| "\n", | ||
| "with tarfile.open(fileobj=stream, mode='r|gz') as tf:\n", | ||
| " tf.extractall()" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# Look at the README from the downloaded data\n", | ||
| "from IPython.display import Markdown, display\n", | ||
| "display(Markdown('qcqmc_data/README.md'))" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# Loading the wavefunctions\n", | ||
| "\n", | ||
| "Here we will reproduce some of the results from Section E of the SI from [QCQMC](https://www.nature.com/articles/s41586-021-04351-z).\n", | ||
| "\n", | ||
| "The variational energy of the trial wavefunction as a function of the number of cliffords used for shadow tomography is reported in Table S1, which we have reproduced here:\n", | ||
| "\n", | ||
| "| NCliffords | repeat 1 | repeat 2 | repeat 3 | repeat 4 |\n", | ||
| "|---|---|---|---|---|\n", | ||
| "| 10 | -1.800644 | -1.764747 | -1.813274 | -1.658202 |\n", | ||
| "| 16 | -1.823041 | -1.802192 | -1.840494 | -1.730591 |\n", | ||
| "| 28 | -1.906644 | -1.839835 | -1.843326 | -1.746749 |\n", | ||
| "| 47 | -1.925654 | -1.888527 | -1.860863 | -1.809656 |\n", | ||
| "| 80 | -1.909567 | -1.869456 | -1.887139 | -1.846339 |\n", | ||
| "| 136 | -1.930880 | -1.902309 | -1.889992 | -1.879164 |\n", | ||
| "| 229 | -1.944249 | -1.921523 | -1.903710 | -1.890947 |\n", | ||
| "| 387 | -1.947362 | -1.934682 | -1.910477 | -1.901883 |\n", | ||
| "| 652 | -1.952416 | -1.939853 | -1.912790 | -1.905250 |\n", | ||
| "| 1100 | -1.955544 | -1.944651 | -1.915073 | -1.909122 |\n", | ||
| "| 1856 | -1.955028 | -1.945966 | -1.909558 | -1.908038 |\n", | ||
| "| 3129 | -1.953877 | -1.947763 | -1.913386 | -1.908835 |\n", | ||
| "| 5276 | -1.954697 | -1.947323 | -1.912284 | -1.909315 |\n", | ||
| "| 8896 | -1.954930 | -1.947458 | -1.913889 | -1.913068 |\n", | ||
| "| 15000 | -1.954356 | -1.948894 | -1.913894 | -1.913082 |\n", | ||
| "\n", | ||
| "Each column represents an independented partitioned shadow tomography experiment.\n" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "We can reproduce this table from the data by using [FQE](https://quantumai.google/openfermion/fqe) to read the wavefunctions and Hamiltonian and recompute the variational energy of the shadow trial wavefunction.\n", | ||
| "\n", | ||
| "First we need to parse the wavefunction and Hamiltonian before computing the energy using FQE:" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import fqe\n", | ||
| "import h5py\n", | ||
| "import numpy as np\n", | ||
| "\n", | ||
| "def compute_energy(wfn_file: str, ham_file: str) -> float:\n", | ||
| " \"\"\"Compute the variational energy of the experimentally reconstructed wavefunction.\n", | ||
| "\n", | ||
| " Args:\n", | ||
| " wfn_file: The path to the FQE wavefunction. \n", | ||
| " ham_file: The path to the hamiltonian.\n", | ||
| "\n", | ||
| " Returns:\n", | ||
| " The variational energy\n", | ||
| " \"\"\"\n", | ||
| " fqe_wfn = fqe.wavefunction.Wavefunction()\n", | ||
| " fqe_wfn.read(filename=wfn_file)\n", | ||
| " with h5py.File(ham_file, 'r') as fh5:\n", | ||
| " ecore = fh5[\"e0\"][()]\n", | ||
| " h1e_act = fh5[\"h1\"][:]\n", | ||
| " eri_act = fh5[\"h2\"][:]\n", | ||
| " # get integrals into openfermion order\n", | ||
| " of_eris = np.transpose(eri_act, (0, 2, 3, 1))\n", | ||
| " # ... and then into FQE format\n", | ||
| " fqe_ham = fqe.hamiltonians.restricted_hamiltonian.RestrictedHamiltonian((h1e_act, np.einsum('ijlk', -0.5 * of_eris)), e_0=ecore)\n", | ||
| " return fqe_wfn.expectationValue(fqe_ham)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Now we can glob all of the wavefunctions from the zenodo repo and recompute the variational energy:" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import glob\n", | ||
| "import pandas as pd\n", | ||
| "for column in [1, 2, 3, 4]:\n", | ||
| " wavefunctions = glob.glob(f'qcqmc_data/h4_sto3g/fqe_wfns/column{column}/wfn*')\n", | ||
| " n_cliffords = [int(x.split('/')[-1].split('_')[-1]) for x in wavefunctions]\n", | ||
| " energies = [compute_energy(wfn_file, f'qcqmc_data/h4_sto3g/fqe_hams/column{column}/chem_ham.h5').real for wfn_file in wavefunctions]\n", | ||
| " if column == 1:\n", | ||
| " df = pd.DataFrame({'n_clifford': n_cliffords, f'repeat {column}': energies})\n", | ||
| " else:\n", | ||
| " new_df = pd.DataFrame({'n_clifford': n_cliffords, f'repeat {column}': energies})\n", | ||
| " df = pd.merge(df, new_df, on='n_clifford', how='outer')\n", | ||
| "\n", | ||
| "reproduced_table = df.sort_values(by='n_clifford')\n", | ||
| "print(reproduced_table)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Given these inputs we can also re-run AFQMC using the shadow wavefunctions as a trial wavefuncktion. To do so, we first need to parse the wavefunction and hamiltonian which is provided in ipie format in the zenodo repo: " | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from ipie.qmc.afqmc import AFQMC\n", | ||
| "\n", | ||
| "num_elec = (2, 2) # H4 molecule, 4 electrons, ms = 0 \n", | ||
| "n_clifford = 15_000\n", | ||
| "ham_file = 'qcqmc_data/h4_sto3g/ipie_ham/column3/ham.h5'\n", | ||
| "wfn_file = f'qcqmc_data/h4_sto3g/ipie_wfns/column3/wfn_{n_clifford}.h5' \n", | ||
| "afqmc = AFQMC.build_from_hdf5(num_elec, ham_file, wfn_file, num_blocks=1_000, num_walkers=100)\n", | ||
| "afqmc.trial.calculate_energy(afqmc.system, afqmc.hamiltonian)\n", | ||
| "afqmc.run(estimator_filename=f'h4_sto3g_n_clifford_{n_clifford}.h5')" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Finally we can analyze the result and compare it to the literature value which we agree with within error bars." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from ipie.analysis.extraction import extract_observable\n", | ||
| "import matplotlib.pyplot as plt\n", | ||
| "from ipie.analysis.blocking import reblock_minimal \n", | ||
| "\n", | ||
| "paper_result = -1.96922\n", | ||
| "analyzed_result = reblock_minimal(afqmc.estimators.filename, start_block=100)\n", | ||
| "notebook_energy = analyzed_result.ETotal_ac.values[0]\n", | ||
| "notebook_error = analyzed_result.ETotal_error_ac.values[0]\n", | ||
| "\n", | ||
| "data = extract_observable(afqmc.estimators.filename)\n", | ||
| "plt.plot(data.ETotal, marker='o', label=\"AFQMC\", color=\"C0\")\n", | ||
| "plt.axhline(paper_result, label=\"Exact Result\", color=\"C1\")\n", | ||
| "plt.axhline(notebook_energy, label=\"Notebook result\", color=\"C2\")\n", | ||
| "plt.legend()\n", | ||
| "plt.xlabel(\"Block number\")\n", | ||
| "plt.ylabel(\"Total Energy (Ha)\")\n", | ||
| "print(f\"paper result = {paper_result}\")\n", | ||
| "print(f\"notebook result = {notebook_energy} +/ {notebook_error}\")" | ||
| ] | ||
| } | ||
| ], | ||
| "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": "3.12.3" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 2 | ||
| } |
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