update ToC

Author: Jue-Xu

_build/.doctrees/average.doctree

@@ -0,0 +1,139 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "2763848a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from qiskit.quantum_info import SparsePauliOp, Statevector\n",
+    "\n",
+    "import quantum_simulation_recipe as qsr\n",
+    "from quantum_simulation_recipe.spin import *"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "8032a8eb",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SparsePauliOp(['IIXX', 'IXXI', 'XXII', 'IIIZ', 'IIZI', 'IZII', 'ZIII'],\n",
+       "              coeffs=[1. +0.j, 1. +0.j, 1. +0.j, 0.2+0.j, 0.2+0.j, 0.2+0.j, 0.2+0.j])"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "H = Nearest_Neighbour_1d(4, Jx=1, hz=0.2)\n",
+    "H.ham"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "a3914396",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[SparsePauliOp(['IIXX', 'XXII', 'IIIZ', 'IZII'],\n",
+       "               coeffs=[1. +0.j, 1. +0.j, 0.2+0.j, 0.2+0.j]),\n",
+       " SparsePauliOp(['IXXI', 'IIZI', 'ZIII'],\n",
+       "               coeffs=[1. +0.j, 0.2+0.j, 0.2+0.j])]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "H.ham_par"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "5c75d90b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SparsePauliOp(['IIXX', 'IXIX', 'XIIX', 'IXXI', 'XIXI', 'XXII', 'IIIZ', 'IIZI', 'IZII', 'ZIII'],\n",
+       "              coeffs=[1.      +0.j, 0.0625  +0.j, 0.012346+0.j, 1.      +0.j, 0.0625  +0.j,\n",
+       " 1.      +0.j, 0.2     +0.j, 0.2     +0.j, 0.2     +0.j, 0.2     +0.j])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "H = Power_Law(4, alpha=4, Jx=1, hz=0.2)\n",
+    "H.ham"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "5cbde227",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[SparsePauliOp(['IIXX', 'IXIX', 'XIIX', 'IXXI', 'XIXI', 'XXII'],\n",
+       "               coeffs=[1.      +0.j, 0.0625  +0.j, 0.012346+0.j, 1.      +0.j, 0.0625  +0.j,\n",
+       "  1.      +0.j]),\n",
+       " SparsePauliOp(['IIIZ', 'IIZI', 'IZII', 'ZIII'],\n",
+       "               coeffs=[0.2+0.j, 0.2+0.j, 0.2+0.j, 0.2+0.j])]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "H.ham_xyz"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3.8.8 ('base')",
+   "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": "3.10.14"
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "4e8ef2f9fcac0817bca9a7ca376f64f20b4df5ea3bf7af756a50bda7d3557ea6"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

_build/.doctrees/basic.doctree

@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 3753b484dde52448cad52d4ef3c998dc
+config: 37d0df7ac0f74f6be2523376967601d2
 tags: 645f666f9bcd5a90fca523b33c5a78b7

_build/.doctrees/channel.doctree

@@ -8,6 +8,9 @@
 <!-- Table of Content -->
 
 This is a pedagogic tutorial on quantum simulation with code.
+The package [quantum-simulation-recipe](https://youtu.be/QDPtcwhpQkE?si=_utI2VstkFiJfvxR) built with [qiskit](https://www.ibm.com/quantum/qiskit), [openfermion](https://quantumai.google/openfermion) etc.
+
+[Qiskit tutorial](https://youtu.be/QDPtcwhpQkE?si=_utI2VstkFiJfvxR)
 
 ```{tableofcontents}
 ```

_build/.doctrees/environment.pickle

@@ -5,7 +5,7 @@
    "id": "93e1e53b",
    "metadata": {},
    "source": [
-    "## LCU"
+    "# LCU"
    ]
   },
   {

_build/.doctrees/fermion.doctree

@@ -181,9 +181,11 @@
     "### Rotation (real-time evolution) of a Pauli string\n",
     "\n",
     "https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/Hamiltonian_simulation.ipynb\n",
+    "\n",
     "$$\n",
     "e^{-i XX t} = \\text{CNOT} (I\\otimes e^{-i X t}) \\text{CNOT}\n",
     "$$\n",
+    "\n",
     "[1] J.D. Whitfield, J. Biamonte and A. Aspuru-Guzik, Molecular Physics, \"Simulation of electronic structure Hamiltonians using quantum computers\" (2011)"
    ]
   },

_build/.doctrees/field.doctree

@@ -25,44 +25,28 @@
     "from quantum_simulation_recipe import spin_ham"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "93e1e53b",
-   "metadata": {},
-   "source": [
-    "## LCU"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "ed26007b",
    "metadata": {},
    "source": [
-    "### Block encoding"
+    "## Block encoding"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "e4dfa4db",
    "metadata": {},
    "source": [
-    "### Amplitude amplification"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e704fe72",
-   "metadata": {},
-   "source": [
-    "## QSP"
+    "## Amplitude amplification"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "9f801c1c",
    "metadata": {},
    "source": [
-    "### Oblivious amplitude amplification"
+    "## Oblivious amplitude amplification"
    ]
   }
  ],

_build/.doctrees/ground.doctree

@@ -18,7 +18,7 @@
     "from qiskit.quantum_info import SparsePauliOp, Statevector\n",
     "\n",
     "import quantum_simulation_recipe as qsr\n",
-    "from quantum_simulation_recipe import spin"
+    "from quantum_simulation_recipe.spin import *"
    ]
   },
   {
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "id": "8032a8eb",
    "metadata": {},
    "outputs": [
@@ -47,30 +47,63 @@
        "              coeffs=[1. +0.j, 1. +0.j, 1. +0.j, 0.2+0.j, 0.2+0.j, 0.2+0.j, 0.2+0.j])"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "H = spin.Nearest_Neighbour_1d(4, Jx=1, hz=0.2)\n",
+    "H = Nearest_Neighbour_1d(4, Jx=1, hz=0.2)\n",
     "H.ham"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "2cf6b1bb",
+   "metadata": {},
+   "source": [
+    "### Parity grouping"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "a3914396",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[SparsePauliOp(['IIXX', 'XXII', 'IIIZ', 'IZII'],\n",
+       "               coeffs=[1. +0.j, 1. +0.j, 0.2+0.j, 0.2+0.j]),\n",
+       " SparsePauliOp(['IXXI', 'IIZI', 'ZIII'],\n",
+       "               coeffs=[1. +0.j, 0.2+0.j, 0.2+0.j])]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "H.ham_par"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "efde70d6",
    "metadata": {},
    "source": [
     "## Power-law interaction\n",
-    "```{math}\n",
+    "\n",
+    "$$\n",
     "H=\\sum_{j=1}^{n} \\sum_{k=j+1}^n \\frac{1}{(j-k)^\\alpha} (J^x X_j X_{k} + J^y Y_j Y_{k} + J^z Z_j Z_{k}) + \\sum_{j=1}^{n} h_j^x X_j + h_j^y Y_j + h_j^z Z_j,\n",
-    "```"
+    "$$"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "id": "5c75d90b",
    "metadata": {},
    "outputs": [
@@ -82,16 +115,49 @@
        " 1.      +0.j, 0.2     +0.j, 0.2     +0.j, 0.2     +0.j, 0.2     +0.j])"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "H = spin.Power_Law(4, alpha=4, Jx=1, hz=0.2)\n",
+    "H = Power_Law(4, alpha=4, Jx=1, hz=0.2)\n",
     "H.ham"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "86aeee6d",
+   "metadata": {},
+   "source": [
+    "### XYZ grouping"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "5cbde227",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[SparsePauliOp(['IIXX', 'IXIX', 'XIIX', 'IXXI', 'XIXI', 'XXII'],\n",
+       "               coeffs=[1.      +0.j, 0.0625  +0.j, 0.012346+0.j, 1.      +0.j, 0.0625  +0.j,\n",
+       "  1.      +0.j]),\n",
+       " SparsePauliOp(['IIIZ', 'IIZI', 'IZII', 'ZIII'],\n",
+       "               coeffs=[0.2+0.j, 0.2+0.j, 0.2+0.j, 0.2+0.j])]"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "H.ham_xyz"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "14bd5369",