Demo_phase&modified_vs_boolean.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 align=\"center\">\n",
    "\tFurther optimizations of Grover’s Search algorithm\n",
    "</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ibmqfactory.load_account:WARNING:2020-07-07 17:13:56,138: Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    }
   ],
   "source": [
    "from qiskit import *\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "from qiskit.compiler import transpile\n",
    "# Loading your IBM Q account(s) + hardware\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider('ibm-q')\n",
    "device=provider.get_backend('ibmq_16_melbourne')\n",
    "# Simulator\n",
    "simulator = Aer.get_backend('qasm_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run boolean_grover.py # boolean_grover()\n",
    "%run phase&modified_grover.py # phase_grover()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nowadays, one of the critical issues to implement quantum algorithms is the required number of elementary gates, qubits, and delay. Current quantum computers and simulators are mainly prototypes, and there is a lack of computational resources. Therefore, it is necessary to optimize the quantum operations to reduce the necessary number of gates and qubits. This work target the oracle and diffuser part of Grover's algorithm where I represent an optimization of them. A quantitative analysis has been performed on the number of qubits, circuit depth, number of gates.\n",
    "\n",
    "The oracle plays an important role in Grover's circuit, where it occurs two times, one in the so called the oracle part, and the other in the diffuser part.\n",
    "\n",
    "As we saw in previous code (the boolean_grover), we implemented the boolean oracle (BO) type for the Grover's circuit, which relies on an additional qubit to carry out the difference of phase on the state of interest. Whereas there is another type of oracle; the phase oracle (PO), this latter don't use any ancillary qubit, it dephase the target ket directly by applying a Z gate on the last qubit (multiply its amplitude by $e^{i\\pi}$). Hence, the PO is better than the BO since it uses fewer qubits to run.\n",
    "\n",
    "The next step is implementing it in the quantum circuit, to do that, the obvious thing is the multi conditioned qubits gate Fig1, but this latter, when transpiled to be run on quantum hardware, will show a high circuit depth which doesn't play in our favor, because the circuit exceeds the limits regarding the coherence time of the quantum computer currently used. So this is a reason why it would be interesting to increase that time to do like those jobs efficiently; it is a good thing to have a very long coherence time so you can fit all your gates $-$in recent quantum superconducting qubits hardware, the highest-coherence qubits fabricated today is around the 100 microseconds. On the other hand, searching for a long time is not the only interest, nowadays scientists are interested in the question of how many operations can we fit within that time? where each of those gates takes some time to apply, so it's a question of how much time do those operations take relative to the coherence time that the qubit has, thus we need to be able to apply those operations very quickly. Decreasing the circuit depth is mandatory to contribute achieving that goal.\n",
    "\n",
    "<img src=\"5_noancilla.png\" alt=\"drawing\" width=\"200\" label=\"figure 1\"/>\n",
    "\n",
    "Another solution rather than expanding circuit depth exponentially is to use ancilla qubit. All we need to use is multiple two-qubits Toffoli gates (`ccx`), each of them can be decomposed to 15 elementary gates, 6 CNOT gates among them, acting just only on the pair of qubits Fig2 (from Mike & Ike book)\n",
    "\n",
    "<img src=\"5_ ancilla.png\" alt=\"drawing\" width=\"800\" label=\"figure 2\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see how many CCNOT when we use ancilla qubit, it is cheaper nevertheless it's still extremely expensive, because increasing the number of controlled qubits will use more ancillas which is out of the scope of the hardware implementation.\n",
    "\n",
    "This is why thinking of decreasing the number of ancillary qubits in the oracle is mandatory. Eventually, this is what I did, playing with those two-qubit Toffoli gates I figure out that the Fig2 can be implemented with 9 qubits rather than 10, hence we reduce the nubmer of qubits (we are going to see by using the phase oracle we reduce the number of qubits by 3 (2 in case of three qubits) compared with the boolean_grover code which uses the boolean oracle and the Mike & Ike $C^n(U)$ implementation) and also the depth since we are going to cancel one Toffoli gate and a the control-U (again by using the phase oracle we reduce the number of ccx by three (and two in the case of three qubits) compared with the previous file which uses the boolean oracle and the Mike & Ike $C^n(U)$ implementation).\n",
    "\n",
    "### -The optimized Oracle:\n",
    "As we can see below the number of qubits is reduced by one and this new design is applicable for n multi-qubit control gate.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 719.992x626.08 with 1 Axes>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "########################### Mike & Ike $C^n(U)$ design: n=5 qubits control gate ###########################\n",
    "# ***** Target qubit is q9 *****\n",
    "s0=boolean_oracle(['11111'], 'ancilla')\n",
    "s0.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 719.992x565.88 with 1 Axes>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "############################## New design n=5-qubits control gate ##############################\n",
    "# ***** Target qubit is q5 *****\n",
    "s=oracle(['111111'], 'ancilla')\n",
    "s.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the new design implementation, ignore the two Hadamard gate (they are added because $HXH=Z$ and this concern the phase oracle), also the length of digits inside the functions of the Mike & Ike design is 4 and not 5 because I used the function boolean_grover circuit which uses one additional qubit, hence she implement 5-qubit control gate.\n",
    "\n",
    "An exceptional case is the three control qubit where it uses two Toffoli gate rather than four following the Mike & Ike design, it is implemented as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 358.792x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "############################## New design 3-qubits control gate ##############################\n",
    "# ***** Target qubit is q2 *****\n",
    "s1=oracle(['111'], 'ancilla')\n",
    "s1.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 479.192x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "############################## Mike & Ike design 3-qubits control gate ##############################\n",
    "# ***** Target qubit is q5 *****\n",
    "s2=boolean_oracle(['111'], 'ancilla')\n",
    "s2.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### -The optimized diffuser\n",
    "In this part there is a set of operation that realize the transition from a difference of phase (made by the oracle) to a difference of amplitude (inversion about the mean):\n",
    "\n",
    "   1-Cancel the superposition by a layer of H gate let's calle it A\n",
    "\n",
    "   2-Multiply the amplitude of the $|0>_n$ state by -1, this is called a mirror operation $M_0=X^{\\otimes n} M_1 X^{\\otimes n}$.\n",
    "    \n",
    "   3-Restoring the superposition by another layer of H gate called $A^\\dagger$, which increases the probability of seeing the desired state.\n",
    "    \n",
    "The overall effect is $D=-AM_0A^\\dagger$ in the standard version of Grover's algorithm $A=H$ whereas in this paper [[1](https://arxiv.org/abs/2005.06468)] they assign to it another operation; whereby their main achievement is a generalization of the inversion about the mean step, thus rather than canceling the superposition they go forward to another state that makes the reflection easier. They succeeded to combine the action of the first layer of step 1 $H^{\\otimes n}$ with the first layer of step 2 $X^{\\otimes n}$ into a more efficient operator B where the Grover diffuser turn into $D=B^\\dagger M_B B$. They supposed an operator B such that $BA=X^{\\otimes n}$, then $A^\\dagger=X^{\\otimes n} B$ and $A=B^\\dagger X^{\\otimes n}$ then the Grover diffusion becomes: $$\\begin{aligned}\n",
    "D &=A M_{0} A^{\\dagger} \\\\\n",
    "&=B^{\\dagger} X^{\\otimes n} M_{0} X^{\\otimes n} B \\\\\n",
    "&=B^{\\dagger} X^{\\otimes n} X^{\\otimes n} M_{1} X^{\\otimes n} X^{\\otimes n} B \\\\\n",
    "&=B^{\\dagger} M_{1} B\n",
    "\\end{aligned}$$\n",
    "In this case, $M_B=M_1$, which uses fewer gates than $M_0$, therefore avoid the $X$ gates on either side of the multi-control gate. The modified version of the algorithm set $B=R_x(\\pi/2)$ and $B^\\dagger=R_x(-\\pi/2)$; in general this leads to save $2n$ X gates per mirror operation.\n",
    "\n",
    "Hence the modification is as follow: $HX \\rightarrow R_x(\\pi/2)$ and $X^\\dagger H^\\dagger \\rightarrow R_x(-\\pi/2)$\n",
    "\n",
    "The preparation layer is also replaced: $H \\rightarrow R_x(\\pi/2)$\n",
    "\n",
    "And now let's do a comparison between the boolean Grover's circuit and phase+modified Grover's circuit by evaluating the circuit depth, widht and quantum cost ( this latter is done by the transpiler where it is the procedded step before running the circuit on the quantum hardware, it does 2 main things: \n",
    "\n",
    "1-Expresses high-level gate definitions in terms of the basis gates actually supported by the quantum hardware, in this case is the `ibmq_16_melbourne`.\n",
    "\n",
    "2-Optimizes the code. )\n",
    "\n",
    "### 1-Phase oracle + new design Grover's circuit evaluation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit width 5\n",
      "Count of operations OrderedDict([('rx', 28), ('ccx', 18), ('h', 12), ('measure', 4)])\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1683.19x806.68 with 1 Axes>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phase=grover(['1111'], 'ancilla',3)\n",
    "print('Circuit width', phase.width() -4) # the method will compute the classical registers wires+the quantum ones,\n",
    "                                        #the quantum registers are what matters us, this is why I subtract 4.\n",
    "print('Count of operations', phase.count_ops())\n",
    "phase.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Phase circuit depth =  336\n",
      "Number of operations    OrderedDict([('cx', 305), ('u1', 113), ('u2', 42), ('measure', 4), ('barrier', 1)])\n"
     ]
    }
   ],
   "source": [
    "tranpile1= transpile(phase, device)\n",
    "print('Phase circuit depth = ',tranpile1.depth())\n",
    "print('Number of operations   ', tranpile1.count_ops())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\Rightarrow$ The $Circuit\\;depth = 336$ and the $Quantum\\;cost=305+113+42=460$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2-Boolean oracle Grover's circuit evaluation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit width 8\n",
      "Count of operations OrderedDict([('ccx', 30), ('h', 30), ('x', 24), ('cx', 6), ('u2', 5), ('measure', 4), ('u3', 1)])\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 1683.19x1769.88 with 1 Axes>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boolean=boolean_grover(['1111'], 'ancilla',3)\n",
    "print('Circuit width', boolean.width() -4)\n",
    "print('Count of operations', boolean.decompose().count_ops())\n",
    "boolean.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boolean circuit depth =  588\n",
      "Number of operation OrderedDict([('cx', 592), ('u1', 196), ('u2', 63), ('measure', 4), ('u3', 3), ('barrier', 1)])\n"
     ]
    }
   ],
   "source": [
    "transpile2= transpile(boolean, device)\n",
    "print('Boolean circuit depth = ',transpile2.depth())\n",
    "print('Number of operation', transpile2.count_ops())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\Rightarrow$ The $Circuit\\;depth = 588$ and the $Quantum\\;cost=592+196+63+3=854$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's us calculate the difference between the two circuits:\n",
    "\n",
    "$\\Rightarrow$ The $Circuit\\;depth\\;diff = 588-336=252$, the $Quantum\\;cost\\;diff=854-460=394$ and the $Circuit\\;width\\;diff=8-5=3$\n",
    "\n",
    "**The $Circuit\\;depth\\;diff$ and the $Quantum\\;cost\\;diff$ will grow up exponentially with the number of qubits, whereas the $Circuit\\;width\\;diff$ will be always different by 3 (2 for the case of three qubits) which means that we saved three qubits (two qubits for the case of three qubits) and reduces the number of gates**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test of the *Phase oracle + new design* Grover's circuit\n",
    "I will do the test with the `ancilla` circuit because the major modification are done on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'110': 7, '011': 966, '100': 4, '001': 7, '000': 11, '111': 8, '101': 9, '010': 12}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "######################## three qubits test ########################\n",
    "test1=grover(['011'],'ancilla',2)\n",
    "count1 = execute(test1,simulator).result().get_counts()\n",
    "print(count1)\n",
    "plot_histogram(count1,color='limegreen')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'111011': 1, '010000': 1, '010101': 1, '110010': 1020, '000001': 1}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "######################## Six qubits test ########################\n",
    "test2=grover(['110010'],'ancilla',6)\n",
    "count2 = execute(test2,simulator).result().get_counts()\n",
    "print(count2)\n",
    "plot_histogram(count2,color='c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "######################## eight qubits test with three solutions ########################\n",
    "test3=grover(['11111111', '00000000','01110111'], 'ancilla', 7)\n",
    "count3 = execute(test3,simulator).result().get_counts()\n",
    "#print(count3)\n",
    "plot_histogram(count3,color='yellowgreen')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 align=\"center\">\n",
    "\tReferences\n",
    "</h1>\n",
    "    \n",
    "[1] [Gilliam, A., Pistoia, M., &amp; Gonciulea, C. (2020, May 26). Optimizing Quantum Search Using a Generalized Version of Grover's Algorithm.](https://arxiv.org/abs/2005.06468)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Format de la Cellule Texte Brut",
  "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}