[Workbook Added] Solutions provided for Task 1.1 and 1.2

KeyDistribution_BB84/KeyDistribution_BB84.ipynb

@@ -62,7 +62,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 1.1. Diagonal Basis\n",
+    "### <a name=\"Task-1.1-diagonal-basis\"></a> Task 1.1. Diagonal basis\n",
     "\n",
     "Try your hand at converting qubits from the computational basis to the diagonal basis.\n",
     "\n",
@@ -90,7 +90,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 1.2. Equal superposition\n",
+    "*Can't come up with a solution? See the explained solution in the [Key Distribution - BB84 Workbook](./Workbook_KeyDistribution_BB84.ipynb#diagonal_basis).*"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### <a name=\"Task-1.2-equal-superposition\"></a> Task 1.2. Equal superposition\n",
     "\n",
     " \n",
     "**Input**: A qubit in the $|0\\rangle$ state.\n",
@@ -110,9 +117,17 @@
     "\n",
     "operation EqualSuperposition (q : Qubit) : Unit {\n",
     "    // ...\n",
+    "\n",
     "}"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "*Can't come up with a solution? See the explained solution in the [Key Distribution - BB84 Workbook](./Workbook_KeyDistribution_BB84.ipynb#equal_superposition).*"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},

KeyDistribution_BB84/Workbook_KeyDistribution_BB84.ipynb

@@ -0,0 +1,170 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Key Distribution - BB84 Workbook\n",
+    "\n",
+    "**What is this workbook?**\n",
+    "A workbook is a collection of problems, accompanied by solutions to them. \n",
+    "The explanations focus on the logical steps required to solve a problem; they illustrate the concepts that need to be applied to come up with a solution to the problem, explaining the mathematical steps required. \n",
+    "\n",
+    "Note that a workbook should not be the primary source of knowledge on the subject matter; it assumes that you've already read a tutorial or a textbook and that you are now seeking to improve your problem-solving skills. You should attempt solving the tasks of the respective kata first, and turn to the workbook only if stuck. While a textbook emphasizes knowledge acquisition, a workbook emphasizes skill acquisition.\n",
+    "\n",
+    "This workbook describes the solutions to the problems offered in the [Key Distribution BB84 kata](./KeyDistribution_BB84.ipynb). \n",
+    "Since the tasks are offered as programming problems, the explanations also cover some elements of Q# that might be non-obvious for a first-time user.\n",
+    "\n",
+    "**What you should know for this workbook**\n",
+    "\n",
+    "You should be familiar with the following concepts before tackling the Key Distribution - BB84 Kata (and this workbook):\n",
+    "1. Basic single-qubit gates\n",
+    "2. The concept of measurement"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Part I. Preparation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### <a name=\"diagonal_basis\"></a>  Task 1.1. Diagonal basis\n",
+    "\n",
+    "Try your hand at converting qubits from the computational basis to the diagonal basis.\n",
+    "\n",
+    "**Input:** $N$ qubits (stored in an array of length $N$). Each qubit is either in $|0\\rangle$ or in $|1\\rangle$ state.\n",
+    "\n",
+    "**Goal:**  Convert the qubits to the diagonal basis: \n",
+    "* if `qs[i]` was in state $|0\\rangle$, it should be transformed to $|+\\rangle = \\frac{1}{\\sqrt2}(|0\\rangle + |1\\rangle)$,\n",
+    "* if `qs[i]` was in state $|1\\rangle$, it should be transformed to $|-\\rangle = \\frac{1}{\\sqrt2}(|0\\rangle - |1\\rangle)$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Solution\n",
+    "\n",
+    "This task is similar to the one mentioned in [task 1.9 of Superposition kata](./../Superposition/Superposition.ipynb#superposition-of-all-basis-vectors). \n",
+    "This task can be solved by applying a Hadamard gate to every qubit, resulting in $|+\\rangle = \\frac{1}{\\sqrt2}(|0\\rangle + |1\\rangle)$ and $|-\\rangle = \\frac{1}{\\sqrt2}(|0\\rangle - |1\\rangle)$ states depending on whether the starting state of each qubit was $|0\\rangle$ or $|1\\rangle$, respectively. \n",
+    "\n",
+    "To get the desired result, we will iterate over the given array of qubits using a foreach-style loop and apply a Hadamard gate to each qubit."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%kata T11_DiagonalBasis\n",
+    "\n",
+    "operation DiagonalBasis (qs : Qubit[]) : Unit {    \n",
+    "    for q in qs {\n",
+    "        H(q);\n",
+    "    }\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Alternative, we can use the [ApplyToEach](https://docs.microsoft.com/en-us/qsharp/api/qsharp/microsoft.quantum.canon.applytoeach) library function from Microsoft.Quantum.Canon namespace to apply the given gate to each element of the array."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%kata T11_DiagonalBasis\n",
+    "\n",
+    "operation DiagonalBasis (qs : Qubit[]) : Unit {    \n",
+    "    // Use the library function of Q#.\n",
+    "    ApplyToEachA(H, qs);\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[Return to task 1.1 of the KeyDistribution_BB84 kata.](./KeyDistribution_BB84.ipynb#Task-1.1-diagonal-basis)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### <a name=\"equal_superposition\"></a> Task 1.2. Equal superposition\n",
+    "\n",
+    " \n",
+    "**Input**: A qubit in the $|0\\rangle$ state.\n",
+    "\n",
+    "**Goal**:  Change the qubit state to a superposition state that has equal probabilities of measuring 0 and 1. \n",
+    "\n",
+    "> Note that this is not the same as keeping the qubit in the $|0\\rangle$ state with 50% probability and converting it to the $|1\\rangle$ state with 50% probability!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Solution\n",
+    "This task is similar to [Task 1.1](./../Superposition/Superposition.ipynb#plus-state) and [Task 1.2](./../Superposition/Superposition.ipynb#minus-state) of the Superposition kata. \n",
+    "This can also be thought as a specific case of the previous task with $N = 1$.\n",
+    "\n",
+    "For a qubit state to have equal probabilities of producing 0 and 1 when measured, both basis states in the superposition need to have absolute values of amplitudes equal to $\\frac{1}{\\sqrt2}$.\n",
+    "This means that any state of the following form will provide the desired results, as the relative phase will not affect the measurement probabilities\n",
+    "\n",
+    "$$|\\psi\\rangle = \\frac{1}{\\sqrt2}(|0\\rangle + e^{i\\phi}|1\\rangle)$$\n",
+    "\n",
+    "There are multiple ways to prepare one of these states using rotation gates.\n",
+    "However, the simplest solution would be to reuse the previous task and to prepare a plus state $|+\\rangle = \\frac{1}{\\sqrt2}(|0\\rangle + |1\\rangle)$ or a minus state $|-\\rangle = \\frac{1}{\\sqrt2}(|0\\rangle - |1\\rangle)$ using the Hadamard gate."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%kata T12_EqualSuperposition \n",
+    "\n",
+    "operation EqualSuperposition (q : Qubit) : Unit {\n",
+    "    // The most straightforward solution - preparing the plus state.\n",
+    "    H(q);\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[Return to task 1.2 of the Key Distribution_BB84 kata.](././KeyDistribution_BB84.ipynb#Task-1.2-equal-superposition)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Q#",
+   "language": "qsharp",
+   "name": "iqsharp"
+  },
+  "language_info": {
+   "file_extension": ".qs",
+   "mimetype": "text/x-qsharp",
+   "name": "qsharp",
+   "version": "0.14"
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+ "nbformat": 4,
+ "nbformat_minor": 2
+}