Convert the GHZ game kata to Jupyter Notebook format (#120)
This commit is contained in:
Jack Hyder
Mariia Mykhailova
Родитель
789ad28a6d
Коммит
42f04ccb07
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@ -63,6 +63,9 @@ RUN jupyter nbconvert CHSHGame/CHSHGame.ipynb --execute --stdout --to markdown
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RUN dotnet build DeutschJozsaAlgorithm
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RUN jupyter nbconvert DeutschJozsaAlgorithm/DeutschJozsaAlgorithm.ipynb --execute --stdout --to markdown --allow-errors --ExecutePreprocessor.timeout=120
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RUN dotnet build GHZGame
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RUN jupyter nbconvert GHZGame/GHZGame.ipynb --execute --stdout --to markdown --allow-errors --ExecutePreprocessor.timeout=120
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RUN dotnet build Measurements
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RUN jupyter nbconvert Measurements/Measurements.ipynb --execute --stdout --to markdown --allow-errors --ExecutePreprocessor.timeout=120
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@ -19,8 +19,4 @@
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<ItemGroup>
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<None Include="README.md" />
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</ItemGroup>
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<ItemGroup>
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<Service Include="{82a7f48d-3b50-4b1e-b82e-3ada8210c358}" />
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</ItemGroup>
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</Project>
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@ -0,0 +1,302 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# GHZ Game\n",
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"\n",
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"The **GHZ Game** quantum kata is a series of exercises designed\n",
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"to get you familiar with the GHZ game.\n",
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"\n",
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"In it three players (Alice, Bob and Charlie) try to win the following game:\n",
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"\n",
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"Each of them is given a bit (r, s and t respectively), and\n",
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"they have to return new bits (a, b and c respectively) so\n",
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"that r ∨ s ∨ t = a ⊕ b ⊕ c. The input bits will have\n",
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"zero or two bits set to true and three or one bits set to false.\n",
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"The trick is, the players can not communicate during the game.\n",
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"\n",
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"* You can read more about the GHZ game in the [lecture notes](https://cs.uwaterloo.ca/~watrous/CPSC519/LectureNotes/20.pdf) by John Watrous. \n",
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"* Another description can be found in the [lecture notes](https://staff.fnwi.uva.nl/m.walter/physics491/lecture1.pdf) by Michael Walter.\n",
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"\n",
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"Each task is wrapped in one operation preceded by the description of the task.\n",
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"Each task has a unit test associated with it, which initially fails.\n",
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"Your goal is to fill in the blank (marked with the `// ...` comments)\n",
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"with some Q# code that solves the task. To verify your answer, run the cell using Ctrl/⌘+Enter.\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"To begin, first prepare this notebook for execution (if you skip this step, you'll get \"Syntax does not match any known patterns\" error when you try to execute Q# code in the next cells):"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%package Microsoft.Quantum.Katas::0.6.1905.301"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"> The package versions in the output of the cell above should always match. If you are running the Notebooks locally and the versions do not match, please install the IQ# version that matches the version of the `Microsoft.Quantum.Katas` package.\n",
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"> <details>\n",
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"> <summary><u>How to install the right IQ# version</u></summary>\n",
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"> For example, if the version of `Microsoft.Quantum.Katas` package above is 0.6.1905.301, the installation steps are as follows:\n",
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">\n",
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"> 1. Stop the kernel.\n",
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"> 2. Uninstall the existing version of IQ#:\n",
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"> dotnet tool uninstall microsoft.quantum.iqsharp -g\n",
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"> 3. Install the matching version:\n",
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"> dotnet tool install microsoft.quantum.iqsharp -g --version 0.6.1905.301\n",
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"> 4. Reinstall the kernel:\n",
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"> dotnet iqsharp install\n",
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"> 5. Restart the Notebook.\n",
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"> </details>\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Part I. Classical GHZ\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Task 1.1. Win Condition\n",
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"**Inputs:** \n",
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"\n",
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" 1. Alice, Bob and Charlie's input bits (r, s and t), stored as an array of length 3,\n",
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"\n",
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" 2. Alice, Bob and Charlie's output bits (a, b and c), stored as an array of length 3.\n",
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"\n",
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"The input bits will have zero or two bits set to true.\n",
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"\n",
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"**Output:** \n",
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"True if Alice, Bob and Charlie won the GHZ game, that is, if r ∨ s ∨ t = a ⊕ b ⊕ c, and false otherwise."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%kata T11_WinCondition_Test \n",
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"\n",
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"function WinCondition (rst : Bool[], abc : Bool[]) : Bool {\n",
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" // ...\n",
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" fail \"Task 1.1 not implemented yet\";\n",
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"}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Task 1.2. Random classical strategy\n",
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"\n",
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"**Input:** The input bit for one of the players (r, s or t).\n",
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"\n",
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"**Output:** A random bit that this player will output (a, b or c).\n",
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"\n",
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"If all players use this strategy, they will win about 50% of the time."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%kata T12_RandomClassical_Test \n",
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"\n",
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"operation RandomClassicalStrategy (input : Bool) : Bool {\n",
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" // ...\n",
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" fail \"Task 1.2 not implemented yet\";\n",
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"}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Task 1.3. Best classical strategy\n",
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"\n",
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"**Input:** The input bit for one of the players (r, s or t).\n",
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"\n",
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"**Output:** A bit that this player will output (a, b or c) to maximize their chance of winning.\n",
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"\n",
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"All players will use the same strategy.\n",
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"The best classical strategy should win about 75% of the time."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%kata T13_BestClassical_Test \n",
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"\n",
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"operation BestClassicalStrategy (input : Bool) : Bool {\n",
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" // ...\n",
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" fail \"Task 1.3 not implemented yet\";\n",
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"}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Task 1.4. Referee classical GHZ game\n",
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"\n",
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"**Inputs:** \n",
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"\n",
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" 1. An operation which implements a classical strategy (i.e., takes an input bit and produces an output bit),\n",
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"\n",
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" 2. An array of 3 input bits that should be passed to the players.\n",
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"\n",
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"**Output:** \n",
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"An array of 3 bits that will be produced if each player uses this strategy."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%kata T14_PlayClassicalGHZ_Test \n",
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"\n",
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"operation PlayClassicalGHZ (strategy : (Bool => Bool), inputs : Bool[]) : Bool[] {\n",
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" // ...\n",
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" fail \"Task 1.4 not implemented yet\";\n",
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"}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Part II. Quantum GHZ\n",
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"\n",
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"In the quantum version of the game, the players still can not\n",
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"communicate during the game, but they are allowed to share \n",
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"qubits from an entangled triple before the start of the game.\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Task 2.1. Entangled triple\n",
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"\n",
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"**Input:** An array of three qubits in the $|000\\rangle$ state.\n",
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"\n",
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"**Goal:** Create the entangled state $|\\Phi\\rangle = \\frac{1}{2} \\big(|000\\rangle - |011\\rangle - |101\\rangle - |110\\rangle \\big)$ on these qubits."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%kata T21_CreateEntangledTriple_Test \n",
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"\n",
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"operation CreateEntangledTriple (qs : Qubit[]) : Unit {\n",
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" // ...\n",
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" fail \"Task 2.1 not implemented yet\";\n",
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"}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Task 2.2. Quantum strategy\n",
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"\n",
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"**Inputs:**\n",
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"\n",
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" 1. The input bit for one of the players (r, s or t),\n",
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"\n",
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" 2. That player's qubit of the entangled triple shared between the players.\n",
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"\n",
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"**Goal:** Measure the qubit in the Z basis if the bit is 0 (false), or the X basis if the bit is 1 (true), and return the result.\n",
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"\n",
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"The state of the qubit after the operation does not matter."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%kata T22_QuantumStrategy_Test \n",
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"\n",
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"operation QuantumStrategy (input : Bool, qubit : Qubit) : Bool {\n",
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" // ...\n",
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" fail \"Task 2.2 not implemented yet\";\n",
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"}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Task 2.3. Play the GHZ game using the quantum strategy\n",
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"\n",
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"**Input:** Operations that return Alice, Bob and Charlie's output bits (a, b and c) based on\n",
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"their quantum strategies and given their respective qubits from the entangled triple.\n",
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"The players have already been told what their starting bits (r, s and t) are.\n",
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"\n",
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"**Goal:** Return an array of players' output bits (a, b and c).\n",
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"\n",
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"Note that this task uses QuantumStrategy which you've implemented in task 2.2.\n",
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"\n",
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"<span style=\"color:red\">*This task is not evaluated properly with version 0.6 of the packages; please return to it after 0.7 release.*</span>"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%kata T23_PlayQuantumGHZ_Test \n",
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"\n",
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"operation PlayQuantumGHZ (strategies : (Qubit => Bool)[]) : Bool[] {\n",
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" // ...\n",
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" fail \"Task 2.3 not implemented yet\";\n",
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"}"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Q#",
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"language": "qsharp",
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"name": "iqsharp"
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},
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"language_info": {
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"file_extension": ".qs",
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"mimetype": "text/x-qsharp",
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"name": "qsharp",
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"version": "0.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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@ -3,6 +3,8 @@
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This kata covers the Greenberger-Horne-Zeilinger game (often abbreviated as GHZ game),
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a well-known example of a nonlocal (entanglement) game.
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You can [run the GHZ Game kata as a Jupyter Notebook](https://mybinder.org/v2/gh/Microsoft/QuantumKatas/master?filepath=GHZGame%2FGHZGame.ipynb)!
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In a nonlocal game, several cooperating players play a game against a referee answering the referee's questions. The players are free to share information
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(and even qubits!) before the game starts, but are forbidden from communicating
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with each other afterwards. Nonlocal games show that quantum entanglement can be
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@ -12,4 +14,4 @@ purely classical strategy.
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#### Theory
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* [Lecture 1](https://staff.fnwi.uva.nl/m.walter/physics491/lecture1.pdf) by Michael Walter.
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* [Lecture 20](https://cs.uwaterloo.ca/~watrous/CPSC519/LectureNotes/20.pdf) by John Watrous.
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* [Lecture 20](https://cs.uwaterloo.ca/~watrous/CPSC519/LectureNotes/20.pdf) by John Watrous.
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@ -10,6 +10,7 @@
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namespace Quantum.Kata.GHZGame {
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open Microsoft.Quantum.Arrays;
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open Microsoft.Quantum.Convert;
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open Microsoft.Quantum.Math;
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open Microsoft.Quantum.Canon;
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@ -41,11 +42,7 @@ namespace Quantum.Kata.GHZGame {
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// Task 1.4. Referee classical GHZ game
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operation PlayClassicalGHZ_Reference (strategy : (Bool => Bool), inputs : Bool[]) : Bool[] {
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mutable results = new Bool[Length(inputs)];
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for (i in 0..Length(inputs) - 1) {
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set results w/= i <- strategy(inputs[i]);
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}
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return results;
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return ForEach(strategy, inputs);
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}
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@ -19,6 +19,7 @@
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"* **[Deutsch–Jozsa algorithm](./DeutschJozsaAlgorithm/DeutschJozsaAlgorithm.ipynb)**.\n",
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" This kata starts with writing quantum oracles which implement classical functions, and continues to introduce the Bernstein–Vazirani and Deutsch–Jozsa algorithms.\n",
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"* **[CHSH game](./CHSHGame/CHSHGame.ipynb)**.\n",
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"* **[GHZ Game](./GHZGame/GHZGame.ipynb)**.\n",
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"\n",
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"For a full list of Quantum Katas, available as Q# projects, see the [QuantumKatas repository](https://github.com/Microsoft/quantumkatas/).\n",
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"\n",
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