C20-Copy1.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": "2019-01-22T14:50:30.552413Z",
     "start_time": "2019-01-22T14:50:29.492630Z"
    }
   },
   "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": "2019-01-22T14:50:30.598471Z",
     "start_time": "2019-01-22T14:50:30.593667Z"
    }
   },
   "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": "2019-01-22T14:50:31.410887Z",
     "start_time": "2019-01-22T14:50:31.407765Z"
    }
   },
   "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": "2019-01-22T14:50:32.111532Z",
     "start_time": "2019-01-22T14:50:32.107644Z"
    }
   },
   "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": "2019-01-22T14:50:33.278282Z",
     "start_time": "2019-01-22T14:50:33.270947Z"
    }
   },
   "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": "2019-01-22T14:50:34.781212Z",
     "start_time": "2019-01-22T14:50:34.776110Z"
    }
   },
   "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": "2019-01-22T14:50:35.398829Z",
     "start_time": "2019-01-22T14:50:35.395854Z"
    }
   },
   "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": "2019-01-22T14:50:36.567045Z",
     "start_time": "2019-01-22T14:50:36.060307Z"
    }
   },
   "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": "2019-01-22T14:50:37.782369Z",
     "start_time": "2019-01-22T14:50:37.774002Z"
    }
   },
   "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": "2019-01-22T14:50:38.485916Z",
     "start_time": "2019-01-22T14:50:38.408001Z"
    }
   },
   "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": "2019-01-22T14:50:38.753289Z",
     "start_time": "2019-01-22T14:50:38.739026Z"
    }
   },
   "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": "2019-01-22T14:50:39.516319Z",
     "start_time": "2019-01-22T14:50:39.503810Z"
    }
   },
   "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": "2019-01-22T14:50:40.264900Z",
     "start_time": "2019-01-22T14:50:40.259556Z"
    }
   },
   "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": "2019-01-22T14:50:40.619361Z",
     "start_time": "2019-01-22T14:50:40.614735Z"
    }
   },
   "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": "2019-01-22T14:50:40.970169Z",
     "start_time": "2019-01-22T14:50:40.955761Z"
    }
   },
   "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": "2019-01-22T14:50:41.299386Z",
     "start_time": "2019-01-22T14:50:41.291556Z"
    }
   },
   "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": "2019-01-22T14:50:41.629839Z",
     "start_time": "2019-01-22T14:50:41.614418Z"
    }
   },
   "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": "2019-01-22T14:50:42.319354Z",
     "start_time": "2019-01-22T14:50:42.315783Z"
    }
   },
   "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": "2019-01-22T14:50:42.853576Z",
     "start_time": "2019-01-22T14:50:42.840313Z"
    }
   },
   "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": "2019-01-22T14:50:43.214525Z",
     "start_time": "2019-01-22T14:50:43.205266Z"
    }
   },
   "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": "2019-01-22T14:50:43.590797Z",
     "start_time": "2019-01-22T14:50:43.573070Z"
    }
   },
   "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": "2019-01-22T14:50:44.052528Z",
     "start_time": "2019-01-22T14:50:44.038460Z"
    }
   },
   "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": "2019-01-22T14:50:44.512042Z",
     "start_time": "2019-01-22T14:50:44.499687Z"
    }
   },
   "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": "2019-01-22T14:50:44.998306Z",
     "start_time": "2019-01-22T14:50:44.991886Z"
    },
    "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": "2019-01-22T14:50:45.350484Z",
     "start_time": "2019-01-22T14:50:45.334741Z"
    }
   },
   "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": "2019-01-22T14:50:45.791697Z",
     "start_time": "2019-01-22T14:50:45.777223Z"
    }
   },
   "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": "2019-01-22T14:50:46.155907Z",
     "start_time": "2019-01-22T14:50:46.151842Z"
    }
   },
   "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": "2019-01-22T14:50:46.760152Z",
     "start_time": "2019-01-22T14:50:46.505523Z"
    }
   },
   "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": "2019-01-22T14:50:46.895357Z",
     "start_time": "2019-01-22T14:50:46.888425Z"
    }
   },
   "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": "2019-01-22T14:50:47.383265Z",
     "start_time": "2019-01-22T14:50:47.372954Z"
    }
   },
   "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": "2019-01-22T14:50:48.743194Z",
     "start_time": "2019-01-22T14:50:48.735649Z"
    }
   },
   "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": "2019-01-22T14:50:49.176363Z",
     "start_time": "2019-01-22T14:50:49.171378Z"
    }
   },
   "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": "2019-01-22T14:50:49.585501Z",
     "start_time": "2019-01-22T14:50:49.577050Z"
    }
   },
   "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": "2019-01-22T14:50:50.259907Z",
     "start_time": "2019-01-22T14:50:50.256003Z"
    }
   },
   "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": "2019-01-22T14:50:50.899702Z",
     "start_time": "2019-01-22T14:50:50.891703Z"
    }
   },
   "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": "2019-01-22T14:50:51.483274Z",
     "start_time": "2019-01-22T14:50:51.475609Z"
    }
   },
   "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": "2019-01-22T14:50:51.975102Z",
     "start_time": "2019-01-22T14:50:51.963139Z"
    }
   },
   "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": "2019-01-22T14:50:52.494908Z",
     "start_time": "2019-01-22T14:50:52.490367Z"
    }
   },
   "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": "2019-01-22T14:50:53.024993Z",
     "start_time": "2019-01-22T14:50:53.015750Z"
    }
   },
   "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": "2019-01-22T14:50:53.520146Z",
     "start_time": "2019-01-22T14:50:53.494980Z"
    }
   },
   "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": "2019-01-22T14:50:54.020714Z",
     "start_time": "2019-01-22T14:50:54.012204Z"
    }
   },
   "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": "2019-01-22T14:50:54.654805Z",
     "start_time": "2019-01-22T14:50:54.631576Z"
    }
   },
   "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": "2019-01-22T14:50:56.166489Z",
     "start_time": "2019-01-22T14:50:56.160041Z"
    }
   },
   "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": "2019-01-22T14:50:57.234609Z",
     "start_time": "2019-01-22T14:50:57.196576Z"
    }
   },
   "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": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:54:22.857814Z",
     "start_time": "2019-01-22T14:54:22.852769Z"
    },
    "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",
    "    print(xi_initial)\n",
    "    dt = total_time/time_steps\n",
    "    xi_diff, xi_new_vec = updater(Ti, omega_1, xi_initial, Lin, dt)\n",
    "    print(xi_new_vec)\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": "2019-01-22T14:54:36.637836Z",
     "start_time": "2019-01-22T14:54:36.633989Z"
    }
   },
   "outputs": [],
   "source": [
    "omega_1 = 0.5\n",
    "total_time = pi/omega_1\n",
    "epsilon = 10**(-6)\n",
    "max_iter = 20#10**4#1000#100#50#20\n",
    "time_steps = 20\n",
    "dt = total_time/time_steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:54:37.767202Z",
     "start_time": "2019-01-22T14:54:37.763567Z"
    }
   },
   "outputs": [],
   "source": [
    "Lin = sigmaz() # Lindbladian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:54:38.606701Z",
     "start_time": "2019-01-22T14:54:38.603012Z"
    }
   },
   "outputs": [],
   "source": [
    "Ti = sigmax() # Target unitary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:55:11.700720Z",
     "start_time": "2019-01-22T14:54:39.274984Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[555.52025554 124.70494869 599.85599251 622.98403826 645.27613256\n",
      " 440.4230612  903.43124524 164.49931813 322.71954801 441.58713235\n",
      "  83.09836212 644.18552965 618.90781557 393.27371108 498.84415162\n",
      " 504.33022746 626.38200659 848.24851208 103.749433   503.36285828]\n",
      "[555.52026211+0.j 124.70495526+0.j 599.85599908+0.j 622.98404483+0.j\n",
      " 645.27613913+0.j 440.42306777+0.j 903.43125181+0.j 164.4993247 +0.j\n",
      " 322.71955458+0.j 441.58713892+0.j  83.09836869+0.j 644.18553622+0.j\n",
      " 618.90782214+0.j 393.27371765+0.j 498.84415819+0.j 504.33023403+0.j\n",
      " 626.38201316+0.j 848.24851865+0.j 103.74943957+0.j 503.36286485+0.j]\n",
      "0\n",
      "(6.569789194024467e-06+0j)\n",
      "1\n",
      "(6.569789180222137e-06+0j)\n",
      "2\n",
      "(6.5697891664222096e-06+0j)\n",
      "3\n",
      "(6.569789152625197e-06+0j)\n",
      "4\n",
      "(6.569789138830265e-06+0j)\n",
      "5\n",
      "(6.569789125037978e-06+0j)\n",
      "6\n",
      "(6.569789111248161e-06+0j)\n",
      "7\n",
      "(6.56978909746099e-06+0j)\n",
      "8\n",
      "(6.5697890836764774e-06+0j)\n",
      "9\n",
      "(6.569789069894239e-06+0j)\n",
      "10\n",
      "(6.5697890561148275e-06+0j)\n",
      "11\n",
      "(6.569789042337314e-06+0j)\n",
      "12\n",
      "(6.56978902856273e-06+0j)\n",
      "13\n",
      "(6.569789014790654e-06+0j)\n",
      "14\n",
      "(6.56978900102108e-06+0j)\n",
      "15\n",
      "(6.569788987254037e-06+0j)\n",
      "16\n",
      "(6.569788973489511e-06+0j)\n",
      "17\n",
      "(6.569788959727665e-06+0j)\n",
      "18\n",
      "(6.569788945967923e-06+0j)\n",
      "19\n",
      "(6.56978893221105e-06+0j)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([555.5203935 +0.j, 124.70508666+0.j, 599.85613047+0.j,\n",
       "       622.98417622+0.j, 645.27627053+0.j, 440.42319916+0.j,\n",
       "       903.4313832 +0.j, 164.4994561 +0.j, 322.71968597+0.j,\n",
       "       441.58727032+0.j,  83.09850008+0.j, 644.18566761+0.j,\n",
       "       618.90795354+0.j, 393.27384905+0.j, 498.84428958+0.j,\n",
       "       504.33036542+0.j, 626.38214455+0.j, 848.24865004+0.j,\n",
       "       103.74957096+0.j, 503.36299625+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": "2019-01-22T14:55:20.474550Z",
     "start_time": "2019-01-22T14:55:20.376846Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.220002568975286"
      ]
     },
     "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": "2019-01-22T14:55:21.158975Z",
     "start_time": "2019-01-22T14:55:21.153440Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:55:21.590728Z",
     "start_time": "2019-01-22T14:55:21.578159Z"
    }
   },
   "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": "2019-01-22T14:55:22.038282Z",
     "start_time": "2019-01-22T14:55:21.935507Z"
    }
   },
   "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}0.242 & (0.066-4.286\\times10^{-04}j) & (0.066+4.286\\times10^{-04}j) & 0.758\\\\(-0.066+0.001j) & (-0.116+6.489\\times10^{-04}j) & (-0.401+0.002j) & (0.066-0.001j)\\\\(-0.066-0.001j) & (-0.401-0.002j) & (-0.116-6.489\\times10^{-04}j) & (0.066+0.001j)\\\\0.758 & (-0.066+4.286\\times10^{-04}j) & (-0.066-4.286\\times10^{-04}j) & 0.242\\\\\\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",
       "[[ 0.24150976+0.j          0.06551032-0.00042865j  0.06551032+0.00042865j\n",
       "   0.75849024+0.j        ]\n",
       " [-0.06556083+0.00135097j -0.11632809+0.00064887j -0.40093747+0.00229106j\n",
       "   0.06556083-0.00135097j]\n",
       " [-0.06556083-0.00135097j -0.40093747-0.00229106j -0.11632809-0.00064887j\n",
       "   0.06556083+0.00135097j]\n",
       " [ 0.75849024+0.j         -0.06551032+0.00042865j -0.06551032-0.00042865j\n",
       "   0.24150976+0.j        ]]"
      ]
     },
     "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": "2019-01-22T14:55:23.913442Z",
     "start_time": "2019-01-22T14:55:23.418518Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 576x432 with 2 Axes>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x10d1ffba8>)"
      ]
     },
     "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": []
  }
 ],
 "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": "3.6.8"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}