quantum_time_evolution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6e99be4b-ebbf-40c3-aff6-2846593b09d4",
   "metadata": {},
   "source": [
    "If running the code on anything except the IBM Quantum Lab, uncomment the following cell to install the required packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a8e60a14-0a20-4295-8602-0e6e9dd09f94",
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install qiskit\n",
    "# !pip install pylatexenc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ced062a3-02e9-4d1b-ad9f-abfbd212d575",
   "metadata": {},
   "source": [
    "If running the code on IBM Quantum Lab, start running the cells from here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7807974f-c9a7-44df-a66d-3eaa35b5fa57",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import *\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.circuit.library import QFT\n",
    "import pylatexenc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b90833c-e112-4dc5-a368-011680925a97",
   "metadata": {},
   "source": [
    "We define some constants required for defining the problem. Feel free to play around with the constants in the next cell to modify the model problem.\n",
    "\n",
    "**The number of qubits should not exceed 6**\n",
    "> Due to the current limitation of the number of qubits available to us, we constraint our problem to the use of only 7 qubits (6 qubits to make the req. spatial grid and 1 ancillary qubit). 6 qubits allow us to form 2^6=64 grid points. In the future as more qubits become available, we can easily scale our model to more complex simulation problems."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d630d32a-a02b-4bdc-97f5-ed8a5913b109",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Number of qubits\n",
    "n=6\n",
    "\n",
    "#Circuit \n",
    "phi=0.1 #time step\n",
    "iterations=30 #iterations\n",
    "\n",
    "#Potential\n",
    "V=1.75 \n",
    "\n",
    "#Spatial Grid\n",
    "N=2**n #grid points\n",
    "xMin=-4\n",
    "xMax=4\n",
    "x = np.linspace(xMin,xMax, num=N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e3b8372-1b1b-41e6-b46f-b5d142c23585",
   "metadata": {},
   "source": [
    "We now define a wavefunction which needs to simulated for our model problem. For simplicity, we consider a Gaussian wavefunction, however, more complex wavefunctions can also be simulated by simply modifying the following cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a57276d1-60ef-40c8-b946-e75217304578",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f396f778910>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jdGj20b24yCy/HOgpl5wytNrj59p5gy6zfHOgp1y3eugAE6NlPxQ1yzEHespVa3Uk2DC8utOK2o2PDfPT87M0vPzfLJcc6ClXae20KOmyP2t8tMx8Izjjo+jMcsmBnnLVLmzMlfBcdLN8c6CnXDf2Qk8sBLofjJrlkgM95c7PXv5Oi4mJseZ+Ll5cZJZPDvSUq/RghO7FRWb55EBPuWqt3pU56ABXrB9iaFBeXGSWUw70lOtmD10SV414LrpZXjnQU645y+Xyts5tNzHmQDfLKwd6ijUa0ZUDotuNjw470M1yqqNAl7Rb0jFJxyXdvcT7r5f0fUl1Sb/Z/TKLaWGnxfLlrxJNNPdzcQ/dLI+WDXRJg8B9wK3ATuAOSTsX3fYk8G7gc90usMheOH6uey2X8bEyPz1fI8LL/83yppMR+i7geEQ8HhGzwAPAnvYbIuJvI+JhoNGDGgurmpxW1NWWS5m5+eCsl/+b5U4ngb4VONF2Pd16bcUk3SnpoKSDp0+fXs1HFEqyF/pYl2a5QNth0e6jm+XOmj4UjYj7I2IqIqYmJibW8qszKdkLvZsj9ImFxUXuo5vlTSeBfhLY1nY92XrNeqybe6Enxsdage4RulnudBLoB4Adkq6XNAzcDuztbVkGUKn1INC9QZdZbi0b6BFRB+4C9gNHgQcj4oikeyXdBiDpH0qaBt4OfFLSkV4WXRS9GKFvWj9EaUDuoZvlUEdJERH7gH2LXrun7ecDNFsx1kXnWyP0kS4G+sCAuMqLi8xyyStFU6xaq1MuDTBc6u5v0/ho2Rt0meWQAz3FKl3cabHduA+LNsslB3qKdXOnxXbN5f8OdLO8caCnWLc35kqMjw3zTHXWy//NcsaBnmK9GqFPjJaZnW9wrjWLxszywYGeYpUu74We8FF0ZvnkQE+x87V6V7fOTSwsLvKDUbNccaCnWK966BNjDnSzPHKgp1izh96Llktrx0W3XMxyxYGeUrX6PLPzjZ7MQ9+8YZjBAXlxkVnOONBTqhf7uCQGBsSVI17+b5Y3DvSUqvZgp8V2Xi1qlj8O9JRKTivqxUNRaPbRT7vlYpYrDvSU6vUIfcLL/81yx4GeUud73XIZa7ZcvPzfLD8c6CnVi/NE242PDlOrNxZORTKz7HOgp1TSQx/rVcultbjo6bMzPfl8M1t7DvSU6vUIfeq6KwH4+tFTPfl8M1t7DvSUeuL0eTZtGGL9UPf3cgHYduUGfv66zXzpB9Puo5vlhAM9pQ5Pn+GmyU1I6tl3/NprtvLjp6sc/UmlZ99hZmvHgZ5C52t1fvx0hZu2berp97zlVS+lNCC+fOhkT7/HzNaGAz2FfnjyLI2Am7dd0dPvuXJkmF9++QRfPvT3zDfcdjHLOgd6Ch2ePgPAqyc39fy79ty8lafOzfDQEz/t+XeZWW850FPo8ImzTG5ev3AQRS+98R9sYbRc4i9/4LaLWdY50FPo0IkzPe+fJ9YPD/Irr7iarz7yFDNz82vynWbWGw70lHmmWuPkmee5eQ3aLYm3vWYrlVqdb/zIc9LNssyBnjIPt/rnazVCB/jFG67iJWNlt13MMs6BnjKHTpxlQPDKrRvX7DsHB8Sv3nQN3zx2ijMXvKWuWVY50FPm8Ikz3LhljA3DvVnyfzFve81W5uaDfY88tabfa2bd01GgS9ot6Zik45LuXuL9sqQvtN5/SNL2rldaABHB4ekz3LyG7ZbEK67ZyA0TI3zhwJM+ycgso5YNdEmDwH3ArcBO4A5JOxfd9h7guYh4GfAnwB91u9AiePLZC5y5MLem/fOEJN71uu0cnj7Lro98nX/2yb/hM99+gpNnnl/zWsxsdTr5e/0u4HhEPA4g6QFgD/Bo2z17gH/f+vmLwJ9JUvRg16cHD57gU//38W5/7KoIMTAgBtTsQ0ti0/ohJjevZ9uVG5jcvJ7JzRt4xTUbGRpc/i9Dh06cAeCmNZzh0u6dt1zH1HVXsv/IU+w/8hT3fuVR7v3Ko1y9cR2lQTE4IAal1r9rX0o0y4V/9YYd/OpN13T9czsJ9K3AibbraeAXLnZPRNQlnQWuAp5pv0nSncCdANdee+2qCt60fogbJkZX9Wu7rRFBI6DRCBoRzAc8e36Wh6fP8NyFuYX7dr50I5+4/WZu3DJ2yc87fOIs64YGuHFLf/79JLHzmo3svGYj//pNN/LEM+fZf+Qpjp+q0mgE8xHMN8LbBJhdpivWD/Xkc9f0yVtE3A/cDzA1NbWqVHjzK67mza+4uqt19UK1Vmf6uQs8Mn2Wj371R7z1T7/NH+z+OX7rddsZGFh6eHt4+gyv2noFpQ5G82vh+vERfucf39DvMsysQ50kx0lgW9v1ZOu1Je+RVAKuAAq9OchoucTPXb2Rt09t43/9/ut5/Y5xPvyVR3nHpx/i75foS8/NN/jhybN9a7eYWfZ1EugHgB2Srpc0DNwO7F10z17gXa2ffxP4Ri/651k1MVbmP/+LKT7666/i0Ikz/MonvsX/O/4z3SiOPVWhVm/05YGomeXDsoEeEXXgLmA/cBR4MCKOSLpX0m2t2z4NXCXpOPB+4EVTG4tOErfvupavvu8f8dIr1vGePz/Id594duH9ZIfFfkxZNLN86KhZGxH7IuLGiLghIj7Seu2eiNjb+nkmIt4eES+LiF3JjBh7seuuGuGzv30L12xax2/9l+/y/SefA5oLiq4cGWZy8/o+V2hmWZWOp28FMzFW5nPvvYXxsTLv+sx3eWT6LIdPnOWmySt6euScmeWbA71Ptmxcx+feewtXrB/inZ95iMdO9f7IOTPLNwd6H23dtJ7Pv/cW1g8N0oi13WHRzPJnbXeAshfZduUGPv/eW/iL70/zuhuu6nc5ZpZhDvQU2D4+wgfe/PJ+l2FmGeeWi5lZTjjQzcxywoFuZpYTDnQzs5xwoJuZ5YQD3cwsJxzoZmY54UA3M8sJ9Wvbckmngb9b5S8fZ9HxdinhulbGda1cWmtzXStzOXVdFxETS73Rt0C/HJIORsRUv+tYzHWtjOtaubTW5rpWpld1ueViZpYTDnQzs5zIaqDf3+8CLsJ1rYzrWrm01ua6VqYndWWyh25mZi+W1RG6mZkt4kA3M8uJzAe6pA9ICknj/a4FQNKHJT0s6ZCkv5Z0Tb9rApD0MUk/atX2JUmb+l0TgKS3SzoiqSGp79PLJO2WdEzScUl397seAEmfkXRK0g/7XUs7SdskfVPSo63fw/f1uyYASeskfVfS4VZd/6HfNbWTNCjpB5K+0u3PznSgS9oGvBl4st+1tPlYRLw6Im4GvgLc0+d6El8DXhkRrwZ+DHywz/Ukfgj8OvCtfhciaRC4D7gV2AncIWlnf6sC4L8Cu/tdxBLqwAciYidwC/C7KfnvVQPeEBE3ATcDuyXd0t+Sfsb7gKO9+OBMBzrwJ8C/AVLzZDcizrVdjpCS2iLiryOi3rr8DjDZz3oSEXE0Io71u46WXcDxiHg8ImaBB4A9fa6JiPgW8Gy/61gsIn4SEd9v/VyhGVJb+1sVRFO1dTnU+icVfw4lTQJvAT7Vi8/PbKBL2gOcjIjD/a5lMUkfkXQC+OekZ4Te7l8CX+13ESm0FTjRdj1NCgIqCyRtB14DPNTnUoCFtsYh4BTwtYhIRV3AJ2gOQhu9+PBUHxIt6evA1Uu89SHg39Jst6y5S9UVEV+OiA8BH5L0QeAu4N+loa7WPR+i+Vflz65FTZ3WZdklaRT4C+D3F/0NtW8iYh64ufWs6EuSXhkRfX0GIemtwKmI+J6kX+7Fd6Q60CPijUu9LulVwPXAYUnQbB98X9KuiHiqX3Ut4bPAPtYo0JerS9K7gbcC/yTWcAHCCv579dtJYFvb9WTrNbsISUM0w/yzEfE/+l3PYhFxRtI3aT6D6PdD5V8CbpP0T4F1wEZJ/y0i3tGtL8hkyyUiHomIl0TE9ojYTvOvxq9dizBfjqQdbZd7gB/1q5Z2knbT/KvebRFxod/1pNQBYIek6yUNA7cDe/tcU2qpOZr6NHA0Ij7e73oSkiaSWVyS1gNvIgV/DiPigxEx2cqs24FvdDPMIaOBnnIflfRDSQ/TbAmlYioX8GfAGPC11pTK/9TvggAkvU3SNPCLwF9J2t+vWloPje8C9tN8wPdgRBzpVz0JSZ8H/gZ4uaRpSe/pd00tvwS8E3hD6/+pQ63RZ7+9FPhm68/gAZo99K5PEUwjL/03M8sJj9DNzHLCgW5mlhMOdDOznHCgm5nlhAPdzCwnHOhmZjnhQDczy4n/D8q+N2fzxggPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Wavefunction\n",
    "mu=-2.25\n",
    "psi= (1/(np.sqrt(2*np.pi)*2*0.4)*np.exp(-(0.5*(x-mu)**2)/(2*0.016)))*np.exp(-300j*x)\n",
    "psi/= np.sqrt(np.sum(np.abs(psi**2)))\n",
    "plt.plot(x,psi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b879884-4349-4ea8-93f7-88b5fa3da80b",
   "metadata": {},
   "source": [
    "Next, we define the quantum well (potential barrier) in our model. The position of this quantum well is determined by the gates we apply the potential propagator to. In this model, we apply exp(i * V * phi) to a qubit, and hence use a phase gate parameterized by the value V * phi. The Potential and momentum operators are defined using the Split Operator Fourier Transform Algorithm. The first qubit in the circuit is defined as the ancillary qubit. Finally, we code a single time step of the split operator algorithm using all the propagators we defined before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "3fdc9078-5306-4d94-90f2-10633075d686",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1631.12x1890.28 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qubits=QuantumRegister(n+1)\n",
    "splitOp=QuantumCircuit(qubits,name=\"splitOp\")\n",
    "'''potential operator''' \n",
    "splitOp.ccx(3,4,0)\n",
    "splitOp.cp(V*phi,0,5)\n",
    "splitOp.ccx(3,4,0)\n",
    "splitOp.barrier()\n",
    "'''momentum operator'''\n",
    "splitOp.append(QFT(n),qubits[1:])\n",
    "for i in range(n):\n",
    "  splitOp.p(phi/2**(n-3+i), n-i)\n",
    "for i in range(n):\n",
    "  for j in range(i+1,n):\n",
    "    splitOp.cx(n-j,0)\n",
    "    splitOp.cx(n-i,0)\n",
    "    splitOp.p(phi*(2**(2-i-j)),0)\n",
    "    splitOp.cx(n-i,0)\n",
    "    splitOp.cx(n-j,0)\n",
    "splitOp.append(QFT(n,inverse=True),qubits[1:])\n",
    "splitOp.barrier()\n",
    "splitOp.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "359de983-b95e-42ca-ac48-e740d7e41f7e",
   "metadata": {},
   "source": [
    "Now, we build our final circuit based on the number of iterations defined at the beginning of the code. We initialize the gaussian wavefunction onto our qubits and then add the splitOp circuit for each time step. Each qubit (except the ancillary) is measured onto a classical bit. The circuit is run on Qiskit’s qasm_simulator (although a hardware backend could also be called for future works) and stored in the answer dictionary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4fbdd37e-37ff-4b35-81f2-36b2076502d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "q=QuantumRegister(n+1)\n",
    "c=ClassicalRegister(n)\n",
    "circuit=QuantumCircuit(q,c)\n",
    "'''initialization'''\n",
    "circuit.initialize(psi,q[1:])\n",
    "circuit.barrier()\n",
    "'''time steps'''\n",
    "for i in range(iterations):\n",
    "  circuit.append(splitOp,q[:])\n",
    "'''measurement'''\n",
    "for i in range(1,n+1):\n",
    "  circuit.measure(i,i-1)\n",
    "#circuit.draw('mpl')\n",
    "answer = execute(circuit, backend=BasicAer.get_backend('qasm_simulator'), shots=5000).result().get_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d17f38e-369a-435f-98b2-819cd2ac2a74",
   "metadata": {},
   "source": [
    "In the final step, we plot our results on a histogram. The histogram presents a unique visualisation of a particle tunneling through a barrier from 001110 to 001111. This visualisation of the Quantum tunneling phenomenon is just one of the many possible use-cases of the Time evolution of quantum operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "df314746-290c-4bf8-bea3-a90add2939ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for a in range(N):\n",
    "    s = bin(a)[2:]\n",
    "    while len(s)!=6:\n",
    "        s='0'+s\n",
    "    if s not in answer.keys():\n",
    "        answer[s] = 0\n",
    "plot_histogram(answer, figsize = [20,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "095e72db-af78-4f54-8311-364a22e57784",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000000002\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_psi=np.zeros(N)\n",
    "count=0\n",
    "for key in sorted(answer.keys()):\n",
    "  new_psi[count]=answer[key]\n",
    "  count+=1\n",
    "new_psi=new_psi/np.sqrt(np.sum(psi**2))\n",
    "barrier=np.zeros(N)\n",
    "barrier[14:16]=20000\n",
    "print(np.sum(np.abs(psi**2)))\n",
    "plt.plot(x,new_psi)\n",
    "plt.plot(x,barrier)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d56a3d03-3588-44b5-9dfe-08648e147d59",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Qiskit v0.35.0 (ipykernel)",
   "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": "3.8.13"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}