test8-Copy2.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": "2019-01-15T06:22:27.144819Z",
     "start_time": "2019-01-15T06:22:25.990472Z"
    }
   },
   "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": "2019-01-15T06:22:29.210341Z",
     "start_time": "2019-01-15T06:22:29.205570Z"
    }
   },
   "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": [
    "## Numpy imports "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:29.589451Z",
     "start_time": "2019-01-15T06:22:29.585723Z"
    }
   },
   "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": [
    "## Scipy imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:29.993179Z",
     "start_time": "2019-01-15T06:22:29.990173Z"
    }
   },
   "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": "2019-01-15T06:22:30.192214Z",
     "start_time": "2019-01-15T06:22:30.186094Z"
    }
   },
   "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": "2019-01-15T06:22:31.981117Z",
     "start_time": "2019-01-15T06:22:31.977582Z"
    }
   },
   "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": "2019-01-15T06:22:32.466914Z",
     "start_time": "2019-01-15T06:22:32.464465Z"
    }
   },
   "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": "2019-01-15T06:22:32.813456Z",
     "start_time": "2019-01-15T06:22:32.810760Z"
    }
   },
   "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": "2019-01-15T06:22:33.676032Z",
     "start_time": "2019-01-15T06:22:33.159676Z"
    }
   },
   "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": "2019-01-15T06:22:34.327244Z",
     "start_time": "2019-01-15T06:22:34.320749Z"
    }
   },
   "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": "2019-01-15T06:22:34.949555Z",
     "start_time": "2019-01-15T06:22:34.878530Z"
    }
   },
   "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[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[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[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[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[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": "2019-01-15T06:22:35.222243Z",
     "start_time": "2019-01-15T06:22:35.212600Z"
    }
   },
   "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[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": "2019-01-15T06:22:35.600852Z",
     "start_time": "2019-01-15T06:22:35.585786Z"
    }
   },
   "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[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": "2019-01-15T06:22:36.872401Z",
     "start_time": "2019-01-15T06:22:36.869166Z"
    }
   },
   "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": "2019-01-15T06:22:37.150378Z",
     "start_time": "2019-01-15T06:22:37.141839Z"
    }
   },
   "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": "2019-01-15T06:22:37.401167Z",
     "start_time": "2019-01-15T06:22:37.387881Z"
    }
   },
   "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[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mdel\u001b[0m \u001b[0mI\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": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:37.676950Z",
     "start_time": "2019-01-15T06:22:37.671059Z"
    }
   },
   "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": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:37.943624Z",
     "start_time": "2019-01-15T06:22:37.931579Z"
    }
   },
   "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": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " tensor(identity(2), T_maker(sigmax()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## level 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:38.490345Z",
     "start_time": "2019-01-15T06:22:38.486870Z"
    }
   },
   "outputs": [],
   "source": [
    "def Hamil(omega_1, xi):\n",
    "    H = H1(omega_1) + xi*H2()\n",
    "    return H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:38.799438Z",
     "start_time": "2019-01-15T06:22:38.785572Z"
    }
   },
   "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": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamil(2, 0.5 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:39.311283Z",
     "start_time": "2019-01-15T06:22:39.305476Z"
    }
   },
   "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 + term2))\n",
    "    return leftover\n",
    "\n",
    "\n",
    "    return x**2\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": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:39.767377Z",
     "start_time": "2019-01-15T06:22:39.755997Z"
    }
   },
   "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": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A(2, 0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:40.133945Z",
     "start_time": "2019-01-15T06:22:40.118347Z"
    }
   },
   "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": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A(0, 0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:40.458162Z",
     "start_time": "2019-01-15T06:22:40.443777Z"
    }
   },
   "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-24-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[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'I' is not defined"
     ]
    }
   ],
   "source": [
    "I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:40.752573Z",
     "start_time": "2019-01-15T06:22:40.746695Z"
    },
    "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": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:41.108778Z",
     "start_time": "2019-01-15T06:22:41.095199Z"
    }
   },
   "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-26-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[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'I' is not defined"
     ]
    }
   ],
   "source": [
    "I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:41.436214Z",
     "start_time": "2019-01-15T06:22:41.420610Z"
    }
   },
   "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 & -1.0j & -1.0j & 0.0\\\\1.0j & -0.200j & 0.0 & -1.0j\\\\1.0j & 0.0 & -0.200j & -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 = False\n",
       "Qobj data =\n",
       "[[0.+0.j  0.-1.j  0.-1.j  0.+0.j ]\n",
       " [0.+1.j  0.-0.2j 0.+0.j  0.-1.j ]\n",
       " [0.+1.j  0.+0.j  0.-0.2j 0.-1.j ]\n",
       " [0.+0.j  0.+1.j  0.+1.j  0.+0.j ]]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_k(0.5, sigmaz())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:41.755328Z",
     "start_time": "2019-01-15T06:22:41.751913Z"
    }
   },
   "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": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:42.129044Z",
     "start_time": "2019-01-15T06:22:42.110348Z"
    }
   },
   "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": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L(0.5, 2, sigmaz(), 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:42.536801Z",
     "start_time": "2019-01-15T06:22:42.530961Z"
    }
   },
   "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": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:43.110865Z",
     "start_time": "2019-01-15T06:22:43.102666Z"
    }
   },
   "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": 31,
     "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": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:44.534843Z",
     "start_time": "2019-01-15T06:22:44.529397Z"
    }
   },
   "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": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:46.119481Z",
     "start_time": "2019-01-15T06:22:46.115010Z"
    }
   },
   "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)/d\n",
    "    f = f_int.tr()\n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:46.828162Z",
     "start_time": "2019-01-15T06:22:46.822029Z"
    }
   },
   "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": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:47.227649Z",
     "start_time": "2019-01-15T06:22:47.222944Z"
    }
   },
   "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": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:47.608909Z",
     "start_time": "2019-01-15T06:22:47.597284Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fidelity_calc(sigmax(), sigmay())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:48.006607Z",
     "start_time": "2019-01-15T06:22:47.995247Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fidelity_calc(sigmay(), sigmay())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:48.408932Z",
     "start_time": "2019-01-15T06:22:48.404714Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2.])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xi_vec_test = array([1.0, 2.0])\n",
    "xi_vec_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:48.892261Z",
     "start_time": "2019-01-15T06:22:48.888004Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xi_vec_test.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:49.444700Z",
     "start_time": "2019-01-15T06:22:49.440336Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 4.0]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_vec = [xi**2 for xi in xi_vec_test]\n",
    "w_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:50.324704Z",
     "start_time": "2019-01-15T06:22:50.307000Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4999000396558212"
      ]
     },
     "execution_count": 41,
     "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": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:50.740786Z",
     "start_time": "2019-01-15T06:22:50.731729Z"
    }
   },
   "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": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:51.277316Z",
     "start_time": "2019-01-15T06:22:51.257935Z"
    }
   },
   "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": 43,
     "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": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:52.678385Z",
     "start_time": "2019-01-15T06:22:52.673175Z"
    }
   },
   "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": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:54.850947Z",
     "start_time": "2019-01-15T06:22:54.805589Z"
    }
   },
   "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-45-8fffc312f438>\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[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[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-44-237dcb7fb593>\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[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[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[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[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'epsilon' is not defined"
     ]
    }
   ],
   "source": [
    "#  updater(Ti, omega_1, xi_vec, Lin, dt)\n",
    "updater(sigmax(), 0.5 , xi_vec_test, sigmaz(), 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:22:55.282395Z",
     "start_time": "2019-01-15T06:22:55.278463Z"
    },
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "def terminator(max_iter, time_steps, Ti, omega_1, Lin, total_time):\n",
    "    r\"\"\"Brief description of the function\"\"\"\n",
    "    xi_initial =  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": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:25:57.854052Z",
     "start_time": "2019-01-15T06:25:57.850221Z"
    }
   },
   "outputs": [],
   "source": [
    "omega_1 = 0.5\n",
    "total_time = pi/omega_1\n",
    "epsilon = 10**(-6)\n",
    "max_iter = 20\n",
    "time_steps = 30\n",
    "dt = total_time/time_steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:25:58.503827Z",
     "start_time": "2019-01-15T06:25:58.497053Z"
    }
   },
   "outputs": [],
   "source": [
    "Lin = 0*sigmaz() # Lindbladian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:25:59.311876Z",
     "start_time": "2019-01-15T06:25:59.307679Z"
    }
   },
   "outputs": [],
   "source": [
    "Ti = sigmax() # Target unitary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:27:11.290558Z",
     "start_time": "2019-01-15T06:25:59.812053Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.76567421, 0.74297457, 0.64672294, 0.63257122, 0.1784033 ,\n",
       "       0.36978299, 0.32553601, 0.41794776, 0.83165388, 0.18595607,\n",
       "       0.62453317, 0.78845003, 0.20981571, 0.14292371, 0.236301  ,\n",
       "       0.89076338, 0.45355486, 0.17862238, 0.03830579, 0.27009325,\n",
       "       0.18725837, 0.1396857 , 0.62000753, 0.98100394, 0.64025456,\n",
       "       0.13344848, 0.32658882, 0.40080259, 0.27622142, 0.25331751])"
      ]
     },
     "execution_count": 59,
     "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": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:27:11.442906Z",
     "start_time": "2019-01-15T06:27:11.293107Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4999505582682572"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F(Ti, omega_1, xi_opt, Lin, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:27:11.450534Z",
     "start_time": "2019-01-15T06:27:11.445320Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:24:14.147743Z",
     "start_time": "2019-01-15T06:24:14.140393Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 1.0\\\\0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0. 0. 0. 1.]\n",
       " [0. 0. 1. 0.]\n",
       " [0. 1. 0. 0.]\n",
       " [1. 0. 0. 0.]]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = T_maker(Ti)\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:24:14.279842Z",
     "start_time": "2019-01-15T06:24:14.150537Z"
    }
   },
   "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}0.238 & (0.131-0.405j) & (0.131+0.405j) & 0.762\\\\(-0.261+0.337j) & (-0.134-0.197j) & (-0.716-0.259j) & (0.261-0.337j)\\\\(-0.261-0.337j) & (-0.716+0.259j) & (-0.134+0.197j) & (0.261+0.337j)\\\\0.762 & (-0.131+0.405j) & (-0.131-0.405j) & 0.238\\\\\\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",
       "[[ 0.23841616+0.j          0.1313599 -0.40536215j  0.1313599 +0.40536215j\n",
       "   0.76158384+0.j        ]\n",
       " [-0.26136306+0.33654606j -0.13405012-0.19716194j -0.7162084 -0.25895071j\n",
       "   0.26136306-0.33654606j]\n",
       " [-0.26136306-0.33654606j -0.7162084 +0.25895071j -0.13405012+0.19716194j\n",
       "   0.26136306+0.33654606j]\n",
       " [ 0.76158384+0.j         -0.1313599 +0.40536215j -0.1313599 -0.40536215j\n",
       "   0.23841616+0.j        ]]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_full_maker(Ti, omega_1, xi_opt, Lin, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-15T06:24:14.914743Z",
     "start_time": "2019-01-15T06:24:14.282868Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<matplotlib.figure.Figure at 0x1104bc080>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x110460fd0>)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1104bc080>"
      ]
     },
     "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": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
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