Multiple plots for Krotov.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "Krotov Algorithm for Quantum gate Implementation\n",
    "Written By Bilal Riaz\n",
    "\n",
    "\n",
    "'''\n",
    "import matplotlib\n",
    "import scipy.stats\n",
    "import scipy.linalg\n",
    "import scipy.sparse.linalg\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import numpy.random as rnd\n",
    "import scipy.linalg as LA\n",
    "from scipy.integrate import ode\n",
    "\n",
    "\n",
    "class Krotov:\n",
    "    def __init__(self,J,lambda_1,ti,tf,steps):\n",
    "        self.J = float(J)\n",
    "        self.lambda_1 = float(lambda_1)\n",
    "        self.ti = ti\n",
    "        self.tf = tf\n",
    "        self.steps = steps\n",
    "        self.t = np.linspace(ti,tf,steps)\n",
    "\n",
    "        self.dt = self.t[1] - self.t[0]\n",
    "        self.sX = np.array([[0, 1], [1, 0]], dtype = 'complex64')\n",
    "        self.sY = np.array([[0, -1j], [1j, 0]], dtype = 'complex64')\n",
    "        self.sZ = np.array([[1, 0], [0, -1]], dtype = 'complex64')\n",
    "        self.I = np.array(np.identity(2), dtype = 'complex64')\n",
    "\n",
    "        self.sZZ = np.kron(self.sZ, self.sZ)\n",
    "        self.sIY = np.kron(self.I, self.sY)\n",
    "        self.sYI = np.kron(self.sY, self.I)\n",
    "        self.sIZ = np.kron(self.I, self.sZ)\n",
    "        self.sZI = np.kron(self.sZ, self.I)\n",
    "\n",
    "        self.delta1 = 0\n",
    "        self.alpha1 = 1\n",
    "        self.delta2 = 1.9\n",
    "        self.alpha2 = 0.3\n",
    "        self.delta3 = 1.6\n",
    "        self.alpha3 = 0.4\n",
    "        self.delta4 = 1.6\n",
    "        self.alpha4 = 0.4\n",
    "\n",
    "       # seed is given values for better debugging and Design Purposes\n",
    "        #rnd.seed(2)\n",
    "        \n",
    "        omega = 10;\n",
    "        \n",
    "        # Controls\n",
    "        self.EYI = np.zeros((self.steps,))\n",
    "        #self.EYI_tilde = self.EYI\n",
    "        self.EYI_tilde = np.zeros((self.steps,))\n",
    "        self.EIY = 10 *rnd.rand(self.steps,) -5\n",
    "        #self.EIY_tilde = self.EIY\n",
    "        self.EIY_tilde = np.zeros((self.steps,))\n",
    "        self.EZI = 10 *rnd.rand(self.steps,) -5\n",
    "        #self.EZI_tilde = self.EZI\n",
    "        self.EZI_tilde = np.zeros((self.steps,))\n",
    "        self.EIZ = 10 *rnd.rand(self.steps,) -5\n",
    "        #self.EIZ_tilde = self.EIZ\n",
    "        self.EIZ_tilde = np.zeros((self.steps,))\n",
    "\n",
    "        self.Ui = np.identity(4, dtype = 'complex128')\n",
    "        self.UT = np.exp(-1j * np.pi/4)*np.array([[1, 0, 0, 0],[0, 1, 0, 0],[0, 0, 0, 1],[0, 0, 1, 0]], dtype = 'complex128')\n",
    "\n",
    "        self.U = np.zeros([self.steps, 4, 4], dtype = 'complex128')\n",
    "        self.B = np.zeros([self.steps, 4, 4], dtype = 'complex128')\n",
    "\n",
    "        self.U[0] = np.identity(4, dtype = 'complex128')\n",
    "        self.B[steps - 1] = self.UT.T.conj()\n",
    "\n",
    "        self. Ho = self.J * self.sZZ\n",
    "\n",
    "    def Hc(self, t_index):\n",
    "        t = t_index\n",
    "        return (self.EYI[t] * self.sYI + self.EIY[t] * self.sIY + self.EZI[t] * self.sZI + self.EIZ[t] * self.sIZ )\n",
    "\n",
    "    def Hc_tilde(self, t_index):\n",
    "        t = t_index\n",
    "        return (self.EYI_tilde[t] * self.sYI + self.EIY_tilde[t] * self.sIY + self.EZI_tilde[t] * self.sZI + self.EIZ_tilde[t]* self.sIZ)\n",
    "\n",
    "    def H(self, t_index):\n",
    "        t = t_index\n",
    "        return (self.Ho + self.Hc(t))\n",
    "\n",
    "    def H_tilde(self, t_index):\n",
    "        t = t_index\n",
    "        return (self. Ho + self.Hc_tilde(t))\n",
    "\n",
    "    def update_U (self, t_index):\n",
    "        t = t_index\n",
    "        self.U[t+1] = np.dot(LA.expm(-1j * self.H(t) * self.dt), self.U[t])\n",
    "\n",
    "    def update_B (self, t_index):\n",
    "        t = t_index\n",
    "        self.B[t-1] = np.dot( self.B[t], LA.expm(-1j * self.H_tilde(t) * self.dt))\n",
    "\n",
    "    def update_E(self, t_index):\n",
    "        t=t_index\n",
    "\n",
    "        EIYpart1 = (1-self.delta2) * self.EIY_tilde[t-1]\n",
    "        EIYpart2 = -self.delta2 * self.lambda_1 * np.imag( np.trace(np.dot(self.B[t-1], np.dot( self.sIY, self.U[t]) ) ) )/ self.alpha2\n",
    "        self.EIY[t] = -(EIYpart1 + EIYpart2)\n",
    "\n",
    "        EZIpart1 = (1-self.delta3) * self.EZI_tilde[t-1]\n",
    "        EZIpart2 = -self.delta3 * self.lambda_1 * np.imag( np.trace(np.dot(self.B[t-1], np.dot( self.sZI, self.U[t]) ) ) )/ self.alpha3\n",
    "        self.EZI[t] = -(EZIpart1 + EZIpart2)\n",
    "\n",
    "        EIZpart1 = (1-self.delta4) * self.EIZ_tilde[t-1]\n",
    "        EIZpart2 = -self.delta4 * self.lambda_1 * np.imag( np.trace(np.dot(self.B[t-1], np.dot( self.sIZ, self.U[t]) ) ) )/ self.alpha4\n",
    "        self.EIZ[t] = -(EIZpart1 + EIZpart2)\n",
    "\n",
    "\n",
    "    def update_E_tilde(self,t_index):\n",
    "        t=t_index\n",
    "\n",
    "        EIYpart1 = (1-self.delta2) * self.EIY[t]\n",
    "        EIYpart2 = -self.delta2 * self.lambda_1 * np.imag( np.trace(np.dot(self.B[t], np.dot( self.sIY, self.U[t]) ) ) )/ self.alpha2\n",
    "        self.EIY_tilde[t] = -(EIYpart1 + EIYpart2)\n",
    "\n",
    "        EZIpart1 = (1-self.delta3) * self.EZI[t]\n",
    "        EZIpart2 = -self.delta3 * self.lambda_1 * np.imag( np.trace(np.dot(self.B[t], np.dot( self.sZI, self.U[t]) ) ) )/ self.alpha3\n",
    "        self.EZI_tilde[t] = -(EZIpart1 + EZIpart2)\n",
    "\n",
    "        EIZpart1 = (1-self.delta4) * self.EIZ[t]\n",
    "        EIZpart2 = -self.delta4 * self.lambda_1 * np.imag( np.trace(np.dot(self.B[t], np.dot( self.sIZ, self.U[t]) ) ) )/ self.alpha4\n",
    "        self.EIZ_tilde[t] = -(EIZpart1 + EIZpart2)\n",
    "\n",
    "    def evolution_U(self,string='not initial'):\n",
    "        if string == 'initial':\n",
    "            for t in range(0,self.steps-1):\n",
    "                self.update_U(t)\n",
    "        else:\n",
    "            for t in range(0,self.steps-1):\n",
    "                self.update_E(t)\n",
    "                self.update_U(t)\n",
    "            t = self.steps-1\n",
    "            self.update_E(t)\n",
    "\n",
    "    def evolution_B(self):\n",
    "        for t in range(self.steps-1,0,-1):\n",
    "            self.update_E_tilde(t)\n",
    "            self.update_B(t)\n",
    "        t = 0\n",
    "        self.update_E_tilde(t)\n",
    "\n",
    "    def O(self,step):\n",
    "        t = step\n",
    "        return( np.dot(self.UT.conj().T, self.U[t] ))\n",
    "    # Some methods might seem redundant but they are maintained to solve complicated optimal control problems in future\n",
    "    # Better Structured Toolboxes can give \n",
    "    def Overlap(self, t_index ):\n",
    "        t = t_index\n",
    "        return( np.abs(np.trace(self.O(t))))\n",
    "\n",
    "    def distance(self,t_index):\n",
    "        t= t_index\n",
    "        return(LA.norm(self.UT - self.U[t], 'fro'))\n",
    "\n",
    "    def Run_Krotov(self, num_iter):\n",
    "        T = self.steps-1\n",
    "        self.evolution_U('initial')\n",
    "        self.overlap = np.zeros([num_iter,1], dtype = 'float64')\n",
    "        self.dis = np.zeros([num_iter,1], dtype = 'float64')\n",
    "\n",
    "        for i in range(0,num_iter):\n",
    "            print (\"Cycle : \" + str(i))\n",
    "            #print (str(self.overlap[i]))\n",
    "            self.B[T] = self.UT.conj().T\n",
    "            self.evolution_B()\n",
    "            self.evolution_U()\n",
    "            self.overlap[i] = self.Overlap(T)\n",
    "            self.dis[i] = self.distance(T)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x210b7000358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if __name__ == '__main__':\n",
    "    # INTITIALIZE : J,lambda_1,ti,tf,steps\n",
    "    k = Krotov(0.1, 5e-1, 0, 8,5000)\n",
    "    k.Run_Krotov(1000)\n",
    "    s = Krotov(0.1, 5e-1 ,0, 8,5000)\n",
    "    s.Run_Krotov(0)\n",
    "            \n",
    "    plt.figure(1)\n",
    "    plt.title('Overlap Vs Iteration')\n",
    "    plt.ylabel('Overlap')\n",
    "    plt.xlabel('Iteration')\n",
    "    plt.plot(np.log(np.abs(k.overlap)/4))\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x210b88a6940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(2)\n",
    "plt.bar(s.t,s.EIZ,linewidth = 0.01, width = s.dt)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x210b5af5710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(3)\n",
    "plt.title('Overlap Vs Iteration')\n",
    "plt.ylabel('Overlap')\n",
    "plt.xlabel('Iteration')\n",
    "plt.loglog(1-np.abs(k.overlap)/max(np.abs(k.overlap)))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now exporting variables to matlab to have comparsion with GRAPE and other standard Implementations\n",
    "\n",
    "\n",
    "\n",
    "import scipy.io as sio\n",
    "\n",
    "\n",
    "Krotov_data = { };\n",
    "Krotov_data['J'] = k.J\n",
    "Krotov_data['lambda_1'] = k.lambda_1 \n",
    "Krotov_data['ti'] = k.ti\n",
    "Krotov_data['tf'] = k.tf\n",
    "Krotov_data['steps'] = k.steps\n",
    "Krotov_data['t'] = k.t\n",
    "Krotov_data['dt'] = k.dt\n",
    "\n",
    "Krotov_data['U'] = k.U\n",
    "Krotov_data['B'] = k.B\n",
    "\n",
    "Krotov_data['EYI'] = k.EYI;\n",
    "Krotov_data['EIY'] = k.EIY;\n",
    "Krotov_data['EIZ'] = k.EIZ;\n",
    "Krotov_data['EZI'] = k.EZI;\n",
    "\n",
    "Krotov_data['EYI_tilde'] = k.EYI_tilde;\n",
    "Krotov_data['EIY_tilde'] = k.EIY_tilde;\n",
    "Krotov_data['EIZ_tilde'] = k.EIZ_tilde;\n",
    "Krotov_data['EZI_tilde'] = k.EZI_tilde;\n",
    "\n",
    "Krotov_data['dis'] = k.dis;\n",
    "Krotov_data['overlap'] = k.overlap;\n",
    "\n",
    "\n",
    "Krotov_data['sI'] = k.I;\n",
    "Krotov_data['sX'] = k.sX;\n",
    "Krotov_data['sY'] = k.sY;\n",
    "Krotov_data['sZ'] = k.sZ;\n",
    "Krotov_data['sIY'] = k.sIY;\n",
    "Krotov_data['sYI'] = k.sYI;\n",
    "Krotov_data['sZI'] = k.sZI;\n",
    "Krotov_data['sIZ'] = k.sIZ;\n",
    "\n",
    "Krotov_data['sIZ'] = k.delta1\n",
    "Krotov_data['sIZ'] = k.alpha1 \n",
    "Krotov_data['sIZ'] = k.delta2 \n",
    "Krotov_data['alpha2'] = k.alpha2\n",
    "Krotov_data['delta3'] = k.delta3\n",
    "Krotov_data['alpha3'] = k.alpha3\n",
    "Krotov_data['delta4'] = k.delta4\n",
    "Krotov_data['alpha4'] = k.alpha4 \n",
    "            \n",
    "            \n",
    "            \n",
    "sio.savemat('Krotov_file2', Krotov_data)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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