{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QuTiP example: Qubism visualizations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "by [Piotr Migdał](http://migdal.wikidot.com/), June 2014\n",
    "\n",
    "For more information about QuTiP see http://qutip.org.\n",
    "\n",
    "For more information about Qubism see:\n",
    "* J. Rodriguez-Laguna, P. Migdał, M. Ibanez Berganza, M. Lewenstein, G. Sierra,\n",
    "  [Qubism: self-similar visualization of many-body wavefunctions](http://dx.doi.org/10.1088/1367-2630/14/5/053028), New J. Phys. 14 053028 (2012), [arXiv:1112.3560](http://arxiv.org/abs/1112.3560),\n",
    "* [its video abstract](https://www.youtube.com/watch?v=8fPAzOziTZo),\n",
    "* [C++ and Mathematica code on GitHub](https://github.com/stared/qubism).\n",
    "\n",
    "This note describes plotting functions `plot_schmidt` and `plot_qubism`, and additionally - `complex_array_to_rgb`, along with their applications.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qutip import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Colors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In quantum mechanics, complex numbers are as natual as real numbers.\n",
    "\n",
    "Before going into details of particular plots, we show how `complex_array_to_rgb` maps $z = x + i y$ into colors.\n",
    "There are two variants, `theme='light'` and `theme='dark'`. For both, we use hue for phase, with red for positive numbers and aqua for negative.\n",
    "\n",
    "For a longer comment on coloring complex functions I recommend IPython Notebook [Visualizing complex-valued functions with Matplotlib and Mayavi](http://nbviewer.ipython.org/github/empet/Math/blob/master/DomainColoring.ipynb) by Emilia Petrisor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DLmOPdYKIaUuMKa0Ni9rOLyAtt5+Oicpuv/m64QwT7OLbP8N5YU48eJddfEsxqHm7dfHt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\natiwYcOGnaT9/78cpYrRdLjiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1180f4da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compl_circ = np.array([[(x + 1j*y) if x**2 + y**2 <= 1 else 0j\n",
    "                        for x in np.arange(-1,1,0.005)]\n",
    "                       for y in np.arange(-1,1,0.005)])\n",
    "\n",
    "fig = plt.figure(figsize=(6, 3))\n",
    "for i, theme in enumerate(['light', 'dark']):\n",
    "    ax = plt.subplot(1, 2, i + 1)\n",
    "    ax.set_xlabel('x', fontsize=14)\n",
    "    ax.set_ylabel('y', fontsize=14)\n",
    "    ax.imshow(complex_array_to_rgb(compl_circ, rmax=1, theme=theme),\n",
    "              extent=(-1,1,-1,1))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Schmidt plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arguably, the easiest way to show entanglement is to plot a wavefunction against two variables.\n",
    "If the plot is a product of them, the state is a product state. If not - it is entangled.\n",
    "\n",
    "As writing a wavefunction as a matrix $|\\psi\\rangle_{ij}$ is the the crucial step in [Schmidt decomposition](http://en.wikipedia.org/wiki/Schmidt_decomposition),\n",
    "we call such plots Schmidt plots.\n",
    "\n",
    "Let us consider two states:\n",
    "\n",
    "* entangled: singlet state $|\\psi^-\\rangle = (|01\\rangle - |10\\rangle)/\\sqrt{2}$,\n",
    "* product $(|01\\rangle - |00\\rangle)/\\sqrt{2}$.\n",
    "\n",
    "They may look seamingly similar, but the later can be decomposed into a product $|0\\rangle(|1\\rangle - |0\\rangle)/\\sqrt{2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "singlet = (ket('01') - ket('10')).unit()\n",
    "separable = (ket('01') - ket('00')).unit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKIAAAChCAYAAABEZmS1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWhYcRMuCg2hZcBAtCw6iZeH/9IR7DP7AoAIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1180fb390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_schmidt(singlet, figsize=(2,2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKIAAAChCAYAAABEZmS1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsuAgWhYcRMuCg2hZcBAtC/8HNVl5b8GrGcUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118195978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_schmidt(separable, figsize=(2,2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we see, for separable state the plot is a product of `x` and `y` coordinates, while for the singlet state - is is not.\n",
    "\n",
    "Let us now consider a product of two singlet states: $|\\psi^-\\rangle|\\psi^-\\rangle$.\n",
    "Schmidt plot, by default, makes spliting of equal numbers of particles.\n",
    "\n",
    "(And just for fun, let's multiply it by the imaginary unit, to get diffeerent colors.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKgAAAChCAYAAABTRPR8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f89c160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_schmidt(1j * tensor([singlet, singlet]), figsize=(2,2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we see, we have a product, as the state is a product state with the respect to the splitting of first 2 vs last 2 particles.\n",
    "\n",
    "But what if we shift particles, getting $|\\psi^-\\rangle_{23}|\\psi^-\\rangle_{41}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKgAAAChCAYAAABTRPR8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nqFNqXKBOqXGBOqXGBeqUmv8BDQupjgm8MVgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118227908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_schmidt(1j * tensor([singlet, singlet]).permute([1,2,3,0]), figsize=(2,2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we see that it is entangled.\n",
    "\n",
    "`plot_schmidt` allows us to specify other splittings. With parameter `splitting` we decide how many particles we want to have as columns. In general, we can plot systems of various numbers of particles, each being of a different dimension.\n",
    "\n",
    "For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARQAAABuCAYAAADmvuxqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d66ceb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_schmidt(1j * tensor([singlet, singlet]), splitting=1, labels_iteration=(1,3), \n",
    "             figsize=(4,2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Qubism plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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p1vhHjhzBjz/+6HkeHx+Pe+65J6xjamV1TswymnJCRNaQ9jDvtcr3F6gLFixAQkKCRbMh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\nOrGYEhER6cRiSkREpNP/AxX7MHMGQS0mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d5e8ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 4))\n",
    "for i in [1, 2]:\n",
    "    ax = plt.subplot(1, 2, i)\n",
    "    plot_qubism(0 * ket('0000'),\n",
    "                legend_iteration=i, grid_iteration=i,\n",
    "                fig=fig, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is, all amplitudes for states starting with:\n",
    "\n",
    "* $|00\\rangle$ go to the upper left quadrant,\n",
    "* $|01\\rangle$ go to the upper right quadrant,\n",
    "* $|10\\rangle$ go to the lower left quadrant,\n",
    "* $|11\\rangle$ go to the lower right quadrant.\n",
    "\n",
    "And we proceed recursively with the next particles. So, for example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO4AAADuCAYAAAA+7jsiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d713438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state = ket('0010') + 0.5 * ket('1111') + 0.5j * ket('0101') - 1j * ket('1101') \\\n",
    "        - 0.2 * ket('0110')\n",
    "plot_qubism(state, figsize=(4,4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or if we want to make sure how did we map amplitudes to particular regions in the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xZvEmRvBZTOBFrOFxePBd+HCApK51rsGPTUiYTQih+eF0OkU+kUhE2O32vN+rq6sTMzMz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\nYnCJFMTgEimIwSVS0P8D76sr3rmDpJkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d75ea58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_qubism(state, legend_iteration=2, figsize=(4,4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or how about making it dark? (E.g. to fit out slides with black background)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO4AAADuCAYAAAA+7jsiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d77fcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_qubism(state, legend_iteration=2, theme='dark', figsize=(4,4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most important property of Qubism is the recursive structure. So that we can add more particles seamlessly.\n",
    "For example, let's consider a plot of `k` copies of the singlet states, i.e. $|\\psi^-\\rangle^{\\otimes k}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1oAAAClCAYAAABFjozPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1184b41d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15, 3))\n",
    "for k in range(1,6):\n",
    "    ax = plt.subplot(1, 5, k)\n",
    "    plot_qubism(tensor([singlet]*k),\n",
    "                fig=fig, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK, but once we can type the wavefunction by hand, plots offer little added value.\n",
    "\n",
    "Let's see how we can plot ground states.\n",
    "Before doing that, we define some functions to easy make a translationally-invariant Hamiltonian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def spinchainize(op, n, bc='periodic'):\n",
    "    \n",
    "    if isinstance(op, list):\n",
    "        return sum([spinchainize(each, n, bc=bc) for each in op])\n",
    "    \n",
    "    k = len(op.dims[0])\n",
    "    d = op.dims[0][0]\n",
    "\n",
    "    expanded = tensor([op] + [qeye(d)]*(n - k))\n",
    "\n",
    "    if bc == 'periodic':\n",
    "        shifts = n\n",
    "    elif bc == 'open':\n",
    "        shifts = n - k + 1\n",
    "\n",
    "    shifteds = [expanded.permute([(i + j) % n for i in range(n)])\n",
    "                for j in range(shifts)]\n",
    "\n",
    "    return sum(shifteds)\n",
    "\n",
    "\n",
    "def gs_of(ham):\n",
    "    gval, gstate = ham.groundstate()\n",
    "    return gstate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, let us consider Hamiltonian for $N$ particles, of the following form (a generalization of the [Majumdar-Ghosh model](http://en.wikipedia.org/wiki/Majumdar%E2%80%93Ghosh_Model)):\n",
    "\n",
    "$$H = \\sum_{i=1}^N \\vec{S}_i \\cdot \\vec{S}_{i+1} + J \\sum_{i=1}^N \\vec{S}_i \\cdot \\vec{S}_{i+2},$$\n",
    "\n",
    "where $\\vec{S}_i = \\tfrac{1}{2} (\\sigma^x, \\sigma^y, \\sigma^z)$ is the spin operator (with sigmas being [Pauli matrices](http://en.wikipedia.org/wiki/Pauli_matrices)).\n",
    "\n",
    "Moreover, we can set two different boundary conditions:\n",
    "\n",
    "* periodic - spin chain forms a loop ($N+1 \\equiv 1$ and $N+2 \\equiv 2$),\n",
    "* open - spin chain forms a line (we remove terms with $N+1$ and $N+2$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QahtRIh5RFW5pj5O10Y+xRr7jKD2OUcBuyyKXs359tWwez08aox6WX/QDyycd\nfXTyMW66yatefc01iW5rfN7X/hNU+bYh3+r3Fassrn7XzlwrymwXCVc34dZpVog239qsp8O1uclk\nOJ48ebLfUei1zZ3rVb9/xx2J5tZUauVbtlTLY3zDkz0acrheIzEmvd+r8hHbt3ttnUr+KxLirUx6\nQMonA7UO1pn5TdLfG5s3e22HjEuhk27W00l6PSmTniVvk56FT1CEEEIKSc0NSkRGi8iXRWRO4Jo5\n5WtG1rqGEEII6Q+hJ6irAVwMPw+X5SEA8wD8WZ6TIoQQQkI+qHcBuNU5Z5XZKzjndorIrQAuQjS5\nYn2wfidNBqn8kJ3VI43PKS7dxsSJyfpJ43OaP9+vL1qU/N7Vq6vlqVP9tt5ev65/DwOcbiP4G8ki\nv6P9VaEhUnS5Mqbd+0CG/CHW5xTirLP8+oMPJr931apq+cQT/TYt1wP473WK8Oy6MKa2dySS9iHF\nGjlCV0bWNhylOtZifecW9V5OCl2Xxue0caNfT7OeXlVevMP9d9N8S3ipgfrzLRH6zZwI4JEEffyq\nfC0hhBCSG6ENaiiS5Vfbi5gceoQQQkhaQhvUC4hJGFvmZEQFtgkhhJBMhHxQ9wD4qIj8u3NuV18X\niMgIAB8F8ON6TC5P7A6awqvjpUe2EiFbTV17wbKk29CPrvbx9Fem/rwqz4vxOWlr93bTNkH5nUyC\ndxzVacVbWgAtVwTEShZ5hKSE9hkxqhdeqBSnp7H1pxnTnM87U7U/FOdzUueAVhl/zInK72Q9qoeN\niCSIb37U7woAcEwKIbGAD/d2c+mlL6vk6EcemXwMwzZVtrJrMBJF31V+9osn2MRBht27K8UHDjnE\na5qt/U7f/a7X1nnxxeF+UxJ6gvo7lNIf3Scip9nG8s/uRclv2JgACUIIIYOGmk9QzrkXROSdABYD\n6BGRl1HNcXccgCMBbAbwTufcCzW6IYQQQvpFUOrIOfcLEZkG4EMAzkNVOHslgH8G8G/OuS217i8S\nGQLQPXObNfFZI0de0hyPq/JM02az3b41Rb/63pCZsytFn83KAWPSS/W705Jbw0xQ8dq1XtUpFelM\nckFaksfMfbYx+T2UQs38YWXW6w5cNyhO49vQ+RTcosx6HzZtly5c6NVfXbCgUo6EvadglMqSC5Ml\n99/N0ZkFSIFa07O/+U2/7fLLK8XfGpNexNSWkVgtPufcqyiZ8GjGI4QQ0jD6/Qe/iIwXkSxplggh\nhJCaBDfSAPPyAAAXNklEQVQoEXmTiPytiPyDiJxe/tnFIrIewAYAr4nIv4gIRWcJIYTkSk0Tn4ic\nD+AulLIZ7AHwMRG5AsBtKCVmXQngVJQ0+1YCuLXuswW88EeY8EesWePXVUjvmLgQ4g0bquXx472m\n0fpek75haBYpnZdUMLeRcJp5hBJVWbzYa7tk3rzkY5hQ05MTSjo1U7qNUPi1CSRHm/r92bQYFu17\ntFe2KRv9c6btOOMLSON3cjXKADBEr8PZs722Bx54wL845HcyYednWCmkGjTVmnhceXFPOcVrsgln\nbtIyXuZ3F+Gee6rlM8/0mj6spI82wKdrge8BSuV32lYNJv/eKD+Y/D16vu96l9f2gR/8IPEQPzH1\nt+v1o3xOlrx9TpbQJ/SvAPwcpfdyNICbAdwC4Bbn3AXOub9wzv0vAF9HKYiCEEIIyY3QBjUdwFec\nczudcw7A3wPoAHCnue6/ARxfp/kRQggZpISi+MYB0JK3B5NJvmKu24LSE1ZjsGY9zZQpNZvWm3pE\nR7yrdmC1NhO1GbOQNcNoYk07Rx1Vs+kqVf6aMelZRWxtLoj0aEx6WuPAzk+bcOzrKnQ21YA5K2KW\n0r+/TZv8NmPaDQpMqizHxxm1+SxrQmqUAf9DttWY9Lb5l3pq2pFPjDXpqZD5A8bUrFd7U60JY9bT\n3GR/oFRS7jNN59lrzz+/9pjqd9JlTLAvm0uP1Comce4HZdZ7j2m6V5XfZk16D5lMSdo9cu65XtPb\nTb/6O+9R0+Z9o2w1Wjqj890KGNxACCGkkMSdg/oTETkoGDsEpT+iLhSRN6pr3lCXmRFCCBnUxG1Q\n1/fxs0/38bOQVYMQQghJTWiDyiC7XEfWrauWJ03y2140muVKsXdiKBMv4CtbGz9Tm/ZxGNVoSZNh\n17JSeZN0WCyAr11ySbXyK1+/fPpb3pJ8jL1+Sq+hce9DmUL7Fwwh5Xeb0Ewr0482PieL/k3/3rRN\n0H6nHNeEPsQwxNjzt2p7v8lwPCqF2rx9T9rVmgjZ/JtpTXxZlT9hG9/8Zq/64q9/XSlHfE4GLWJl\ncxV0ar+TyZJ7pM32nUI5/5eqfLZZW29Ta8/Kub1uwuCDPPaYV2079dRKOXgwJWefkyUkFmuPdxBC\nCCENg0EShBBCCgk3KEIIIYUkVs28cITk8LU8EAAMTfHysviS+stXvlItX3FF7etm2oQbKUjzHjQp\n+myX9UHtNvXRKdJQ6KzCRxs/k77XmX6yrKQh+ve1c2fN65zxOaUZsz1LJuEm4RM/Vkm+3/EOr+2X\nyucEAGfvUgnDOzqC/Y5R5bH2u0hlGN5vfE5Z3uGzH364Ur7ZrMOrVfn1nh7/xu5Q8hTD9On9mFn9\n4RMUIYSQQsINihBCSCEppP3nh6pshUU6TjqpUj5g2obYzKYBIrItSVXJM5gCnwEwX9UXfe1ryW5M\nGBreJwNhuqwH2pxi5K6GaxOVMYuNHG5yIIfej40bverR6phC6L4s7/Ayc7/bt6/WpbmN2SomPf35\nf9W0jdVmvS1+0u+zx4zxLw6Z9cwxjbH6szjC5tOukuUd3g//9Rx+xhmV8tWRqxVpTHqWgroCEs9K\nRM4BcCmAY1ESjdU459ycPCdGCCFkcJNogxKRKwH8K0pCsasR9T23yJ/phBBCikLSJ6hPAFgI4P3O\nuT11nA8hhBACIPkGdRSA/8hzcypn570CADo6OtBdw376ubwGHAieecar7t69G2vV68xgMW48Nsz6\ntdeq5cNT5QetSdI10dSYDMcjRozAiXVeExFpoxT3etJLOV6blEGxJkzY/+rVq3FenV9nltQpXvoh\n22h9qBl9W+LsF09fF4n8AsB/OuduyzRaDbq7u12PjeFvBebP96rda9ei7q8zcF4nFp3O3gaN6LMi\ngJ/6+sILK8Xu7m709PRkNvm27Jowv4/uWbPqviY2mvqEPq/qGx1yYsJNYE5TeXZ/HT7ANRHDq36I\nR/d559V9TWT5o0WHnIyxja+YdIH6j1f1nZJ0TST9Q+djAD4uIn+Y8HpCCCEkE0mfv+5EKaHnz0Rk\nB/xNFChF8R2X68wIIYQMapJuUEvR5DmfsthcQ+kclpv611X5a4sW+Y0p7Mp6vnau9rXo+pAYk56+\n1j7mD1OP4E+atpPsWRFl1mtWrIkq1dmVgGSSfV+1aWyfNcGm8TUExoysb5V6ZoJJSR/pVt+3fbvX\nNnzkyGrFnDFrM2fMap8Kah7sKbQ0HhRtlIv8Vm++2as+fHX1RNMZWXy4gdTxVhRuhDK/tY8dG+xW\nG/Q7fvlLr23M2WdXyj+Gzzti+k1LovffOffeXEclhBBCYqDUESGEkEKSRkniNACfAvCHAA4H8Gbn\n3HIR+RKAXzjn7q7THHPBPrqniVrRZjyby3a1qX80Rb95kcb2qt8HmyVWG4JawVwTR5uRsUkjKdWr\nTGw2l+04U98Xio5MgVZNt4ZcMTJNOOqoxP2KztRrpaE0BZXDyZOVpn5qn1f1TbdWMDcZdeVqX6TI\nabOZMpml5XVl1rMZdUeYrMve0ZAYU1yHMhG/2cxPa8G/48tf9trwiUj+4kwk+rSIyNkAHgbwBygd\n2NX3HQBwVa6zIoQQMuhJ+ufcDQB+AmA6gGtM23IAGRIWEUIIIVGSPrPPBPBu55wTEWtR6gUwPt9p\nEUIIGewk3aB2obZb4kgAr9Voy59QRlSbKVRd2x5nP39J5U81J7vforNNXuVbMy9JmjKjLwIqHqJf\nm3ldYsJJg+HR69d71faJEyvlUPDxpFCfRSO0Jg74SVn2Kh9Qe5zPabfSRtjjq3x1jhpVrYwe7bVt\n1T4dIJ3fKeGaeNG0ealBYthk6uPN/GuSJe1Lg9G/gcirM3JTeOMbK8VTY1KR/EyVDzFtZ2q/0733\nem3ubW/zL07hd/KkhV5+2Ws79MgjK+UHzH2zTdZl2Lrmvvv8+nnnVYq/RoCcfU6WpJ+cX6KkJKF/\newc/SR8A8NNcZ0UIIWTQk/QJ6lMAHgTwGIAlKG1Ol4vITQBmAXhTfaZHCCFksJL0oO5jZR2+GwFc\nj1KU60dQeqo8xzn3VP2maAgpJQQez81DPWbZC3RYrgnRXazK84xJz4Zq68Dl2EDfwGvxlKHN67IK\nCNpk02U7UiY9e++z5tIpqmwTfllzRqEIrQljXtNGqgfNpWfZe3XmXpPFd7YqP2BNesas6M0vTrw3\n1P7cc5Xi0ccZZTFr3tZzMKY56zD21prtR629LGosjSZotJwV+fRX+clP/Prb3+5Vzw10+y5V/oE1\n6X3ve15123veUymPQhjv069MegCADRsqxdld/qff1wQBHlJlm6lcm/SAUmDBQTqvMXFxN91UKT5u\nujnF9puRxAcbnHPLAcwRkQ4AYwG86pyzahqEEEJILqQ+Neic2wVgLzcnQggh9STxBiUi54jI/SKy\nE8AGEdkpIj9nCg5CCCH1IJGJT0TmAfgvlJR9bkQpB1oXgIsA/FRELnHOLanbLDUB9V4bHg4l1zHr\n5JPD/f5eeZN+6gclzrvkkmplua9ffsTMDGeUdUixsf0P0WHxxsfRZsKCI34nzRY/M0rbmGqKsSn2\nWkWhfU6W0JqwckYqEdxZZ5wR7NZT+Z4922t74IFqUG9EFT2DnJFeE08Zf9Q05Xeyqa2H2dcdCpc2\nPrIher6B+4rsc4rw299Wy6ed5jV901x6mSqL8TlF0IruCxd6TT/4wAcqZeuUn6Z8TkC838lDfa8t\nNMrnC7Tf6ZZbvLaRH/6wV4/4nRSR+eqK8jlZ8vY5WZL6oD4H4H8AzHXOVVa3iPwNgB8C+DxK0X2E\nEEJILiT9U28ygH/VmxMAlOu3oMnOdRJCCCk+STeop1Fbzmg8gDX5TIcQQggpkdTEdz2AfxaRVc65\n3xz8oYi8BcBn0MgsEyruP5JSYLc5vTN5cvJ+778/2X2n5Gh11b6AHSYoUvuZskjMGNl/KB9Uy6Cz\nwB52mN+2xv/b6YDyO8X9dSZnnlkpu4ce8ttUOc+kas8qv9PxgeuyiA7tNz6yVJmEm4TvKr/Txabt\n8gd8UaDdyr8Y63u9885KcZnyOQH+2cpp27b5941K5XXyeFn5nRbcfrvfeOmlleJq43OammKMoqbX\nSbpBXQugA8AjIvICSkESEwAcUy5/UkQ+Wb7WOefOyX2mhBBCBhVJN6j9AH5X/neQZxEVIyCEEEJy\nIanU0R/VeR4eWhrdBAmjU5n1bDbbqSkUneeb+qJ585LdmMHcth/+aztMh/SGFKVDWU7jODqkWd48\n7FJlIySEEcqst8q0nXjiiV49ZI6zUkcPKrNeKMQ6U/j1zp3Aymoe18laOb9OY7aMSU9niDXHCS5W\nyt3m8AkON0cGQmY9k6cYEy6uGgwDgkmZTHoHAGjDvCdupEx6ljQmPcsxGe6tJ3mazwkhhJDcSKMk\ncaSI/IOI/EZE1pb//3sRCZ4TJYQQQvpDog1KRKYCeBTAx1ASyf11+f8/B/CoiJxQtxkSQggZlCQN\nkvg7lJJUvsU5t+7gD0XkOAD3lNvfndekDou/BEA6m6sV61iU4l6dvdR6dLaYuhJCwUTT1obkr82T\n2TFt1i+3QpWDdnHTr1X7PTQwxkDnUu1IeN2J8ZdUmGvqNv1GCB0dZA8l7DL1jn37qhWb2Xn4cCCh\n38k7lmDllEwmXqfC1eP8Va5GGTB/wdpsv3GpQ+qNPVJQg8PjL6lgo75SHFTBZlUeZxvXrfOquyZN\nqpTt2h4C/7MYRGd6HjbMa7LpNkZqObcjjgh266VgsRJyKuzdfv/lfYglqYnvXACf0psTADjnnkPp\nHFQoTQohhBCSmqQb1DAA22q0bSu3E0IIIbmRdIN6FMBHRcS7XkQEwIfL7YQQQkhupFEzvwvAKhFZ\nBOBllLI8zANwAoD/XZ/p9UEotcKzxoL8ox9VitdcfXW4Xy2T9PLLXtPRyl6MJ5/02sacdJJfD4/i\no236JgWC6Nf20kteW7uReAr6ncz5EFHnuEJ27oH2OaVCv4/WL2LTr190UaV4x/e/H+5WlcWsrcla\nDkunYADQYc+tWb9TcNDqqAfMa9FpMSIpPsy1Qe+Q8SVJUn/VQPuc0qDTzBh5r2Xm0lnqMz3ZfJ4j\n6N+18QOOO6R6ospfEcBw/R2C5D5VAN4a3mrGHK39Tr29XttIdRYMQNDvFPGb6srhtb149RZOS3pQ\n924RuQDAF1DS5ROUPr/LAFzgnLunflMkhBAyGEn8p51z7m4Ad4vICJQ2zi1M+04IIaRepLA9lChv\nSgO3MT3/fLVsVcefecavx2XH1LzwQrXcEXgAnxLKQ5sSbX6y6sf6sTqNiciyx+RezaKM3oxc7GtZ\nO2XWizNYyeOPVyuBjMx7jUkvk9J4QnNbmzVdpsniW7Rw8TpwuzLrWXGgWUbWbOXixZVyXMD/U+p3\nPc1+thTDc3yPd6jf7eif/cxvPLcaQH2PMemFMuhaOjZt8n8wvlZ2pcZCqSNCCCGFhBsUIYSQQsIN\nihBCSCHJ4NyoHzolhZXrOEr5nb5o2q6fMyfxGD809QuT+paG9f9McjDdRiCUEynSiEQ4NLFoSqHx\npFcC9n2bNGXxkiX+pYExnjD1kxNmT87k1XPOOwrQltRHmMbnlOe9RUJL8JhQ/0uPrCapWAGfGcrn\nBMT4nUy/07S/MfRdkMHntA/AK6o+VjeeW1u0J43PKUJBfE6WFlmphBBCWg1uUIQQQgpJIU18h9Uo\nAwBuvrlSvN6qQ6xZ49dfV3kpTz3Va7rQ9qsVKmwIrza7ZAgfjaiZa5Xr3/3Ov1iHNevXAaQz27VI\nSLHR2PIbZ86sFBcvX+637fBPRBwYMaLvPgHYQHKt1mBVvr0PTpb3WKT2+tpv9CLUcQM7nzS/1Sz3\nFgptFrcm8htvrBRnXHut1/RV081HtAKDVV+wqiCvVI1v+8d6xjcvU3GW93gojFlPqWJ8y6hiXKYr\nKgM0AODMMxOPab5hkqup1xk+QRFCCCkk3KAIIYQUEm5QhBBCCkkhfVBau/s7pu2Tyu+02LTNSyFD\nFFHv1SHfViVdkzF8VOsNd2oJo4CUTqZQ8Sb1OUVQvplZ5jUtU36niC1d+ZyAmL/ItE8QQFtSiamM\n77Gnmq77CoyfZcQWWRHAruqn+C4jT3aB9js94R8g+Ij9rFm/kx7C1DuU3ynwLZHtPd63D9is8vOO\nq+bnvayPyyuk8DlZiuJzsvAJihBCSCHhBkUIIaSQcIMihBBSSArpg/qGKk8NXHdBhjH6L1jUf6yE\nSW3LN7GcpHwzKwPXHWrPDoX8iZYB8Nc5+OetCvmBLCjLlN/pAnsGUvmjtxqf0+gUY3QYv2Sm1DdJ\nGTIEUNl5BzN8giKEEFJIuEERQggpJMWwKCxb5plXrrfSMTUYHn9JTQZiZ+5A2GRJFCtXeqH3Tz5h\ntcZrkMakl+e9/URQlA9hE7B/P7B1a6U6a7Qy1gWOmKQx6UVohEnPMmQIMHJk48ctIHyCIoQQUki4\nQRFCCCkk3KAIIYQUEnEJ/T11nYTIJgDPDfQ8GkAnfLWjVuQ451zm9JxcEy0F10Q6uCbKFGKDGiyI\nSI9zrnug50GKA9cEsXBNVKGJjxBCSCHhBkUIIaSQcINqLF8f6AmQwsE1QSxcE2XogyKEEFJI+ARF\nCCGkkHCDIoQQUki4QRFCCCkk3KAIIYQUEm5QhBBCCgk3KEIIIYWEGxQhhJBCwg2KEEJIIeEG1Qci\n8hERcSIyvU79HyMiS0TkNRHZKiLfF5FjG3U/SU+R14SI/FF5bvbfq/WYKylRzzUhIkeLyFdE5GER\n2VEeZ1LKPpr+e4LZpvvmNAA7APwu745FZASAnwLYDeByAA7AFwD8TERmOOder+f9pN8Udk0oPgbg\nN6q+L9eJEkvd1gSAKQAuBrAMwAMAzk9zc6t8T3CD6pvTAKxwzu2vQ98fAvAGANOcc2sAQERWAHga\nwJUAbqrz/aR/FHlNHGSVc+6ROsyP9E0918QvnHMTAEBEPoiUGxRa5HuCJj6DiLQDmA7gt3Ua4kIA\njxxcNADgnHsWwIMA3tmA+0lKmmBNkAZT7zXhnDuQsYuWWFPcoKJMBzAMwPK+GqXE0AT/2gL9P9HH\nz1cCOCnh/LLcT9JT9DVxkO+IyH4R2SwiC5vN39Bk1HtN5DG/pv+e4AYV5bTy/30uPADnANib4N/S\nGvePBbClj5+/AmBMgvllvZ+kp+hr4jUAXwbwQQBvBfB5AOcBeFhEjkhwP0lPvddEVlrie4I+qCin\nobRw+vrrAyg5Ld+UoJ9tuc2IDDSFXhPOud/CNzXdLyK/APBrAB8F8Kl6jDvIKfSaaBW4QUU5DcBK\n59yeGu3bATyaoJ9aiba2oO+/YGr9xZP3/SQ9RV8T0YGcWy4iqwG8uT/3k1jqvSay0hLfEzTxKURE\nAJyK2o/tQPZH95Uo2YctJwF4MsE0s95PUtAka4I0kAatiay0xJriE5TP8QBGIRyZk/XR/YcA/kFE\n3uCcewYAygfwzgJwXYJ+s95P0tEMayKCiHQDmAZgSX/uJ0EasSay0hLfE0z5rhCReQC+C+As59xD\ndRrjUACPAdgJ4K9ResT/PEoLfoZzbru69hyU/sJ6v3PuW2nvJ9lpkjXxbQBrUfrC3IqS+ekvUTpE\nOtM511uPeQ9WGrEmyuNcVC7OAXAVgA8D2ARgk3PufnVdy35P8AnK50wAexB+dM+Ec+51EXkrgH8E\n8J8ABKXF9fE+Fo0AaIMyxaa8n2Sn8GsCJXPOpQA+DmAEgA0Avg/gb7g51YW6r4kyi039lvL/9wP4\nI/Xzlv2e4BNUGRE5BMBTAB51zs0d6PmQgYdrgli4JhrLoH+CKp8TmQngzwB0AfjswM6IDDRcE8TC\nNTEwMIqvZBb5DkqmkdnlMyVkcMM1QSxcEwMATXyEEEIKCZ+gCCGEFBJuUIQQQgoJNyhCCCGFhBsU\nIYSQQsINihBCSCHhBkUIIaSQcIMihBBSSP4/vGRWfsOpIDIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d5aef60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "heis = sum([tensor([pauli]*2) for pauli in [sigmax(), sigmay(), sigmaz()]])\n",
    "heis2 = sum([tensor([pauli, qeye(2), pauli]) for pauli in [sigmax(), sigmay(), sigmaz()]])\n",
    "\n",
    "N = 10\n",
    "Js = [0., 0.5, 1.]\n",
    "\n",
    "fig = plt.figure(figsize=(2*len(Js), 4.4))\n",
    "\n",
    "for b in [0, 1]: \n",
    "    for k, J in enumerate(Js):\n",
    "        ax = plt.subplot(2, len(Js), b*len(Js) + k + 1)\n",
    "        \n",
    "        if b == 0:\n",
    "            spinchain = spinchainize([heis, J*heis2], N, bc='periodic')\n",
    "        elif b ==1:\n",
    "            spinchain = spinchainize([heis, J*heis2], N, bc='open')\n",
    "\n",
    "        plot_qubism(gs_of(spinchain), ax=ax)\n",
    "        \n",
    "        if k == 0:\n",
    "            if b == 0:\n",
    "                ax.set_ylabel(\"periodic BC\",\n",
    "                              fontsize=16)\n",
    "            else:\n",
    "                ax.set_ylabel(\"open BC\",\n",
    "                              fontsize=16)\n",
    "        if b == 1:\n",
    "            ax.set_xlabel(\"$J={0:.1f}$\".format(J),\n",
    "                          fontsize=16)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are not restricted to qubits. We can have it for other dimensions, e.g. qutrits.\n",
    "\n",
    "Let us consider [AKLT model](http://en.wikipedia.org/wiki/AKLT_Model) for spin-1 particles:\n",
    "\n",
    "$$H = \\sum_{i=1}^N \\vec{S}_i \\cdot \\vec{S}_{i+1} + \\tfrac{1}{3} \\sum_{i=1}^N (\\vec{S}_i \\cdot \\vec{S}_{i+1})^2.$$\n",
    "\n",
    "where $\\vec{S}_i$ is [spin operator](http://en.wikipedia.org/wiki/Pauli_matrices#Physics) for spin-1 particles (or for `qutip`: `jmat(1, 'x')`, `jmat(1, 'y')` and `jmat(1, 'z')`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO4AAADuCAYAAAA+7jsiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCRcCCRcCPQ/qmL2fMQ7tO4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d59c780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ss = sum([tensor([jmat(1, s)]*2) for s in ['x', 'y', 'z']])\n",
    "H = spinchainize([ss, (1./3.) * ss**2], n=6, bc='periodic')\n",
    "plot_qubism(gs_of(H), figsize=(4,4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Qubism for qutrits works similarly as for qubits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sVOgTsKbT8ePH45e//CX+/ve/Y9++fSgtLcX9998fsdyMGTOwd+9evPbaa1CU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bb2eba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 5))\n",
    "for i in [1, 2]:\n",
    "    ax = plt.subplot(1, 2, i)\n",
    "    plot_qubism(0 * ket('0000', dim=3),\n",
    "                legend_iteration=i, grid_iteration=i,\n",
    "                fig=fig, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just in this case we interpret:\n",
    "\n",
    "* 0 as $s_z=-1$,\n",
    "* 1 as $s_z=\\ \\ 0$,\n",
    "* 2 as $s_z=+1$.\n",
    "\n",
    "While qubism works best for translationally-invariants states (so in particular, all particles need to have the same dimension), we can do it for others.\n",
    "\n",
    "Also, there are a few other Qubism-related plotting schemes. For example `how='pairs_skewed'`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ns7MTXV1dbm1ZWVmKp5LVGMs5ISJlLKYS6+zs9PoB69LSUoNmo7+SkhKvtnfe\neQdCiKD6qamp8Wrz/F1StcZ6TohIGYupxDzfAeXl5Sl+yzVWFRQUIDs7263t7NmzaGhoUN2H0+lE\ndXW1V/vKlStDmtNYzwkRKWMxlZjnZ3Nj8XTiU0895dVWUVGh+ib1L730kte3gOfNm4c77rgjpPkw\nJ0SkhMVUUj///DOamprc2qLh8otwKy8vx4033ujW1tbWhqeffjrg6d7GxkZs2rTJq72ysjKkuTAn\nROQLi6mkPv74YwwPD7seWywW3HrrrQbOyBjjx4/HK6+84tVeVVWFhx9+WPHORk6nE2+99RaWLl2K\nwcFBt22lpaUhX8bCnBCRL9JdZ/rkk09ix44dPrcrnd7bsWOH35/AKiwsxIEDB6Ji/FGen80Z+Q7I\n6DV56KGHUF5ejm3btrm1v//++9i7dy+Ki4uRk5ODlJQUfPfdd6ivr1e8SYPZbMb27dtVjalEppwQ\nkVykK6YDAwPo7+8Pah+n0+l3n8uXL0fN+AAwODiIQ4cOubUZ+dmcDGtSVVWF3t5efPDBB27tg4OD\n+PDDDwPuP3XqVDQ0NIR8P17ZckJEcuFpXgl99tlnbsVm0qRJKCwsNHBGxktISMCuXbvw/PPPK/7W\nqT8LFy6EzWZDTk5OyOMzJ0TkD4uphDxPJxYXFyMhQbqTCLqLj4/Hhg0bcOLECTz66KNITU31+dy4\nuDgUFhZiz549OHz4MKZNm6ZpbOaEiPyR7tWgpqZG8SL7sTK+EAL79+93azP6dKLRa+IpJycH27dv\nR1VVFWw2G9ra2tDT04ORkRGkpqZixowZmDdvnuLPuIVCxpwQkVykK6Zj3bFjx/Djjz+6HicnJ+Oe\ne+4xcEbySkpKwvz58yP+O6LMCREFwtO8kvH8BuyiRYuQkpJi0GwIYE6IKDAWU8nw8gv5MCdEFAiL\nqUROnz6Nb7/91vU4Pj6eN1E3GHNCRGqwmErE8x1QQUEBbrjhBoNmQwBzQkTqsJhKhKcT5TPWclJT\nU4PVq1cbPQ2XOXPm4MiRIyHty1giJ9RYYiUOJSymEmlqaoIQwvX3zDPPGD2lMW+s52Tnzp1YsGAB\nJkyYAIvFovv20tJS1NXVaQ9Eh7kODw+joqICmZmZSE9PR1lZGa5cuWJILIHmIkteIh2HnjlhMSUi\nnyZNmoS1a9di48aNhmwP54tdpOe6efNm1NfX4/jx4+jo6EBXVxcqKipc2/WMJdBcZMlLpOPQMydu\n/+sO9JeEtx+sAAADRUlEQVSfny/8qaysFABcf0VFRX6fT9oxJ3ICYBNBHFt6//n6d1NdXS3Kysq8\n2nfv3i2mT5/uM95IbR8ZGRFTpkwR7e3tPveVJRaz2Sxqa2tdj5uamkRycrIYGBgQQugbS6C5BNo/\n0PZAscgSRzhyovZY5jtTIpJWfHw8SkpKvD67lk1fXx+6u7uRn5/vasvLy4PD4UB7ezsA/WJRMxet\n9IhFaxx654TFlIikVlxcjIMHDxo9Db8uXboEAEhPT3e1mUwmJCUl4eLFi642PWJROxetIh2L1jj0\nzgmLKRFJraurC1lZWUZPw6/RH1249mcH7XY7hoaGkJaW5mrTIxa1c9Eq0rFojUPvnIS1mK5fv97t\nHHJjY2M4u6cQMCcU7erq6qS/UUZGRgbMZjNaW1tdba2trUhOTsbMmTNdbXrEonYuWkU6Fq1x6J0T\nvjMlIp9GRkbgcDjgdDohhIDD4YDD4dBte19fH2w2G5YsWSJ9LOXl5diyZQt++OEH/PTTT3juueew\ncuVKmEwm3WMJNBdZ8hLpOPTMSVi/zUv6Y07khBj5Nm91dbXbt8FH//Ta/u6774ply5b5XWtZYnE6\nnWLdunVi4sSJIjU1VaxatUpcvnzZkFgCzSXSeZEljnDkRO2xzGIa5ZgTOcVKMTXaihUrRFVVld/n\nMBb9BYolVuIQQv2xzNO8RCSt7OzsmPkhdsYin3DGwR8HJyKX3NxcZGRkGD0NlxdffDHkfRlL5IQa\nS6zEoYTFlIhccnNzkZuba/Q0woKxyCdW4lDC07xEREQasZgSERFpxGJKRESkEYspERGRRiymRERE\nGrGYEhERacRiSkREpBGLKRERkUYspkRERBqxmBIREWnEYkpERKQRiykREZFGLKZEREQasZgSERFp\nxGJKRESkEYspERGRRiymREREGsUJIdQ/OS7uAoCuyE2HQnA9gB6jJ0FepgshJhs9CV9i7FiOpWMg\nVmKJlTgAlcdyUMWU5BMXF2cTQliNngeRUWLpGIiVWGIljmDwNC8REZFGLKZEREQasZhGvzeNngCR\nwWLpGIiVWGIlDtX4mSkREZFGfGdKRESkEYspERGRRiymREREGrGYEhERacRiSkREpNH/AzjnMHM4\nXOtFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118195780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 4))\n",
    "for i in [1, 2]:\n",
    "    ax = plt.subplot(1, 2, i)\n",
    "    plot_qubism(0 * ket('0000'),\n",
    "                how='pairs_skewed',\n",
    "                legend_iteration=i, grid_iteration=i,\n",
    "                fig=fig, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The one above emphasis ferromagnetic (put on the left) vs antiferromagnetic (put on the right) states.\n",
    "\n",
    "Another one `how='before_after'` (inspired by [this](http://commons.wikimedia.org/wiki/File:Ising-tartan.png)) works in a bit different way: it uses typical recursion, but starting from middle particles. For example, the top left quadrant correspons to $|00\\rangle_{N/2,N/2+1}$: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9VFVV+bX53gNTq/b2dr+bihcXF+vqi8zBnBCREhbTX+Tl5SEjI8Or7fTp06ir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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d43e470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 4))\n",
    "for i in [1, 2]:\n",
    "    ax = plt.subplot(1, 2, i)\n",
    "    plot_qubism(0 * ket('0000'),\n",
    "                how='before_after',\n",
    "                legend_iteration=i, grid_iteration=i,\n",
    "                fig=fig, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is very similar to the Schmidt plot (for the default splitting), with the only difference being ordering of the `y` axis (particle order is reversed). All entanglement properties are the same.\n",
    "\n",
    "So how does it work on the same example? \n",
    "Well, let us take spin chain for (Majumdar-Ghosh model for $J=0$), i.e.\n",
    "$$H = \\sum_{i=1}^N \\vec{S}_i \\cdot \\vec{S}_{i+1}$$\n",
    "for qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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al5LzWpYu2FqfKukfrk76h2FaaEFaYCrZfldk22/Bdt2vtMBMLz80/D/N7MUd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\nADBXMMAq85ikMztun1GXZeXTeUy3umR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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1181f5dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "heis = sum([tensor([pauli]*2) for pauli in [sigmax(), sigmay(), sigmaz()]])\n",
    "N = 10\n",
    "gs = gs_of(spinchainize(heis, N, bc='periodic'))\n",
    "\n",
    "fig = plt.figure(figsize=(12, 4))\n",
    "for i, how in enumerate(['schmidt_plot', 'pairs', 'pairs_skewed', 'before_after']):\n",
    "    ax = plt.subplot(1, 4, i + 1)\n",
    "    if how == 'schmidt_plot':     \n",
    "        plot_schmidt(gs,\n",
    "                     fig=fig, ax=ax)\n",
    "    else:\n",
    "        plot_qubism(gs,\n",
    "                    how=how,\n",
    "                    fig=fig, ax=ax)\n",
    "    ax.set_title(how)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Seeing entanglement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "product_1 = ket('0000')\n",
    "product_2 = tensor([(ket('0') + ket('1')).unit()]*4)\n",
    "w = (ket('0001') + ket('0010') + ket('0100') + ket('1000')).unit()\n",
    "dicke_2of4 = (ket('0011') + ket('0101') + ket('0110') + ket('1001') + ket('1010') + ket('1100')).unit()\n",
    "ghz = (ket('0000') + ket('1111')).unit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bb97cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "states = ['product_1', 'product_2', 'w', 'dicke_2of4', 'ghz']\n",
    "fig = plt.figure(figsize=(2 * len(states), 2))\n",
    "for i, state_str in enumerate(states):\n",
    "    ax = plt.subplot(1, len(states), i + 1)\n",
    "    plot_qubism(eval(state_str), fig=fig, ax=ax)\n",
    "    ax.set_title(state_str)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then entanglement (or exactly: Schmidt rank) for a given partition is equal to number to different, non-zero squares. (We don't allow rotations, we do allow multiplication by a factor and, what may be more tricky, linear superposition.)\n",
    "\n",
    "Here we use partition of first 2 particles vs last 2, as indicated by lines.\n",
    "\n",
    "That is,\n",
    "* `product_1` - only 1 non-zero square: Schmidt rank 1,\n",
    "* `product_2` - 4 non-zero squares, but they are the same: Schmidt rank 1,\n",
    "* `w` - 3 non-zero quares, but two of them are the same: Schmidt rank 2,\n",
    "* `dicke_2of4` - 4 non-zero squares, but two of them are the same: Schmidt rank 3,\n",
    "* `ghz` - 2 non-zero squares, each one different: Schmidt rank 2.\n",
    "\n",
    "This is basis-independent, but it may be easier to work in one basis rather than another.\n",
    "\n",
    "And for a comparision, let us see product states:\n",
    "\n",
    "$$\\left( \\cos(\\theta/2) |0\\rangle + \\sin(\\theta/2) e^{i \\varphi} |1\\rangle \\right)^N $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IiAy2WZOUuz8DPLMfxiIiItKhlwKzIiIyR6rcUwktkoiNN1dLt+usOHGhmb2/rngiIiJ1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\nUiIikqz/D/7nGQ4Zm5bDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d7dee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def product_state(theta, phi=0, n=1):\n",
    "    single = Qobj([[np.cos(theta/2.)], [np.sin(theta/2.) * np.exp(1j*phi)]])\n",
    "    return tensor([single]*n)\n",
    "\n",
    "thetas = 0.5 * np.pi * np.array([0., 0.5, 0.75, 1.])\n",
    "phis = np.pi * np.array([0., 0.1, 0.2, 0.3])\n",
    "\n",
    "fig, axes2d = plt.subplots(nrows=len(phis), ncols=len(thetas),\n",
    "                           figsize=(6,6))\n",
    "\n",
    "for i, row in enumerate(axes2d):\n",
    "    for j, cell in enumerate(row):\n",
    "        plot_qubism(product_state(thetas[j], phi=phis[i], n=8),\n",
    "                    grid_iteration=1,\n",
    "                    ax=cell)\n",
    "        if i == len(axes2d) - 1:\n",
    "            cell.set_xlabel(\"$\\\\theta={0:s}\\pi$\".format([\"0\", \"(1/4)\", \"(3/8)\", \"(1/2)\"][j]),\n",
    "                            fontsize=16)\n",
    "        if j == 0:\n",
    "            cell.set_ylabel(\"$\\\\varphi={0:.1f}\\pi$\".format(phis[i] / np.pi),\n",
    "                            fontsize=16)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In each plot squares are the same, up to a factor (which is visualized as intensity and hue).\n",
    "\n",
    "You can lookup previous plots. Setting `grid_iteration=2` would show splitting of the first 4 particles vs N-4 others.\n",
    "And for `how='before_after'` it is the middle particles vs all others."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Versions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>QuTiP</td><td>4.3.0.dev0+6e5b1d43</td></tr><tr><td>Numpy</td><td>1.13.1</td></tr><tr><td>SciPy</td><td>0.19.1</td></tr><tr><td>matplotlib</td><td>2.0.2</td></tr><tr><td>Cython</td><td>0.25.2</td></tr><tr><td>Number of CPUs</td><td>2</td></tr><tr><td>BLAS Info</td><td>INTEL MKL</td></tr><tr><td>IPython</td><td>6.1.0</td></tr><tr><td>Python</td><td>3.6.2 |Anaconda custom (x86_64)| (default, Jul 20 2017, 13:14:59) \n",
       "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td colspan='2'>Thu Jul 20 22:29:31 2017 MDT</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qutip.ipynbtools import version_table\n",
    "version_table()"
   ]
  }
 ],
 "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}