Example-CompositeHamiltonian.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algebra: Composite-Hamiltonian and Time Evolution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. https://numpy.org/doc/stable/reference/routines.linalg.html\n",
    "2. http://qutip.org/docs/latest/guide/dynamics/dynamics-master.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qutip import *\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a Hamiltonian, we can calculate the unitary (non-dissipative) time-evolution of an arbitrary state vector |ψ0⟩ (psi0) using the QuTiP function ```qutip.sesolve```. It evolves the state vector and evaluates the expectation values for a set of operators expt_ops at the points in time in the list times, using an ordinary differential equation solver. \n",
    "\n",
    "Scrodinger Equation: $$i\\hbar\\frac{d}{dt}\\left|\\psi\\right> = H \\left|\\psi\\right>$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time evolution: <img src=\"https://miro.medium.com/max/1016/1*bupc_zDBvvA0jWG0GTejng@2x.png\" width=200 height=200> </img>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A . Single qubit System"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 1. Consider a single qubit hamiltonian constructed by implementing pauli x operator: \n",
    "$$H = 2 \\pi \\sigma_x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 6.283\\\\6.283 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0.         6.28318531]\n",
       " [6.28318531 0.        ]]"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# single qubit hamiltonian\n",
    "H =  2.0*np.pi * sigmax()\n",
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 2. Create  the initial state of the system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.]\n",
       " [1.]]"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#initial state of the single qubit system\n",
    "#psi0 = basis(2,0)\n",
    "psi0 = basis(2,1)\n",
    "#psi0 = (1/np.sqrt(2))*basis(2,0)+ (1/np.sqrt(2))*basis(2,1)\n",
    "psi0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 3. Create time array to conduct measurement time points during the evolution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.52631579,  1.05263158,  1.57894737,  2.10526316,\n",
       "        2.63157895,  3.15789474,  3.68421053,  4.21052632,  4.73684211,\n",
       "        5.26315789,  5.78947368,  6.31578947,  6.84210526,  7.36842105,\n",
       "        7.89473684,  8.42105263,  8.94736842,  9.47368421, 10.        ])"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "times = np.linspace(0.0, 10.0, 20)\n",
    "times"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 4. Simulate the time evolution by implementing ```sesolve``` function by supplying hamiltonian ```H```, initial state ```psi0```, time array ```times``` and list of operators ```[sigmaz(), sigmay()]``` representing what you want to measure as expectation value of."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = sesolve(H, psi0, times, [sigmaz(), sigmay()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 5. Explore the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Result object with sesolve data.\n",
       "--------------------------------\n",
       "expect = True\n",
       "num_expect = 2, num_collapse = 0"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 6. Where are the expectation value of the implemented operator for measurement during time evolution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([-1.        , -0.94581561, -0.78913418, -0.54693623, -0.24546751,\n",
       "         0.08260204,  0.40171988,  0.67730341,  0.87948895,  0.9863673 ,\n",
       "         0.98635446,  0.87945165,  0.67724451,  0.4016443 ,  0.08252413,\n",
       "        -0.24554292, -0.54700067, -0.78917951, -0.94583863, -1.        ]),\n",
       " array([ 0.00000000e+00,  3.24704211e-01,  6.14220851e-01,  8.37174272e-01,\n",
       "         9.69404818e-01,  9.96582612e-01,  9.15762600e-01,  7.35703806e-01,\n",
       "         4.75919309e-01,  1.64558631e-01, -1.64635573e-01, -4.75988221e-01,\n",
       "        -7.35758027e-01, -9.15795752e-01, -9.96589067e-01, -9.69385719e-01,\n",
       "        -8.37132169e-01, -6.14162600e-01, -3.24637165e-01,  7.13395936e-05])]"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.expect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 7 Plot the time evolution of the expection values of the implemented operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize = [20,4])\n",
    "plt.plot(result.times, result.expect[0])\n",
    "plt.plot(result.times, result.expect[1])\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Expectation values')\n",
    "plt.legend((\"sigmaz\", \"sigmay\"))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets repeat the same steps for multi-qubit system. Before that, we need to construct the composite hamiltonian representing the quantum mechanical system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### B. Constructing composite Hamiltonians\n",
    "\n",
    "#### 1. Two coupled qubits\n",
    "\n",
    "Consider a Hamiltonial of a 2 qubits system representated by composite hamiltonian shwn below. The first term represents the contribution of second qubit Z spin operator (sigmaz()) while first qubit remains inactive(identity); the second term represents the contribution of first qubit spin operator while second qubit remains inactive(identity); the third represents the contribution of first and second qubit X spin operator.\n",
    "\n",
    "$H = 0.2(\\sigma_z \\otimes I) + 0.4(I \\otimes \\sigma_z) + \\frac{1}{4} (\\sigma_x \\otimes \\sigma_x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "H2 = 0.2*np.pi*tensor(sigmaz(), identity(2)) \\\n",
    "    + 0.4*np.pi*tensor(identity(2),sigmaz()) \\\n",
    "    + 0.25 *np.pi*tensor(sigmax(), sigmax())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "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}1.885 & 0.0 & 0.0 & 0.785\\\\0.0 & -0.628 & 0.785 & 0.0\\\\0.0 & 0.785 & 0.628 & 0.0\\\\0.785 & 0.0 & 0.0 & -1.885\\\\\\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",
       "[[ 1.88495559  0.          0.          0.78539816]\n",
       " [ 0.         -0.62831853  0.78539816  0.        ]\n",
       " [ 0.          0.78539816  0.62831853  0.        ]\n",
       " [ 0.78539816  0.          0.         -1.88495559]]"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Three Coupled Qubit\n",
    "\n",
    "Consider a Hamiltonial of a 3 qubits system representated by composite hamiltonian shwn below. The first term represents the contribution of third qubit Z spin operator (sigmaz()) while rest of the qubits remains inactive(identity); the second term represents the contribution of second qubit spin operator while remaining qubits inactive and so on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H = (\\sigma_z \\otimes I \\otimes I) + (I \\otimes \\sigma_z \\otimes I) + (I  \\otimes I  \\otimes \\sigma_z ) +  1/2 (\\sigma_x \\otimes \\sigma_x \\otimes I) +  1/4 (  I  \\otimes \\sigma_x \\otimes \\sigma_x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "H3 = (tensor(sigmaz(), identity(2), identity(2)) +\n",
    "     tensor(identity(2), sigmaz(), identity(2)) +\n",
    "    tensor(identity(2), identity(2), sigmaz()) +\n",
    "     0.5 * tensor(sigmax(), sigmax(), identity(2)) +\n",
    "     0.25 * tensor(identity(2), sigmax(), sigmax())) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "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}3.0 & 0.0 & 0.0 & 0.250 & 0.0 & 0.0 & 0.500 & 0.0\\\\0.0 & 1.0 & 0.250 & 0.0 & 0.0 & 0.0 & 0.0 & 0.500\\\\0.0 & 0.250 & 1.0 & 0.0 & 0.500 & 0.0 & 0.0 & 0.0\\\\0.250 & 0.0 & 0.0 & -1.0 & 0.0 & 0.500 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.500 & 0.0 & 1.0 & 0.0 & 0.0 & 0.250\\\\0.0 & 0.0 & 0.0 & 0.500 & 0.0 & -1.0 & 0.250 & 0.0\\\\0.500 & 0.0 & 0.0 & 0.0 & 0.0 & 0.250 & -1.0 & 0.0\\\\0.0 & 0.500 & 0.0 & 0.0 & 0.250 & 0.0 & 0.0 & -3.0\\\\\\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",
       "[[ 3.    0.    0.    0.25  0.    0.    0.5   0.  ]\n",
       " [ 0.    1.    0.25  0.    0.    0.    0.    0.5 ]\n",
       " [ 0.    0.25  1.    0.    0.5   0.    0.    0.  ]\n",
       " [ 0.25  0.    0.   -1.    0.    0.5   0.    0.  ]\n",
       " [ 0.    0.    0.5   0.    1.    0.    0.    0.25]\n",
       " [ 0.    0.    0.    0.5   0.   -1.    0.25  0.  ]\n",
       " [ 0.5   0.    0.    0.    0.    0.25 -1.    0.  ]\n",
       " [ 0.    0.5   0.    0.    0.25  0.    0.   -3.  ]]"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### C. Time Evolution with composite Hamiltonian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### How to generate a initial state vector?\n",
    "\n",
    "This is 2 qubit quantum mechanical system, there are 4 basis states $|00 \\rangle, |01 \\rangle, |10 \\rangle, |11 \\rangle$ in 4 dimentional complex vector space. All operators in 2 qubit system should be 4 by 4 matrices while state vector need to be 4 element column ket(bra) vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
       "Qobj data =\n",
       "[[1.]\n",
       " [0.]\n",
       " [0.]\n",
       " [0.]]"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi0 = basis(4, 0)\n",
    "psi0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q: Could we start with random ket vector?**\n",
    "- Answer: yes!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\1.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.]\n",
       " [1.]\n",
       " [0.]\n",
       " [0.]]"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 1\n",
    "psi1 = basis(4, 1)\n",
    "psi1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500\\\\0.500\\\\0.500\\\\0.500\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [1]], shape = (4, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.5]\n",
       " [0.5]\n",
       " [0.5]\n",
       " [0.5]]"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 2\n",
    "psi2 = (1/2)*basis(4, 0) + (1/2)*basis(4,1)  + (1/2)*basis(4,2) + (1/2)*basis(4,3) \n",
    "psi2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets perform the time evolution with two new operators for measurement (```m1-operator, m2-operator``` defined below in code block) of size 4 by 4 (why? remember, measurement operator in 2 qubit system also need to be 4 by 4 matrices)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [],
   "source": [
    "# time array\n",
    "times = np.linspace(0.0, 10.0, 100)\n",
    "\n",
    "# measurement operator\n",
    "m1_operator = tensor(identity(2), sigmaz())\n",
    "m2_operator = tensor(sigmax(), sigmay())\n",
    "\n",
    "# time evolution of state psi2 with hamiltonian H2 to calculate expectation \n",
    "# value of m-operator and m-2 operator at 100 different time points\n",
    "result = sesolve(H2, psi2, times, [m1_operator,m2_operator])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Result object with sesolve data.\n",
       "--------------------------------\n",
       "expect = True\n",
       "num_expect = 2, num_collapse = 0"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# array holding multiple subarray of results\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0.        , 0.01990965, 0.07693353, 0.16338415, 0.26780409,\n",
       "        0.37676296, 0.47694252, 0.55716702, 0.6100466 , 0.63296734,\n",
       "        0.62827241, 0.60261422, 0.56559699, 0.52794726, 0.49952837,\n",
       "        0.48753968, 0.49520857, 0.52119896, 0.55983745, 0.60211928,\n",
       "        0.63732295, 0.65495828, 0.64671514, 0.60807788, 0.5393257 ,\n",
       "        0.44574105, 0.33698063, 0.22570382, 0.12567867, 0.04967351,\n",
       "        0.00747984, 0.00439134, 0.04038908, 0.11016689, 0.20399138,\n",
       "        0.30925384, 0.41245688, 0.50130765, 0.56657378, 0.60339885,\n",
       "        0.61186652, 0.5967288 , 0.56635478, 0.53108657, 0.50128824,\n",
       "        0.48542398, 0.48849536, 0.51110591, 0.54931383, 0.59529942,\n",
       "        0.6387351 , 0.66862566, 0.6753056 , 0.65225216, 0.59740204,\n",
       "        0.51374158, 0.40906153, 0.29490684, 0.1848873 , 0.09262206,\n",
       "        0.0296538 , 0.00367407, 0.01735098, 0.06795116, 0.14781638,\n",
       "        0.24561427, 0.34815462, 0.44247004, 0.51781734, 0.56727093,\n",
       "        0.58864968, 0.5846312 , 0.56204482, 0.53047246, 0.50040267,\n",
       "        0.4812572 , 0.47963015, 0.49804245, 0.53442637, 0.58243045,\n",
       "        0.63249529, 0.67351942, 0.69483308, 0.68814418, 0.64912366,\n",
       "        0.57835608, 0.48148692, 0.36853161, 0.25245172, 0.1472267 ,\n",
       "        0.06573458, 0.01778779, 0.00864563, 0.0382465 , 0.10128381,\n",
       "        0.18811041, 0.28631891, 0.38273458, 0.46548989, 0.5258384 ]),\n",
       " array([ 0.        ,  0.24807532,  0.46250991,  0.61497901,  0.68691127,\n",
       "         0.67231624,  0.57853938,  0.42482815,  0.23895805,  0.05249073,\n",
       "        -0.10453705, -0.20860165, -0.24652328, -0.21750119, -0.13301915,\n",
       "        -0.01464653,  0.10988487,  0.21165762,  0.26575066,  0.25574337,\n",
       "         0.17677289,  0.03661915, -0.14537537, -0.34137929, -0.51963064,\n",
       "        -0.64971981, -0.70771236, -0.6802516 , -0.56694875, -0.38065373,\n",
       "        -0.14555266,  0.10659923,  0.34148914,  0.5276749 ,  0.64153252,\n",
       "         0.67090663,  0.61686403,  0.493268  ,  0.324255  ,  0.14004515,\n",
       "        -0.02820489, -0.15363968, -0.21815444, -0.21531163, -0.15124055,\n",
       "        -0.04337637,  0.08274019,  0.19805446,  0.27519744,  0.29340795,\n",
       "         0.24233764,  0.12408733, -0.0468794 , -0.24594165, -0.44228493,\n",
       "        -0.60396499, -0.7032264 , -0.72118534, -0.65108967, -0.49960562,\n",
       "        -0.28590896, -0.03872439,  0.20820059,  0.42144006,  0.57316865,\n",
       "         0.64550295,  0.63319037,  0.54420723,  0.39817726,  0.22288599,\n",
       "         0.04948365, -0.09281286, -0.18162714, -0.20511603, -0.1638308 ,\n",
       "        -0.0704398 ,  0.05263326,  0.17724956,  0.27458447,  0.32028959,\n",
       "         0.29890787,  0.20678744,  0.05299223, -0.14195583, -0.34930263,\n",
       "        -0.53672363, -0.67364595, -0.7363421 , -0.71194204, -0.60068927,\n",
       "        -0.41605836, -0.18270779,  0.06739733,  0.30005268,  0.48423444,\n",
       "         0.5969749 ,  0.62688952,  0.5757772 ,  0.45803793,  0.29801709])]"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# expectation value of m1 and m2 operator at 20 different time point\n",
    "result.expect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize = [20,4])\n",
    "plt.plot(result.times, result.expect[0])\n",
    "plt.plot(result.times, result.expect[1])\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Expectation values')\n",
    "plt.legend((\"m1-operator\", \"m2-operator\"))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "1. [Pauli basis for any 2 by 2 matrices](https://physics.stackexchange.com/questions/292102/how-do-one-show-that-the-pauli-matrices-together-with-the-unit-matrix-form-a-bas)"
   ]
  }
 ],
 "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": "3.7.3"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}