timeC20.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Qutip imports 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:46.074347Z",
     "start_time": "2019-01-22T13:37:44.795185Z"
    }
   },
   "outputs": [],
   "source": [
    "from qutip.operators import sigmax, sigmay, sigmaz, identity\n",
    "# position, momentum, num, create, destroy, commutator, qeye \n",
    "from qutip.tensor import tensor\n",
    "from qutip.qip.gates import swap, rx, ry, rz\n",
    "from qutip.qobj import Qobj\n",
    "from qutip.visualization import hinton\n",
    "from qutip.visualization import matrix_histogram_complex, matrix_histogram\n",
    "from qutip.random_objects import rand_herm, rand_unitary, rand_dm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Numpy imports "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:47.764209Z",
     "start_time": "2019-01-22T13:37:47.760790Z"
    }
   },
   "outputs": [],
   "source": [
    "from numpy import sin, cos, tan, real, imag,  log, conj\n",
    "from numpy import array, append, linspace, arange\n",
    "from numpy import add, sqrt, abs, dot\n",
    "from numpy.random import random, random_sample, random\n",
    "from numpy import concatenate, trace\n",
    "from numpy import ones, zeros, ones_like, zeros_like\n",
    "from numpy import amax, amin, nanmax, nanmin\n",
    "# from numpy import pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "## Scipy imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:48.037524Z",
     "start_time": "2019-01-22T13:37:48.034212Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import ode, odeint, complex_ode\n",
    "from scipy.optimize import minimize\n",
    "from scipy.linalg import eigh, inv, norm, expm\n",
    "# from scipy.linalg import \n",
    "# from scipy import"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matplotlib imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:48.341711Z",
     "start_time": "2019-01-22T13:37:48.336768Z"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import plot, figure, show, savefig, axes\n",
    "from matplotlib.pyplot import xlabel, ylabel, title, legend\n",
    "from matplotlib import rcParams\n",
    "from matplotlib.pyplot import style \n",
    "from matplotlib.pyplot import xlim, ylim, axis \n",
    "# beware not same as axes\n",
    "from matplotlib.pyplot import subplot, subplots, text\n",
    "from matplotlib.pyplot import GridSpec\n",
    "\n",
    "\n",
    "\n",
    "pgf_with_rc_fonts = {\"pgf.texsystem\": \"pdflatex\"}\n",
    "rcParams.update(pgf_with_rc_fonts)\n",
    "style.use('seaborn-whitegrid')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Math imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:48.776873Z",
     "start_time": "2019-01-22T13:37:48.773867Z"
    }
   },
   "outputs": [],
   "source": [
    "from math import pi\n",
    "from math import exp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cmath imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Date and datetime imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:49.370359Z",
     "start_time": "2019-01-22T13:37:49.367281Z"
    }
   },
   "outputs": [],
   "source": [
    "from datetime import date\n",
    "from datetime import datetime# now\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Os imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:49.558279Z",
     "start_time": "2019-01-22T13:37:49.554611Z"
    }
   },
   "outputs": [],
   "source": [
    "from os import getcwd, mkdir, chdir\n",
    "from os.path import abspath, join \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sympy imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:50.773306Z",
     "start_time": "2019-01-22T13:37:50.184758Z"
    }
   },
   "outputs": [],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, symbols\n",
    "# x, y, z, t = symbols('x y z t')\n",
    "# k, m, n = symbols('k m n', integer=True)\n",
    "# f, g, h = symbols('f g h', cls=Function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Miscellaneous imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extra useful functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:51.150673Z",
     "start_time": "2019-01-22T13:37:51.145812Z"
    }
   },
   "outputs": [],
   "source": [
    "def rint(x):\n",
    "    print(\"x = \", x)\n",
    "    return None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building parts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:51.781578Z",
     "start_time": "2019-01-22T13:37:51.715411Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'omega_1' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-3e38f81848f0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mdel\u001b[0m \u001b[0momega_1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtotal_time\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0momega_1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mtotal_time\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mpi\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0momega_1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mepsilon\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mmax_iter\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'omega_1' is not defined"
     ]
    }
   ],
   "source": [
    " del omega_1, total_time, epsilon, \n",
    "omega_1 = 0.5\n",
    "total_time = 2*pi/omega_1\n",
    "epsilon = 10**(-6)\n",
    "max_iter = 100\n",
    "time_steps = 200\n",
    "dt = total_time/time_steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:52.012267Z",
     "start_time": "2019-01-22T13:37:51.999928Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'Lin' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-11-e6d48350e5b4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mdel\u001b[0m \u001b[0mLin\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mTi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'Lin' is not defined"
     ]
    }
   ],
   "source": [
    "del Lin, Ti"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:52.289099Z",
     "start_time": "2019-01-22T13:37:52.275282Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'Lin' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-12-3ce5abe2615e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mLin\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'Lin' is not defined"
     ]
    }
   ],
   "source": [
    "Lin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## level 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:52.977987Z",
     "start_time": "2019-01-22T13:37:52.975010Z"
    }
   },
   "outputs": [],
   "source": [
    "def H1(omega_1):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    H1 = omega_1*sigmaz()\n",
    "    return H1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:53.285447Z",
     "start_time": "2019-01-22T13:37:53.278945Z"
    }
   },
   "outputs": [],
   "source": [
    "def H2():\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    H2 = sigmay()\n",
    "    return H2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:53.598280Z",
     "start_time": "2019-01-22T13:37:53.587366Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'I' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-7d62117bf249>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#I = identity(2)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mdel\u001b[0m \u001b[0mI\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'I' is not defined"
     ]
    }
   ],
   "source": [
    "#I = identity(2)\n",
    "del I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:54.110076Z",
     "start_time": "2019-01-22T13:37:54.107172Z"
    }
   },
   "outputs": [],
   "source": [
    "def T_maker(Ti):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    T = tensor(Ti.trans(), Ti)\n",
    "    return T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:54.441502Z",
     "start_time": "2019-01-22T13:37:54.426018Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = (8, 8), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0. 0. 0. 1. 0. 0. 0. 0.]\n",
       " [0. 0. 1. 0. 0. 0. 0. 0.]\n",
       " [0. 1. 0. 0. 0. 0. 0. 0.]\n",
       " [1. 0. 0. 0. 0. 0. 0. 0.]\n",
       " [0. 0. 0. 0. 0. 0. 0. 1.]\n",
       " [0. 0. 0. 0. 0. 0. 1. 0.]\n",
       " [0. 0. 0. 0. 0. 1. 0. 0.]\n",
       " [0. 0. 0. 0. 1. 0. 0. 0.]]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " tensor(identity(2), T_maker(sigmax()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## level 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:55.244223Z",
     "start_time": "2019-01-22T13:37:55.239372Z"
    }
   },
   "outputs": [],
   "source": [
    "def Hamil(omega_1, xi):\n",
    "    H = H1(omega_1) + xi*H2()\n",
    "    return H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:55.723262Z",
     "start_time": "2019-01-22T13:37:55.712113Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}2.0 & -0.500j\\\\0.500j & -2.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 2.+0.j   0.-0.5j]\n",
       " [ 0.+0.5j -2.+0.j ]]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamil(2, 0.5 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:56.204974Z",
     "start_time": "2019-01-22T13:37:56.196124Z"
    }
   },
   "outputs": [],
   "source": [
    "def leftover(Lin):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    d = Lin.shape[0]\n",
    "    I = identity(d)\n",
    "    term1 = tensor(Lin.trans(), Lin)\n",
    "    term2 = tensor(I, ((Lin.dag())*(Lin)))\n",
    "    term3 = tensor(((Lin.trans())*(Lin.conj())), I)\n",
    "    leftover = 1j*(0.1)*(term1 - 0.5*(term2 + term3))\n",
    "    return leftover\n",
    "\n",
    "\n",
    "def A(omega_1, xi, Lin):\n",
    "    H = Hamil(omega_1, xi)\n",
    "    d = Lin.shape[0]\n",
    "    I = identity(d)\n",
    "    A = tensor(I, H) - tensor((H.conj()), I) + leftover(Lin)\n",
    "    return A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:56.591204Z",
     "start_time": "2019-01-22T13:37:56.576873Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -0.500j & -0.500j & 0.0\\\\0.500j & (-4.0-0.200j) & 0.0 & -0.500j\\\\0.500j & 0.0 & (4.0-0.200j) & -0.500j\\\\0.0 & 0.500j & 0.500j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[ 0.+0.j   0.-0.5j  0.-0.5j  0.+0.j ]\n",
       " [ 0.+0.5j -4.-0.2j  0.+0.j   0.-0.5j]\n",
       " [ 0.+0.5j  0.+0.j   4.-0.2j  0.-0.5j]\n",
       " [ 0.+0.j   0.+0.5j  0.+0.5j  0.+0.j ]]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A(2, 0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:56.940986Z",
     "start_time": "2019-01-22T13:37:56.925352Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -0.500j & -0.500j & 0.0\\\\0.500j & -0.200j & 0.0 & -0.500j\\\\0.500j & 0.0 & -0.200j & -0.500j\\\\0.0 & 0.500j & 0.500j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[0.+0.j  0.-0.5j 0.-0.5j 0.+0.j ]\n",
       " [0.+0.5j 0.-0.2j 0.+0.j  0.-0.5j]\n",
       " [0.+0.5j 0.+0.j  0.-0.2j 0.-0.5j]\n",
       " [0.+0.j  0.+0.5j 0.+0.5j 0.+0.j ]]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A(0, 0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:57.264018Z",
     "start_time": "2019-01-22T13:37:57.253762Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'I' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-23-bde71cc9b50e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mI\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'I' is not defined"
     ]
    }
   ],
   "source": [
    "I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:57.563333Z",
     "start_time": "2019-01-22T13:37:57.559175Z"
    },
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "#term1 = tensor(Lin.trans(), Lin)\n",
    "#term2 = tensor(I, ((Lin.dag())*(Lin)))\n",
    "#term3 = tensor(((Lin.trans())*(Lin.conj())), I)\n",
    "#leftover = 1j*(0.1)*(term1 - 0.5*(term2 + term2))\n",
    "def x_k(omega_1, Lin ):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    #H11 = H1(omega_1)\n",
    "    #H2_i = H2()\n",
    "    d = Lin.shape[0]\n",
    "    I = identity(d)\n",
    "    x_k = tensor(I, H2()) - tensor((H2().conj()), I) #+ leftover(Lin)\n",
    "    return x_k\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:58.145220Z",
     "start_time": "2019-01-22T13:37:58.135129Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'I' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-25-bde71cc9b50e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mI\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'I' is not defined"
     ]
    }
   ],
   "source": [
    "I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:58.626051Z",
     "start_time": "2019-01-22T13:37:58.612066Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -1.0j & -1.0j & 0.0\\\\1.0j & 0.0 & 0.0 & -1.0j\\\\1.0j & 0.0 & 0.0 & -1.0j\\\\0.0 & 1.0j & 1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0.+0.j 0.-1.j 0.-1.j 0.+0.j]\n",
       " [0.+1.j 0.+0.j 0.+0.j 0.-1.j]\n",
       " [0.+1.j 0.+0.j 0.+0.j 0.-1.j]\n",
       " [0.+0.j 0.+1.j 0.+1.j 0.+0.j]]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_k(0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:37:59.156774Z",
     "start_time": "2019-01-22T13:37:59.149522Z"
    }
   },
   "outputs": [],
   "source": [
    "def L(omega_1, xi, Lin, dt):\n",
    "    #H = H1\n",
    "    L = (-1j*A(omega_1, xi, Lin)*dt).expm()\n",
    "    return L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:00.207777Z",
     "start_time": "2019-01-22T13:37:59.995594Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}1.000 & (-0.002-9.999\\times10^{-07}j) & (-0.002+9.999\\times10^{-07}j) & 4.000\\times10^{-06}\\\\(0.002+9.999\\times10^{-07}j) & (1.000+9.998\\times10^{-04}j) & -3.999\\times10^{-06} & (-0.002-9.999\\times10^{-07}j)\\\\(0.002-9.999\\times10^{-07}j) & -3.999\\times10^{-06} & (1.000-9.998\\times10^{-04}j) & (-0.002+9.999\\times10^{-07}j)\\\\4.000\\times10^{-06} & (0.002+9.999\\times10^{-07}j) & (0.002-9.999\\times10^{-07}j) & 1.000\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[ 9.99996000e-01+0.00000000e+00j -1.99979435e-03-9.99865260e-07j\n",
       "  -1.99979435e-03+9.99865260e-07j  3.99972768e-06+0.00000000e+00j]\n",
       " [ 1.99979435e-03+9.99865260e-07j  9.99795521e-01+9.99797187e-04j\n",
       "  -3.99946104e-06+0.00000000e+00j -1.99979435e-03-9.99865260e-07j]\n",
       " [ 1.99979435e-03-9.99865260e-07j -3.99946104e-06+0.00000000e+00j\n",
       "   9.99795521e-01-9.99797187e-04j -1.99979435e-03+9.99865260e-07j]\n",
       " [ 3.99972768e-06+0.00000000e+00j  1.99979435e-03+9.99865260e-07j\n",
       "   1.99979435e-03-9.99865260e-07j  9.99996000e-01+0.00000000e+00j]]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L(0.5, 2, sigmaz(), 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:01.869448Z",
     "start_time": "2019-01-22T13:38:01.863554Z"
    }
   },
   "outputs": [],
   "source": [
    "def L_I(Ti):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    d = Ti.shape[0]\n",
    "    I = identity(d)\n",
    "    L_I = tensor(I, I)\n",
    "    return L_I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:02.448603Z",
     "start_time": "2019-01-22T13:38:02.436567Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[1. 0. 0. 0.]\n",
       " [0. 1. 0. 0.]\n",
       " [0. 0. 1. 0.]\n",
       " [0. 0. 0. 1.]]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_I(sigmay())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sub sub topic 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:03.690332Z",
     "start_time": "2019-01-22T13:38:03.687167Z"
    }
   },
   "outputs": [],
   "source": [
    "# building the function to optimize (optimizee)\n",
    "def L_vec(omega_1, xi_vec, Lin, dt):\n",
    "    #xi_vec_size = 2#xi_vec.size # finding the size of xi\n",
    "    L_vec = [L(omega_1, xi, Lin, dt) for xi in xi_vec] \n",
    "    # constructing L #[L(1.0), L(2.0)]\n",
    "    \n",
    "    return L_vec\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:04.320263Z",
     "start_time": "2019-01-22T13:38:04.316621Z"
    }
   },
   "outputs": [],
   "source": [
    "def fidelity_calc(A, B):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    d1 = A.shape[0] # Assuming no rectangular shaped matrices\n",
    "    d2 = B.shape[0] # Assuming no rectangular shaped matrices\n",
    "    d = d1*d2\n",
    "    first_part = (A - B).dag()\n",
    "    second_part = (A - B)\n",
    "    f_int = (first_part* second_part)\n",
    "    f = f_int.tr()\n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:06.410926Z",
     "start_time": "2019-01-22T13:38:06.405650Z"
    }
   },
   "outputs": [],
   "source": [
    "def L_full_maker(Ti, omega_1, xi_vec, Lin, dt):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    xi_vec_size = xi_vec.size # finding the size of xi\n",
    "    L_full = L_I(Ti) # Identity for the for loop of L\n",
    "    L_v = L_vec(omega_1, xi_vec, Lin, dt) # calling L_vec\n",
    "    for i in range(xi_vec_size): # generating L_full\n",
    "        L_full = L_full*L_v[xi_vec_size - 1 - i]\n",
    "    return L_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:06.982922Z",
     "start_time": "2019-01-22T13:38:06.979043Z"
    }
   },
   "outputs": [],
   "source": [
    "def F(Ti, omega_1, xi_vec, Lin, dt):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    L_full = L_full_maker(Ti, omega_1, xi_vec, Lin, dt)\n",
    "    T = T_maker(Ti)\n",
    "    F = real(-fidelity_calc(T, L_full))   \n",
    "    return F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:08.154264Z",
     "start_time": "2019-01-22T13:38:08.147647Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fidelity_calc(sigmax(), sigmay())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:08.699118Z",
     "start_time": "2019-01-22T13:38:08.686685Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fidelity_calc(sigmay(), sigmay())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:09.348078Z",
     "start_time": "2019-01-22T13:38:09.340575Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2.])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xi_vec_test = array([1.0, 2.0])\n",
    "xi_vec_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:10.184637Z",
     "start_time": "2019-01-22T13:38:10.179945Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xi_vec_test.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:10.755860Z",
     "start_time": "2019-01-22T13:38:10.750124Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 4.0]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_vec = [xi**2 for xi in xi_vec_test]\n",
    "w_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:11.982520Z",
     "start_time": "2019-01-22T13:38:11.964081Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7.998400634493139"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# F(Ti, omega_1, xi_vec, Lin, dt)\n",
    "F(sigmax(), 0.5 , xi_vec_test, sigmaz(), 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:14.684164Z",
     "start_time": "2019-01-22T13:38:14.679485Z"
    }
   },
   "outputs": [],
   "source": [
    "def L_comma_k_maker(Ti, omega_1, xi_vec, k, Lin, dt):\n",
    "    N = xi_vec.size\n",
    "    L_v = L_vec(omega_1, xi_vec, Lin, dt)\n",
    "    \n",
    "    inner_part = L_I(Ti)\n",
    "    for i in range(N):\n",
    "        if i == ( N - 1 - k ):\n",
    "            inner_part = inner_part*x_k(omega_1, Lin )*L_v[k - 1]\n",
    "        else:\n",
    "            inner_part = inner_part*L_v[N - 1 - i]\n",
    "    l_comma_k = inner_part\n",
    "    return l_comma_k\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:15.274129Z",
     "start_time": "2019-01-22T13:38:15.255382Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}1.000 & (-0.003-3.499\\times10^{-06}j) & (-0.003+3.499\\times10^{-06}j) & 8.999\\times10^{-06}\\\\(0.003+2.499\\times10^{-06}j) & (1.000+0.002j) & (-8.998\\times10^{-06}+2.999\\times10^{-09}j) & (-0.003-2.499\\times10^{-06}j)\\\\(0.003-2.499\\times10^{-06}j) & (-8.998\\times10^{-06}-2.999\\times10^{-09}j) & (1.000-0.002j) & (-0.003+2.499\\times10^{-06}j)\\\\8.999\\times10^{-06} & (0.003+3.499\\times10^{-06}j) & (0.003-3.499\\times10^{-06}j) & 1.000\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[ 9.99991001e-01+0.00000000e+00j -2.99927960e-03-3.49898670e-06j\n",
       "  -2.99927960e-03+3.49898670e-06j  8.99883703e-06+0.00000000e+00j]\n",
       " [ 2.99948056e-03+2.49939255e-06j  9.99589083e-01+1.99918650e-03j\n",
       "  -8.99750347e-06+2.99899242e-09j -2.99948056e-03-2.49939255e-06j]\n",
       " [ 2.99948056e-03-2.49939255e-06j -8.99750347e-06-2.99899242e-09j\n",
       "   9.99589083e-01-1.99918650e-03j -2.99948056e-03+2.49939255e-06j]\n",
       " [ 8.99883703e-06+0.00000000e+00j  2.99927960e-03+3.49898670e-06j\n",
       "   2.99927960e-03-3.49898670e-06j  9.99991001e-01+0.00000000e+00j]]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#L_comma_k_maker(Ti, omega_1, xi_vec, k, Lin, dt)\n",
    "L_comma_k_maker(sigmax(), 0.5 , xi_vec_test, 2, sigmaz(), 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:15.832772Z",
     "start_time": "2019-01-22T13:38:15.824211Z"
    }
   },
   "outputs": [],
   "source": [
    "def updater(Ti, omega_1, xi_vec, Lin, dt):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    xi_vec_size = xi_vec.size # finding the size of xi\n",
    "    T = T_maker(Ti)\n",
    "    L_full = L_full_maker(Ti, omega_1, xi_vec, Lin, dt)\n",
    "    di = []\n",
    "    for k in range(xi_vec_size):\n",
    "        L_comma_k = L_comma_k_maker(Ti, omega_1, xi_vec, k, Lin, dt)\n",
    "        differentiated = T - L_comma_k\n",
    "        plain = T - L_full\n",
    "        c = differentiated.dag()*plain\n",
    "        d = plain.dag()*differentiated\n",
    "        inside = c.tr() + d.tr()\n",
    "        di.append(epsilon*inside)\n",
    "\n",
    "    diff = array(di)\n",
    "    xi_new_vec = xi_vec + diff\n",
    "    return diff, xi_new_vec\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:16.512243Z",
     "start_time": "2019-01-22T13:38:16.471832Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'epsilon' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-44-8fffc312f438>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#  updater(Ti, omega_1, xi_vec, Lin, dt)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mupdater\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msigmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.5\u001b[0m \u001b[0;34m,\u001b[0m \u001b[0mxi_vec_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msigmaz\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.001\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-43-4b39b877af56>\u001b[0m in \u001b[0;36mupdater\u001b[0;34m(Ti, omega_1, xi_vec, Lin, dt)\u001b[0m\n\u001b[1;32m     12\u001b[0m         \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplain\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mdifferentiated\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m         \u001b[0minside\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m         \u001b[0mdi\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mepsilon\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0minside\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m     \u001b[0mdiff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'epsilon' is not defined"
     ]
    }
   ],
   "source": [
    "#  updater(Ti, omega_1, xi_vec, Lin, dt)\n",
    "updater(sigmax(), 0.5 , xi_vec_test, sigmaz(), 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:17.150437Z",
     "start_time": "2019-01-22T13:38:17.143983Z"
    },
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "def terminator(max_iter, time_steps, Ti, omega_1, Lin, total_time):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    \n",
    "    xi_initial =  1000*random_sample((time_steps,))\n",
    "    dt = total_time/time_steps\n",
    "    xi_diff, xi_new_vec = updater(Ti, omega_1, xi_initial, Lin, dt)\n",
    "    \n",
    "    #xi_diff = xi_new_vec - xi_initial\n",
    "    for i in range(max_iter):\n",
    "        if amax(xi_diff) < epsilon**2 :\n",
    "            xi_final = xi_new_vec\n",
    "            break\n",
    "        else :\n",
    "            xi_diff, xi_new_vec = updater(Ti, omega_1, xi_new_vec, Lin, dt)\n",
    "            print(i)\n",
    "            print(amax(xi_diff))\n",
    "            \n",
    "        \n",
    "    xi_final = xi_new_vec    \n",
    "    return xi_final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:47.269251Z",
     "start_time": "2019-01-22T13:38:47.266263Z"
    }
   },
   "outputs": [],
   "source": [
    "omega_1 = 0.5\n",
    "total_time = 10*pi/omega_1\n",
    "epsilon = 10**(-6)\n",
    "max_iter = 100#50#20\n",
    "time_steps = 20\n",
    "dt = total_time/time_steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:47.753803Z",
     "start_time": "2019-01-22T13:38:47.749453Z"
    }
   },
   "outputs": [],
   "source": [
    "Lin = sigmaz() # Lindbladian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:38:48.236434Z",
     "start_time": "2019-01-22T13:38:48.227861Z"
    }
   },
   "outputs": [],
   "source": [
    "Ti = sigmax() # Target unitary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:41:16.589590Z",
     "start_time": "2019-01-22T13:38:50.390304Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    },
    {
     "data": {
      "text/plain": [
       "array([314.31405429+0.j, 156.48348865+0.j, 234.76318357+0.j,\n",
       "       627.39627954+0.j, 817.31170092+0.j, 705.07224648+0.j,\n",
       "       391.34386214+0.j,  26.95167144+0.j, 708.73079833+0.j,\n",
       "       151.05307941+0.j, 538.8196842 +0.j, 901.11570264+0.j,\n",
       "       799.17968458+0.j, 885.19737833+0.j, 579.58529298+0.j,\n",
       "       422.75061263+0.j, 553.12980655+0.j, 845.71322167+0.j,\n",
       "         4.58905801+0.j, 740.01983051+0.j])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# terminator(20, 20, Ti, omega_1, Lin, total_time)\n",
    "xi_opt = terminator(max_iter, time_steps, Ti, omega_1, Lin, total_time)\n",
    "xi_opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:41:16.676637Z",
     "start_time": "2019-01-22T13:41:16.592030Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.000020046642919"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F(Ti, omega_1, xi_opt, Lin, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:41:16.685526Z",
     "start_time": "2019-01-22T13:41:16.679147Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:41:16.695343Z",
     "start_time": "2019-01-22T13:41:16.687803Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 1.0\\\\0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0. 0. 0. 1.]\n",
       " [0. 0. 1. 0.]\n",
       " [0. 1. 0. 0.]\n",
       " [1. 0. 0. 0.]]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = T_maker(Ti)\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:41:16.801978Z",
     "start_time": "2019-01-22T13:41:16.697517Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.499 & (3.274\\times10^{-04}-2.192\\times10^{-06}j) & (3.274\\times10^{-04}+2.192\\times10^{-06}j) & 0.501\\\\(-3.271\\times10^{-04}+1.195\\times10^{-04}j) & (-8.609\\times10^{-04}+6.277\\times10^{-06}j) & (-8.640\\times10^{-04}+5.547\\times10^{-06}j) & (3.271\\times10^{-04}-1.195\\times10^{-04}j)\\\\(-3.271\\times10^{-04}-1.195\\times10^{-04}j) & (-8.640\\times10^{-04}-5.547\\times10^{-06}j) & (-8.609\\times10^{-04}-6.277\\times10^{-06}j) & (3.271\\times10^{-04}+1.195\\times10^{-04}j)\\\\0.501 & (-3.274\\times10^{-04}+2.192\\times10^{-06}j) & (-3.274\\times10^{-04}-2.192\\times10^{-06}j) & 0.499\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[ 4.99139330e-01+0.00000000e+00j  3.27396686e-04-2.19191563e-06j\n",
       "   3.27396686e-04+2.19191563e-06j  5.00860670e-01+0.00000000e+00j]\n",
       " [-3.27083095e-04+1.19493524e-04j -8.60872673e-04+6.27657844e-06j\n",
       "  -8.63968409e-04+5.54705049e-06j  3.27083095e-04-1.19493524e-04j]\n",
       " [-3.27083095e-04-1.19493524e-04j -8.63968409e-04-5.54705049e-06j\n",
       "  -8.60872673e-04-6.27657844e-06j  3.27083095e-04+1.19493524e-04j]\n",
       " [ 5.00860670e-01+0.00000000e+00j -3.27396686e-04+2.19191563e-06j\n",
       "  -3.27396686e-04-2.19191563e-06j  4.99139330e-01+0.00000000e+00j]]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_full_maker(Ti, omega_1, xi_opt, Lin, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:41:17.336143Z",
     "start_time": "2019-01-22T13:41:16.804240Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 576x432 with 2 Axes>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x10f5fc320>)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hinton(L_full_maker(Ti, omega_1, xi_opt, Lin, dt))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.268631Z",
     "start_time": "2019-01-22T12:54:09.260823Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.31350478e-05"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.31350478e-05 # 40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.282435Z",
     "start_time": "2019-01-22T12:54:09.275593Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.31390107e-05"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.31390107e-05 # 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.289486Z",
     "start_time": "2019-01-22T12:54:09.286073Z"
    }
   },
   "outputs": [],
   "source": [
    "α = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.304573Z",
     "start_time": "2019-01-22T12:54:09.292309Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'random_sample' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-e03955631bdf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnew_array\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrandom_sample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'random_sample' is not defined"
     ]
    }
   ],
   "source": [
    "new_array = random_sample((4,3,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.305812Z",
     "start_time": "2019-01-22T12:54:09.273Z"
    }
   },
   "outputs": [],
   "source": [
    "new_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.307248Z",
     "start_time": "2019-01-22T12:54:09.276Z"
    }
   },
   "outputs": [],
   "source": [
    "new_array.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.313592Z",
     "start_time": "2019-01-22T12:54:09.279Z"
    }
   },
   "outputs": [],
   "source": [
    "new_array[0] = 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.322354Z",
     "start_time": "2019-01-22T12:54:09.284Z"
    }
   },
   "outputs": [],
   "source": [
    "new_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.323425Z",
     "start_time": "2019-01-22T12:54:09.287Z"
    }
   },
   "outputs": [],
   "source": [
    "new_array.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.324600Z",
     "start_time": "2019-01-22T12:54:09.290Z"
    }
   },
   "outputs": [],
   "source": [
    "new_array.all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.329873Z",
     "start_time": "2019-01-22T12:54:09.292Z"
    }
   },
   "outputs": [],
   "source": [
    "max(new_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.339003Z",
     "start_time": "2019-01-22T12:54:09.295Z"
    }
   },
   "outputs": [],
   "source": [
    "max(new_array, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.340362Z",
     "start_time": "2019-01-22T12:54:09.301Z"
    }
   },
   "outputs": [],
   "source": [
    "from numpy import amax "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T12:54:09.342531Z",
     "start_time": "2019-01-22T12:54:09.305Z"
    }
   },
   "outputs": [],
   "source": [
    "amax(new_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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