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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Tutorial: Quantum Adder\n",
+    "An adder has two basic building blocks:\n",
+    "1. Addition modulo 2\n",
+    "2. Carry output\n",
+    "\n",
+    "For a quantum computer, both blocks can be implemented using CNOT gate."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from projectq import MainEngine\n",
+    "from projectq.backends import CircuitDrawer\n",
+    "from projectq.ops import X, CNOT, Measure, All, ControlledGate\n",
+    "\n",
+    "def qsum_(c, a, b):\n",
+    "    CNOT|(a, b)    # CNOT (control bit, target bit)\n",
+    "    CNOT|(c, b)\n",
+    "    return b       # b -> b' = (a+b+c mod 2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The quantum circuit of qsum_ is:\n",
+    "<img src=\"Images/sum.png\" width=\"30%\">"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def qcarry_(eng, a, b, c):\n",
+    "    ancilla = eng.allocate_qubit()\n",
+    "    ControlledGate(X,2) | (a,b,ancilla) # a,b are control qubits, ancilla is a target qubit\n",
+    "    CNOT|(a,b)\n",
+    "    ControlledGate(X,2) | (c,b,ancilla)\n",
+    "    return (c,a,b,ancilla)  # (carry, a, a+b mod 2, next carry)\n",
+    "                            # (a+b mod 2) can be uncomputed later using CNOT"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The quantum circuit of qcarry_ is:\n",
+    "<img src=\"Images/carry.png\" width=\"27%\">"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Finally we can start to construct a quantum adder:\n",
+    "1. The input are two n-qubit quantum states, the output is a (n+1)-qubit quantum state which is converted into an integer.\n",
+    "2. We start from least significant bits $a_0$ and $b_0$, compute the carry $c_0$ and pass it to next bit.\n",
+    "3. The most significant bit is the carry $c_n$.\n",
+    "4. We uncompute registers-b, then use qsum_ to get less significant bits."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def qadd_(eng, qureg_A, qureg_B):\n",
+    "    assert len(qureg_A)==len(qureg_B)\n",
+    "    n=len(qureg_A)\n",
+    "    carries = [None for i in range(n+1)]\n",
+    "    carries[0] = eng.allocate_qubit()\n",
+    "    for i in range(n):\n",
+    "        _, _, _, carries[i+1] = qcarry_(eng,qureg_A[i],qureg_B[i],carries[i])\n",
+    "        CNOT|(qureg_A[i],qureg_B[i])      # uncompute a+b mod 2 to b\n",
+    "        qsum_(carries[i],qureg_A[i],qureg_B[i])\n",
+    "        \n",
+    "    All(Measure)|qureg_B # less significant bits\n",
+    "    Measure|carries[n]   # most significant bit\n",
+    "    eng.flush()\n",
+    "    \n",
+    "    result = ''\n",
+    "    for bit in qureg_B:\n",
+    "        result += str(int(bit))\n",
+    "    result += str(int(carries[n]))\n",
+    "    return result[::-1] # reverse"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "A sample test run"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(Note: This is the (slow) Python simulator.)\n",
+      "1011\n"
+     ]
+    }
+   ],
+   "source": [
+    "if __name__ == \"__main__\":\n",
+    "    eng = MainEngine()\n",
+    "    qureg_A=eng.allocate_qureg(3)\n",
+    "    X|qureg_A[0]\n",
+    "    X|qureg_A[1]\n",
+    "    X|qureg_A[2]\n",
+    "    qureg_B=eng.allocate_qureg(3)\n",
+    "    X|qureg_B[2]\n",
+    "    print(qadd_(eng,qureg_A,qureg_B))\n",
+    "\n",
+    "    del eng"
+   ]
+  }
+ ],
+ "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": "3.7.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}