docs: format notebooks with tensorflow-docs nbfmt (#1322)

Formats tracked Jupyter notebooks with `tensorflow_docs.tools.nbfmt`
(--indent=1).

Merge before #1299. Related: #1274.

Author: rosspeili

docs/fqe/guide/introduction.ipynb

@@ -2,15 +2,20 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "b000658d0d2b"
+   },
    "source": [
     "##### Copyright 2020 The OpenFermion Developers"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "cellView": "form",
+    "id": "906e07f6e562"
+   },
    "outputs": [],
    "source": [
     "#@title Licensed under the Apache License, Version 2.0 (the \"License\");\n",
@@ -28,14 +33,18 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "7cac3ba4e0b6"
+   },
    "source": [
     "# FQE vs OpenFermion vs Cirq: Diagonal Coulomb Operators"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "194e5ebc2e40"
+   },
    "source": [
     "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
     "  <td>\n",
@@ -55,15 +64,19 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "027a78b74a41"
+   },
    "source": [
     "Special routines are available for evolving under a diagonal Coulomb operator.  This notebook describes how to use these built in routines and how they work."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "1b44f1bf44c3"
+   },
    "outputs": [],
    "source": [
     "try:\n",
@@ -75,7 +88,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "a623fa4c377a"
+   },
    "outputs": [],
    "source": [
     "from itertools import product\n",
@@ -92,7 +107,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "07eb37e66cea"
+   },
    "outputs": [],
    "source": [
     "#Utility function\n",
@@ -151,7 +168,9 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "4f4ed62f910c"
+   },
    "source": [
     "The first example we will perform is diagonal Coulomb evolution on the Hartree-Fock state.  The diagonal Coulomb operator is defined as\n",
     "\n",
@@ -170,7 +189,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "2d22924fcb4e"
+   },
    "outputs": [],
    "source": [
     "norbs = 4\n",
@@ -192,15 +213,19 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "f4b8c93472be"
+   },
    "source": [
     "Now we can define a random 2-electron operator $V$.  To define $V$ we need a $4 \\times 4$ matrix.  We will generate this matrix by making a full random two-electron integral matrix and then just take the diagonal elements"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "56aa8604a016"
+   },
    "outputs": [],
    "source": [
     "tei_compressed = np.random.randn(tedim**2).reshape((tedim, tedim))\n",
@@ -221,15 +246,19 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "5270f0939273"
+   },
    "source": [
     "Evolution under $V$ can be computed by looking at each bitstring, seeing if $n_{p\\alpha}n_{q\\beta}$ is non-zero and then phasing that string by $V_{pq}$.  For the Hartree-Fock state we can easily calculate this phase accumulation.  The alpha and beta bitstrings are \"0001\" and \"0001\". "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "d7ee0994bdc2"
+   },
    "outputs": [],
    "source": [
     "alpha_occs = [list(range(fci_graph.nalpha()))]\n",
@@ -251,15 +280,19 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "9797ff1de370"
+   },
    "source": [
     "We can now try this out for more than 2 electrons.  Let's reinitialize a wavefunction on 6-orbitals with 4-electrons $S_{z} = 0$ to a random state."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "7a26d169c115"
+   },
    "outputs": [],
    "source": [
     "norbs = 6\n",
@@ -278,15 +311,19 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "89354765d52a"
+   },
    "source": [
     "We need to build our Diagoanl Coulomb operator For this bigger system."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "eec8fa7be891"
+   },
    "outputs": [],
    "source": [
     "tei_compressed = np.random.randn(tedim**2).reshape((tedim, tedim))\n",
@@ -307,15 +344,19 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "0bab89d13edf"
+   },
    "source": [
     "Now we can convert our wavefunction to a cirq wavefunction, evolve under the diagonal_coulomb operator we constructed and then compare the outputs."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "e28ac36062b7"
+   },
    "outputs": [],
    "source": [
     "cirq_wfn = fqe.to_cirq(fqe_wfn).reshape((-1, 1))\n",
@@ -327,7 +368,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "5a1a81b3c86a"
+   },
    "outputs": [],
    "source": [
     "fqe_wfn = fqe_wfn.time_evolve(1, dc_ham)\n",
@@ -338,7 +381,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "866925b171a5"
+   },
    "outputs": [],
    "source": [
     "print(\"From Cirq Evolution\")\n",
@@ -350,15 +395,19 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "id": "7108f16f2401"
+   },
    "source": [
     "Finally, we can compare against evolving each term of $V$ individually."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "id": "8a5588d11373"
+   },
    "outputs": [],
    "source": [
     "fqe_wfn = fqe.Wavefunction([[n_elec, sz, norbs]])\n",
@@ -372,34 +421,18 @@
     "               fqe_wfn.get_coeff((n_elec, sz)))\n",
     "print(\"Individual term evolution is equivalent\")"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
+  "colab": {
+   "name": "diagonal_coulomb_evolution.ipynb",
+   "toc_visible": true
+  },
   "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": "3.6.8"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 4
+ "nbformat_minor": 0
 }