test8-Copy3.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": "2019-01-21T13:04:19.249606Z",
     "start_time": "2019-01-21T13:04:18.092788Z"
    }
   },
   "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": [
    "## Qutip imports 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:19.256562Z",
     "start_time": "2019-01-21T13:04:19.251955Z"
    }
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-2-09c8a0c03c80>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-2-09c8a0c03c80>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    from\u001b[0m\n\u001b[0m         ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "from "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Numpy imports "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:20.485686Z",
     "start_time": "2019-01-21T13:04:20.480352Z"
    }
   },
   "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": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:21.129754Z",
     "start_time": "2019-01-21T13:04:21.126274Z"
    }
   },
   "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": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:21.951560Z",
     "start_time": "2019-01-21T13:04:21.944766Z"
    }
   },
   "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": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:22.690697Z",
     "start_time": "2019-01-21T13:04:22.686482Z"
    }
   },
   "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": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:24.063000Z",
     "start_time": "2019-01-21T13:04:24.059837Z"
    }
   },
   "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": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:24.752338Z",
     "start_time": "2019-01-21T13:04:24.748120Z"
    }
   },
   "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": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:25.849950Z",
     "start_time": "2019-01-21T13:04:25.354944Z"
    }
   },
   "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": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:26.687909Z",
     "start_time": "2019-01-21T13:04:26.680286Z"
    }
   },
   "outputs": [],
   "source": [
    "def rint(x):\n",
    "    print(\"x = \", x)\n",
    "    return None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building parts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:27.309750Z",
     "start_time": "2019-01-21T13:04:27.229323Z"
    }
   },
   "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-11-3e38f81848f0>\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": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:27.532294Z",
     "start_time": "2019-01-21T13:04:27.519380Z"
    }
   },
   "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-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": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:27.830352Z",
     "start_time": "2019-01-21T13:04:27.817983Z"
    }
   },
   "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-13-3ce5abe2615e>\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": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:28.667814Z",
     "start_time": "2019-01-21T13:04:28.660238Z"
    }
   },
   "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": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:29.059284Z",
     "start_time": "2019-01-21T13:04:29.055173Z"
    }
   },
   "outputs": [],
   "source": [
    "def H2():\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    H2 = sigmay()\n",
    "    return H2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:29.430492Z",
     "start_time": "2019-01-21T13:04:29.419631Z"
    }
   },
   "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-16-7d62117bf249>\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": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:50.558208Z",
     "start_time": "2019-01-21T13:04:50.551357Z"
    }
   },
   "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": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:50.944998Z",
     "start_time": "2019-01-21T13:04:50.932532Z"
    }
   },
   "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": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " tensor(identity(2), T_maker(sigmax()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## level 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:51.547552Z",
     "start_time": "2019-01-21T13:04:51.544185Z"
    }
   },
   "outputs": [],
   "source": [
    "def Hamil(omega_1, xi):\n",
    "    H = H1(omega_1) + xi*H2()\n",
    "    return H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:51.915570Z",
     "start_time": "2019-01-21T13:04:51.903573Z"
    }
   },
   "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": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamil(2, 0.5 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:52.227080Z",
     "start_time": "2019-01-21T13:04:52.221597Z"
    }
   },
   "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": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:52.652253Z",
     "start_time": "2019-01-21T13:04:52.622596Z"
    }
   },
   "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": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A(2, 0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:53.008988Z",
     "start_time": "2019-01-21T13:04:52.996941Z"
    }
   },
   "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": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A(0, 0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:53.323609Z",
     "start_time": "2019-01-21T13:04:53.309258Z"
    }
   },
   "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-42-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": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:53.752359Z",
     "start_time": "2019-01-21T13:04:53.741876Z"
    },
    "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": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:54.138286Z",
     "start_time": "2019-01-21T13:04:54.122731Z"
    }
   },
   "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-44-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": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:54.682762Z",
     "start_time": "2019-01-21T13:04:54.668846Z"
    }
   },
   "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": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_k(0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:55.218903Z",
     "start_time": "2019-01-21T13:04:55.206799Z"
    }
   },
   "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": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:55.717829Z",
     "start_time": "2019-01-21T13:04:55.704319Z"
    }
   },
   "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": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L(0.5, 2, sigmaz(), 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:56.236971Z",
     "start_time": "2019-01-21T13:04:56.225233Z"
    }
   },
   "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": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:56.743557Z",
     "start_time": "2019-01-21T13:04:56.732793Z"
    }
   },
   "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": 49,
     "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": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:58.393211Z",
     "start_time": "2019-01-21T13:04:58.389818Z"
    }
   },
   "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": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:58.991862Z",
     "start_time": "2019-01-21T13:04:58.987210Z"
    }
   },
   "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": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:04:59.720348Z",
     "start_time": "2019-01-21T13:04:59.712316Z"
    }
   },
   "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": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:00.435070Z",
     "start_time": "2019-01-21T13:05:00.429663Z"
    }
   },
   "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": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:01.101046Z",
     "start_time": "2019-01-21T13:05:01.089876Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fidelity_calc(sigmax(), sigmay())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:01.625306Z",
     "start_time": "2019-01-21T13:05:01.609078Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fidelity_calc(sigmay(), sigmay())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:02.020722Z",
     "start_time": "2019-01-21T13:05:02.010734Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2.])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xi_vec_test = array([1.0, 2.0])\n",
    "xi_vec_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:02.495299Z",
     "start_time": "2019-01-21T13:05:02.490620Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xi_vec_test.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:03.144850Z",
     "start_time": "2019-01-21T13:05:03.139610Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 4.0]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_vec = [xi**2 for xi in xi_vec_test]\n",
    "w_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:03.680883Z",
     "start_time": "2019-01-21T13:05:03.652109Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7.998400634493139"
      ]
     },
     "execution_count": 59,
     "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": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:04.274746Z",
     "start_time": "2019-01-21T13:05:04.270344Z"
    }
   },
   "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": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:04.951238Z",
     "start_time": "2019-01-21T13:05:04.926410Z"
    }
   },
   "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": 61,
     "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": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:05.584100Z",
     "start_time": "2019-01-21T13:05:05.579395Z"
    }
   },
   "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*2*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": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:06.531127Z",
     "start_time": "2019-01-21T13:05:06.491856Z"
    }
   },
   "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-63-8fffc312f438>\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-62-237dcb7fb593>\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[0;36m2\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": 64,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:05:07.154337Z",
     "start_time": "2019-01-21T13:05:07.147208Z"
    },
    "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",
    "            \n",
    "        \n",
    "    xi_final = xi_new_vec    \n",
    "    return xi_final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:22:59.164550Z",
     "start_time": "2019-01-21T13:22:59.161228Z"
    }
   },
   "outputs": [],
   "source": [
    "omega_1 = 0.5\n",
    "total_time = 20*pi/omega_1\n",
    "epsilon = 10**(-6)\n",
    "max_iter = 100\n",
    "time_steps = 20\n",
    "dt = total_time/time_steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:22:59.617796Z",
     "start_time": "2019-01-21T13:22:59.610036Z"
    }
   },
   "outputs": [],
   "source": [
    "Lin = sigmaz() # Lindbladian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:22:59.991057Z",
     "start_time": "2019-01-21T13:22:59.988070Z"
    }
   },
   "outputs": [],
   "source": [
    "Ti = sigmax() # Target unitary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:25:23.605319Z",
     "start_time": "2019-01-21T13:23:00.416073Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([532.4772707 , 465.65232314, 985.36050475, 985.938968  ,\n",
       "       304.29829433, 403.9433729 , 714.55706739, 338.47060721,\n",
       "       186.34279195, 681.41618071, 856.71975569, 370.39626079,\n",
       "       938.13183602,  25.76322193, 382.23392484, 653.56237403,\n",
       "       981.25756336, 830.56982161, 137.19657251, 909.62607159])"
      ]
     },
     "execution_count": 124,
     "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": 125,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:25:23.686798Z",
     "start_time": "2019-01-21T13:25:23.608426Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.000000005723951"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F(Ti, omega_1, xi_opt, Lin, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:25:23.693593Z",
     "start_time": "2019-01-21T13:25:23.688751Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:25:23.703615Z",
     "start_time": "2019-01-21T13:25:23.696217Z"
    }
   },
   "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": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = T_maker(Ti)\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:25:23.783870Z",
     "start_time": "2019-01-21T13:25:23.706349Z"
    }
   },
   "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}0.500 & (1.411\\times10^{-06}+1.462\\times10^{-09}j) & (1.411\\times10^{-06}-1.462\\times10^{-09}j) & 0.500\\\\(-1.412\\times10^{-06}+1.267\\times10^{-09}j) & (1.021\\times10^{-06}-5.519\\times10^{-09}j) & (1.021\\times10^{-06}-3.025\\times10^{-09}j) & (1.412\\times10^{-06}-1.267\\times10^{-09}j)\\\\(-1.412\\times10^{-06}-1.267\\times10^{-09}j) & (1.021\\times10^{-06}+3.025\\times10^{-09}j) & (1.021\\times10^{-06}+5.519\\times10^{-09}j) & (1.412\\times10^{-06}+1.267\\times10^{-09}j)\\\\0.500 & (-1.411\\times10^{-06}-1.462\\times10^{-09}j) & (-1.411\\times10^{-06}+1.462\\times10^{-09}j) & 0.500\\\\\\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",
       "[[ 5.00001023e-01+0.00000000e+00j  1.41122276e-06+1.46188680e-09j\n",
       "   1.41122282e-06-1.46188681e-09j  4.99998977e-01+0.00000000e+00j]\n",
       " [-1.41193536e-06+1.26726964e-09j  1.02135875e-06-5.51858389e-09j\n",
       "   1.02134707e-06-3.02513224e-09j  1.41193533e-06-1.26726954e-09j]\n",
       " [-1.41193533e-06-1.26726958e-09j  1.02134707e-06+3.02513224e-09j\n",
       "   1.02135875e-06+5.51858389e-09j  1.41193536e-06+1.26726961e-09j]\n",
       " [ 4.99998977e-01+0.00000000e+00j -1.41122282e-06-1.46188673e-09j\n",
       "  -1.41122276e-06+1.46188673e-09j  5.00001023e-01+0.00000000e+00j]]"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_full_maker(Ti, omega_1, xi_opt, Lin, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-21T13:25:24.090531Z",
     "start_time": "2019-01-21T13:25:23.786401Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 576x432 with 2 Axes>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x1a1d19fb38>)"
      ]
     },
     "execution_count": 129,
     "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": 113,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T09:01:09.196613Z",
     "start_time": "2019-01-09T09:01:09.185414Z"
    }
   },
   "outputs": [],
   "source": [
    "α = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T09:01:09.202575Z",
     "start_time": "2019-01-09T09:01:09.199292Z"
    }
   },
   "outputs": [],
   "source": [
    "new_array = random_sample((4,3,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:19:52.287183Z",
     "start_time": "2019-01-09T08:19:52.279221Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5727494 , 0.38293601, 0.36874311],\n",
       "       [0.92736909, 0.71153787, 0.61927054],\n",
       "       [0.77571877, 0.06657134, 0.25520209],\n",
       "       [0.27701559, 0.31532412, 0.21852523]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:20:08.302375Z",
     "start_time": "2019-01-09T08:20:08.295382Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_array.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:20:53.907366Z",
     "start_time": "2019-01-09T08:20:53.904137Z"
    }
   },
   "outputs": [],
   "source": [
    "new_array[0] = 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:21:08.822956Z",
     "start_time": "2019-01-09T08:21:08.817068Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.        , 0.        ],\n",
       "       [0.92736909, 0.71153787, 0.61927054],\n",
       "       [0.77571877, 0.06657134, 0.25520209],\n",
       "       [0.27701559, 0.31532412, 0.21852523]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:21:32.660926Z",
     "start_time": "2019-01-09T08:21:32.655914Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_array.any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:21:47.067130Z",
     "start_time": "2019-01-09T08:21:47.062537Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_array.all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:22:42.419037Z",
     "start_time": "2019-01-09T08:22:42.406561Z"
    }
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-84-26b90b14af80>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_array\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()"
     ]
    }
   ],
   "source": [
    "max(new_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:23:42.601098Z",
     "start_time": "2019-01-09T08:23:42.584333Z"
    }
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'axis' is an invalid keyword argument for this function",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-85-e882e7469d49>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_array\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'axis' is an invalid keyword argument for this function"
     ]
    }
   ],
   "source": [
    "max(new_array, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:42:10.899886Z",
     "start_time": "2019-01-09T08:42:10.881792Z"
    }
   },
   "outputs": [],
   "source": [
    "from numpy import amax "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-09T08:42:43.276455Z",
     "start_time": "2019-01-09T08:42:43.269364Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9273690900033358"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "amax(new_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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