Adders.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Arithmetic circuit library: Adders\n",
    "\n",
    "PR [#6164](https://github.com/Qiskit/qiskit-terra/pull/6164)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why care about an arithmetic circuit library?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general:\n",
    "$$\n",
    "    |a\\rangle_n|b\\rangle_n|0\\rangle \\mapsto |a\\rangle_n |a + b\\rangle_{n+1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, to add 1 and 3 using 2-bit numbers:\n",
    "\n",
    "$$\n",
    "    |1\\rangle_2 |3\\rangle_2 |0\\rangle \\mapsto |1\\rangle_2 |4\\rangle_3\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 479.671x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit import QuantumCircuit, QuantumRegister\n",
    "from qiskit.circuit.library import RippleCarryAdder\n",
    "\n",
    "n = 2  # adding 2 bit numbers\n",
    "\n",
    "a = QuantumCircuit(n)  # encodes |a> = |1>\n",
    "a.x(0)\n",
    "\n",
    "b = QuantumCircuit(n)  # encodes |b> = |3>\n",
    "b.x(0)\n",
    "b.x(1)\n",
    "\n",
    "adder = RippleCarryAdder(n)\n",
    "adder.compose(a, qubits=range(n), front=True, inplace=True)\n",
    "adder.compose(b, qubits=range(n, 2 * n), front=True, inplace=True)\n",
    "\n",
    "adder.draw('mpl', style='iqx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do we expect?\n",
    "\n",
    "     0     1    0  0  0  1\n",
    "    cin0 cout0 b1 b0 a1 a0\n",
    "     |   \\_________/ \\___/\n",
    "     |      = 4       = 1\n",
    "     |\n",
    "     scratch qubit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'010001': 1.0}\n"
     ]
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "\n",
    "sv = Statevector(adder)\n",
    "print(sv.probabilities_dict())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supported implementations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720.471x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import QFTAdder\n",
    "\n",
    "QFTAdder(n).draw('mpl', style='iqx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 660.271x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import ClassicalAdder\n",
    "\n",
    "ClassicalAdder(n).draw('mpl', style='iqx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ClassicalAdder: True\n",
      "RippleCarryAdder: True\n",
      "QFTAdder: True\n"
     ]
    }
   ],
   "source": [
    "from qiskit.circuit.library import Adder\n",
    "\n",
    "for addertype in [ClassicalAdder, RippleCarryAdder, QFTAdder]:\n",
    "    print(f'{addertype.__name__}: {issubclass(addertype, Adder)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modular adders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "    |a\\rangle_n|b\\rangle_n \\mapsto |a\\rangle_n |a + b \\text{ mod } 2^n\\rangle_n\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Supported by `QFTAdder(..., modular=True)` and `RippleCarryAdder(..., modular=True)`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, adding 1 and 3 with 2-bit numbers, modulo $2^2$:\n",
    "\n",
    "$$\n",
    "    |1\\rangle_2 |3\\rangle_2 \\mapsto |1\\rangle_2 |4 \\text{ mod } 4\\rangle_2 = |1\\rangle_2 |0\\rangle_2\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'0001': 1.0}\n"
     ]
    }
   ],
   "source": [
    "adder = QFTAdder(n, modular=True)\n",
    "adder.compose(a, qubits=range(n), front=True, inplace=True)\n",
    "adder.compose(b, qubits=range(n, 2 * n), front=True, inplace=True)\n",
    "\n",
    "adder.draw('mpl', style='iqx')\n",
    "\n",
    "sv = Statevector(adder)\n",
    "print(sv.probabilities_dict(decimals=10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Next up\n",
    "\n",
    "* Multiplier (done)\n",
    "* Subtractor (almost done)\n",
    "* Polynomials\n",
    "* Tutorials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Should `Adder(n)` be usable with some default implementation?"
   ]
  },
  {
   "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": "3.7.9"
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 },
 "nbformat": 4,
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}