{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A4 - Quantum ising models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/OpenJij/OpenJijTutorial/blob/master/source/en/A004-QuantumSystem.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "id": "view-in-github"
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   "source": [
    "In this section, we introduce ising model with quantum effects (mainly transverse magnetic fields).  \n",
    "First, let us define the Graph and determine $J_{ij}, h_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cxxjij.graph as G\n",
    "# set the size of problem 100\n",
    "N = 100\n",
    "\n",
    "graph = G.Dense(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "mu, sigma = 0, 1\n",
    "\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        # normalize with 1/N to avoid large Jij\n",
    "        graph[i,j] = 0 if i == j else np.random.normal()/N\n",
    "\n",
    "for i in range(N):\n",
    "    graph[i] = np.random.normal()/N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transeverse field ising model\n",
    "\n",
    "In this case, transverse field ising model is used for the system.\n",
    "\n",
    "\\begin{align}\n",
    "H &= s \\left(\\sum_{i<j}J_{ij}\\sigma_i^z \\sigma_j^z + \\sum_{i=1}^{N}h_i \\sigma_i^z \\right) - \\sum_{i=1}\\Gamma (1-s) \\sigma_i^x \\\\\n",
    "\\end{align}\n",
    "\n",
    "## Continuous imaginary-time quantum MonteCarlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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