R20.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": "2019-01-22T13:15:42.137237Z",
     "start_time": "2019-01-22T13:15:40.808941Z"
    }
   },
   "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": "2019-01-22T13:15:42.144607Z",
     "start_time": "2019-01-22T13:15:42.140023Z"
    }
   },
   "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": "2019-01-22T13:15:43.094529Z",
     "start_time": "2019-01-22T13:15:43.091335Z"
    }
   },
   "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": "2019-01-22T13:15:44.396412Z",
     "start_time": "2019-01-22T13:15:44.390087Z"
    }
   },
   "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": "2019-01-22T13:15:45.254249Z",
     "start_time": "2019-01-22T13:15:45.248072Z"
    }
   },
   "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": "2019-01-22T13:15:46.911276Z",
     "start_time": "2019-01-22T13:15:46.904618Z"
    }
   },
   "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": "2019-01-22T13:15:47.686169Z",
     "start_time": "2019-01-22T13:15:47.675852Z"
    }
   },
   "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": "2019-01-22T13:15:48.917307Z",
     "start_time": "2019-01-22T13:15:48.345411Z"
    }
   },
   "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": "2019-01-22T13:15:49.839826Z",
     "start_time": "2019-01-22T13:15:49.828362Z"
    }
   },
   "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": "2019-01-22T13:15:50.340223Z",
     "start_time": "2019-01-22T13:15:50.274079Z"
    }
   },
   "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": "2019-01-22T13:15:50.622108Z",
     "start_time": "2019-01-22T13:15:50.606269Z"
    }
   },
   "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": "2019-01-22T13:15:50.952498Z",
     "start_time": "2019-01-22T13:15:50.933318Z"
    }
   },
   "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": "2019-01-22T13:15:51.542437Z",
     "start_time": "2019-01-22T13:15:51.537226Z"
    }
   },
   "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": "2019-01-22T13:15:51.866365Z",
     "start_time": "2019-01-22T13:15:51.860369Z"
    }
   },
   "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": "2019-01-22T13:15:52.163098Z",
     "start_time": "2019-01-22T13:15:52.151364Z"
    }
   },
   "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": "2019-01-22T13:15:52.489678Z",
     "start_time": "2019-01-22T13:15:52.480342Z"
    }
   },
   "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": "2019-01-22T13:15:52.889795Z",
     "start_time": "2019-01-22T13:15:52.870674Z"
    }
   },
   "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": "2019-01-22T13:15:54.243911Z",
     "start_time": "2019-01-22T13:15:54.240798Z"
    }
   },
   "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": "2019-01-22T13:15:54.659524Z",
     "start_time": "2019-01-22T13:15:54.643899Z"
    }
   },
   "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": "2019-01-22T13:15:55.130032Z",
     "start_time": "2019-01-22T13:15:55.125003Z"
    }
   },
   "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": "2019-01-22T13:15:55.484107Z",
     "start_time": "2019-01-22T13:15:55.462832Z"
    }
   },
   "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": "2019-01-22T13:15:55.936057Z",
     "start_time": "2019-01-22T13:15:55.922327Z"
    }
   },
   "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": "2019-01-22T13:15:56.761747Z",
     "start_time": "2019-01-22T13:15:56.752482Z"
    }
   },
   "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": "2019-01-22T13:15:57.341738Z",
     "start_time": "2019-01-22T13:15:57.335682Z"
    },
    "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": "2019-01-22T13:15:57.910687Z",
     "start_time": "2019-01-22T13:15:57.899063Z"
    }
   },
   "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": "2019-01-22T13:15:58.396820Z",
     "start_time": "2019-01-22T13:15:58.377940Z"
    }
   },
   "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": "2019-01-22T13:15:58.945609Z",
     "start_time": "2019-01-22T13:15:58.942089Z"
    }
   },
   "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": "2019-01-22T13:15:59.781521Z",
     "start_time": "2019-01-22T13:15:59.558699Z"
    }
   },
   "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": "2019-01-22T13:16:00.085808Z",
     "start_time": "2019-01-22T13:16:00.079409Z"
    }
   },
   "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": "2019-01-22T13:16:00.704827Z",
     "start_time": "2019-01-22T13:16:00.691464Z"
    }
   },
   "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": "2019-01-22T13:16:02.629022Z",
     "start_time": "2019-01-22T13:16:02.624980Z"
    }
   },
   "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": "2019-01-22T13:16:03.042431Z",
     "start_time": "2019-01-22T13:16:03.037020Z"
    }
   },
   "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": "2019-01-22T13:16:03.478899Z",
     "start_time": "2019-01-22T13:16:03.467199Z"
    }
   },
   "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": "2019-01-22T13:16:03.927996Z",
     "start_time": "2019-01-22T13:16:03.922831Z"
    }
   },
   "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": "2019-01-22T13:16:04.349257Z",
     "start_time": "2019-01-22T13:16:04.340150Z"
    }
   },
   "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": "2019-01-22T13:16:05.060685Z",
     "start_time": "2019-01-22T13:16:05.051774Z"
    }
   },
   "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": "2019-01-22T13:16:05.615619Z",
     "start_time": "2019-01-22T13:16:05.606007Z"
    }
   },
   "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": "2019-01-22T13:16:05.988220Z",
     "start_time": "2019-01-22T13:16:05.976871Z"
    }
   },
   "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": "2019-01-22T13:16:06.354839Z",
     "start_time": "2019-01-22T13:16:06.342051Z"
    }
   },
   "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": "2019-01-22T13:16:06.691562Z",
     "start_time": "2019-01-22T13:16:06.669886Z"
    }
   },
   "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": "2019-01-22T13:16:06.992256Z",
     "start_time": "2019-01-22T13:16:06.987183Z"
    }
   },
   "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": "2019-01-22T13:16:07.364051Z",
     "start_time": "2019-01-22T13:16:07.341418Z"
    }
   },
   "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": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:16:36.146016Z",
     "start_time": "2019-01-22T13:16:36.140922Z"
    }
   },
   "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*real(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": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:16:36.943217Z",
     "start_time": "2019-01-22T13:16:36.897753Z"
    }
   },
   "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-46-8fffc312f438>\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-45-81f57fdfb949>\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[0mreal\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[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": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T13:16:37.891918Z",
     "start_time": "2019-01-22T13:16:37.887333Z"
    },
    "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": 75,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:22:51.925662Z",
     "start_time": "2019-01-22T14:22:51.921830Z"
    }
   },
   "outputs": [],
   "source": [
    "omega_1 = 0.5\n",
    "total_time = pi/omega_1\n",
    "epsilon = 10**(-6)\n",
    "max_iter = 1000#100  #20,50\n",
    "time_steps = 20\n",
    "dt = total_time/time_steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:22:52.528803Z",
     "start_time": "2019-01-22T14:22:52.525833Z"
    }
   },
   "outputs": [],
   "source": [
    "Lin = sigmaz() # Lindbladian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:22:52.858148Z",
     "start_time": "2019-01-22T14:22:52.854656Z"
    }
   },
   "outputs": [],
   "source": [
    "Ti = sigmax() # Target unitary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:48:15.716997Z",
     "start_time": "2019-01-22T14:22:53.149988Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    },
    {
     "data": {
      "text/plain": [
       "array([672.20170339, 833.65739636, 679.92574559, 474.28082244,\n",
       "       460.64824687, 663.15453015, 767.50774985, 257.32403908,\n",
       "        67.13784043, 854.9536184 , 239.56565343, 811.58710705,\n",
       "       532.0299296 , 585.26909793, 415.11381088, 315.4078595 ,\n",
       "       831.5440831 , 918.56895243, 668.24571025, 817.04990173])"
      ]
     },
     "execution_count": 78,
     "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": 79,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:48:15.822546Z",
     "start_time": "2019-01-22T14:48:15.719608Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.218505524351835"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F(Ti, omega_1, xi_opt, Lin, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:48:15.831010Z",
     "start_time": "2019-01-22T14:48:15.825501Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:48:15.844966Z",
     "start_time": "2019-01-22T14:48:15.833729Z"
    }
   },
   "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": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = T_maker(Ti)\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:48:15.960848Z",
     "start_time": "2019-01-22T14:48:15.847152Z"
    }
   },
   "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}0.235 & (0.030-0.002j) & (0.030+0.002j) & 0.765\\\\(-0.030+0.002j) & (-0.123-3.488\\times10^{-04}j) & (-0.407-5.503\\times10^{-05}j) & (0.030-0.002j)\\\\(-0.030-0.002j) & (-0.407+5.503\\times10^{-05}j) & (-0.123+3.488\\times10^{-04}j) & (0.030+0.002j)\\\\0.765 & (-0.030+0.002j) & (-0.030-0.002j) & 0.235\\\\\\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",
       "[[ 0.23485774+0.00000000e+00j  0.03004741-2.16157599e-03j\n",
       "   0.03004741+2.16157599e-03j  0.76514226+0.00000000e+00j]\n",
       " [-0.03019654+1.92316983e-03j -0.12262023-3.48788455e-04j\n",
       "  -0.40721516-5.50277685e-05j  0.03019654-1.92316983e-03j]\n",
       " [-0.03019654-1.92316983e-03j -0.40721516+5.50277685e-05j\n",
       "  -0.12262023+3.48788455e-04j  0.03019654+1.92316983e-03j]\n",
       " [ 0.76514226+0.00000000e+00j -0.03004741+2.16157599e-03j\n",
       "  -0.03004741-2.16157599e-03j  0.23485774+0.00000000e+00j]]"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_full_maker(Ti, omega_1, xi_opt, Lin, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-22T14:48:16.360081Z",
     "start_time": "2019-01-22T14:48:15.963203Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 576x432 with 2 Axes>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x1a20c9e780>)"
      ]
     },
     "execution_count": 83,
     "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
}