Migrate nonlocal games #1596 task1 classical

katas/content/index.json

@@ -19,5 +19,6 @@
   "marking_oracles",
   "deutsch_algo",
   "deutsch_jozsa",
+  "nonlocal_games",
   "qec_shor"
 ]

katas/content/nonlocal_games/chsh_classical_strategy/Placeholder.qs

@@ -0,0 +1,13 @@
+namespace Kata {
+    function AliceClassical (x : Bool) : Bool {
+        // Implement your solution here...
+
+        return false;
+    }
+
+    function BobClassical (y : Bool) : Bool {
+        // Implement your solution here...
+
+        return true;
+    }
+}

katas/content/nonlocal_games/chsh_classical_strategy/Solution.qs

@@ -0,0 +1,9 @@
+namespace Kata {
+    function AliceClassical (x : Bool) : Bool {
+        return false;
+    }
+
+    function BobClassical (y : Bool) : Bool {
+        return false;
+    }
+}

katas/content/nonlocal_games/chsh_classical_strategy/Verification.qs

@@ -0,0 +1,27 @@
+namespace Kata.Verification {
+    open Microsoft.Quantum.Convert;
+    open Microsoft.Quantum.Random;
+
+    @EntryPoint()
+    operation CheckSolution() : Bool {
+        mutable wins = 0;
+        for i in 1..1000 {
+            let x = DrawRandomInt(0, 1) == 1 ? true | false;
+            let y = DrawRandomInt(0, 1) == 1 ? true | false;
+            let (a, b) = (Kata.AliceClassical(x), Kata.BobClassical(y));
+            if ((x and y) == (a != b)) {
+                set wins = wins + 1;
+            }
+        }
+        Message($"Win rate {IntAsDouble(wins) / 1000.}");
+        if (wins < 700) {
+            Message("Alice and Bob's classical strategy is not optimal");
+            return false;
+        }
+        else {
+            Message("Correct!");
+        }
+        true
+    }
+
+}

katas/content/nonlocal_games/chsh_classical_strategy/index.md

@@ -0,0 +1,8 @@
+In this task you have to implement two functions, one for Alice's classical strategy and one for Bob's. 
+Note that they are covered by one test, so you have to implement both to pass the test.
+
+**Input:** 
+* Alice and Bob's starting bits (X and Y).
+
+**Output:**
+  Alice and Bob's output bits (A and B) to maximize their chance of winning.

katas/content/nonlocal_games/chsh_classical_strategy/solution.md

@@ -0,0 +1,7 @@
+If Alice and Bob always return TRUE, they will have a 75% win rate, since TRUE ⊕ TRUE = FALSE, and the AND operation on their input bits will be false with 75% probability.
+Alternatively, Alice and Bob could agree to always return FALSE to achieve the same 75% win probability. A classical strategy cannot achieve a higher success probability.
+
+@[solution]({
+    "id": "nonlocal_games__chsh_classical_strategy_solution",
+    "codePath": "Solution.qs"
+})

katas/content/nonlocal_games/chsh_classical_win_condition/Placeholder.qs

@@ -0,0 +1,7 @@
+namespace Kata {
+    function WinCondition (x : Bool, y : Bool, a : Bool, b : Bool) : Bool {
+        // Implement your solution here...
+
+        return false;
+    }
+}

katas/content/nonlocal_games/chsh_classical_win_condition/Solution.qs

@@ -0,0 +1,5 @@
+namespace Kata {
+    function WinCondition (x : Bool, y : Bool, a : Bool, b : Bool) : Bool {
+        return (x and y) == (a != b);
+    }
+}

katas/content/nonlocal_games/chsh_classical_win_condition/Verification.qs

@@ -0,0 +1,24 @@
+namespace Kata.Verification {
+    open Microsoft.Quantum.Convert;
+
+    function WinCondition_Reference(x : Bool, y : Bool, a : Bool, b : Bool) : Bool {
+        return (x and y) == (a != b);
+    }
+
+    @EntryPoint()
+    function CheckSolution() : Bool {
+        for i in 0..1 <<< 4 - 1 {
+            let bits = IntAsBoolArray(i, 4);
+            let actual = WinCondition_Reference(bits[0], bits[1], bits[2], bits[3]);
+            let expected = Kata.WinCondition(bits[0], bits[1], bits[2], bits[3]);
+
+            if actual != expected {
+                Message("Win condition is wrong for " + $"X = {bits[0]}, " + $"Y = {bits[1]}, " + 
+		                $"A = {bits[2]}, " +  $"B = {bits[3]}");
+                return false;
+            }
+        }
+        Message("Correct!");
+        true
+    }
+}

katas/content/nonlocal_games/chsh_classical_win_condition/index.md

@@ -0,0 +1,7 @@
+**Input:** 
+* Alice and Bob's starting bits (X and Y).
+* Alice and Bob's output bits (A and B).
+
+**Output:**
+  True if Alice and Bob won the CHSH game, that is, if X ∧ Y = A ⊕ B, and false otherwise.
+

katas/content/nonlocal_games/chsh_classical_win_condition/solution.md

@@ -0,0 +1,10 @@
+There are four input pairs (X, Y) possible, (0,0), (0,1), (1,0), and (1,1), each with 25% probability.
+In order to win, Alice and Bob have to output different bits if the input is (1,1), and same bits otherwise.
+
+To check whether the win condition holds, you need to compute $x ∧ y$ and $a ⊕ b$ and to compare these values: if they are equal, Alice and Bob won. [`Microsoft.Quantum.Logical`](https://docs.microsoft.com/qsharp/api/qsharp/microsoft.quantum.logical) library offers you logical functions `And` and `Xor` which you can use for this computation. Alternatively, you can compute these values using built-in operators: $x ∧ y$ as `x and y` and $a ⊕ b$ as `a != b`.
+
+
+@[solution]({
+    "id": "nonlocal_games__chsh_classical_win_condition_solution",
+    "codePath": "Solution.qs"
+})

katas/content/nonlocal_games/index.md

@@ -0,0 +1,68 @@
+# Nonlocal Games
+
+@[section]({
+    "id": "nonlocal_games__overview",
+    "title": "Overview"
+})
+
+For our context, "nonlocal" means that the playing parties are separated by a great distance,
+so they cannot communicate with each other during the game.
+In a new kata, we discuss three quantum nonlocal games that display "quantum pseudo-telepathy" -
+the use of quantum entanglement to eliminate the need for classical communication.
+Another characteristics of these games is that they are "refereed", which means the players try to win against the referee.
+
+**This kata covers the following topics:**
+ - Clauser, Horne, Shimony, and Hold thought experiment (often abbreviated as CHSH game)
+ - Greenberger-Horne-Zeilinger game (often abbreviated as GHZ game)
+ - The Mermin-Peres Magic Square (entanglement) game
+
+**What you should know to start working on this kata:**
+ - Basic linear algebra
+ - Single and multi-qubit systems
+ - Single and multi-qubit gates
+ - Single-qubit system measurements
+
+@[section]({
+    "id": "nonlocal_games__chsh_game",
+    "title": "CHSH game"
+})
+
+The **CHSH Game** quantum kata is a series of exercises designed
+to get you familiar with the CHSH game.
+
+In it, two players (Alice and Bob) try to win the following game:
+
+Each of them is given a bit (Alice gets X and Bob gets Y), and
+they have to return new bits (Alice returns A and Bob returns B)
+so that X ∧ Y = A ⊕ B. The trick is, they can not communicate during the game.
+
+> * ∧ is the standard bitwise AND operator.
+> * ⊕ is the exclusive or, or XOR operator, so (P ⊕ Q) is true if exactly one of P and Q is true.
+
+* You can read more about CHSH game in the [lecture notes](https://cs.uwaterloo.ca/~watrous/QC-notes/QC-notes.20.pdf) by
+  John Watrous.
+* At the end of the section you can find an implementation of the CHSH game that includes an explanation of the history and theory behind the game. 
+
+@[section]({
+    "id": "nonlocal_games__chsh_game_classical",
+    "title": "Part I. Classical CHSH"
+})
+
+@[exercise]({
+    "id": "nonlocal_games__chsh_classical_win_condition",
+    "title": "Win Condition",
+    "path": "./chsh_classical_win_condition/"
+})
+
+@[exercise]({
+    "id": "nonlocal_games__chsh_classical_strategy",
+    "title": "Alice and Bob's classical strategy",
+    "path": "./chsh_classical_strategy/"
+})
+
+@[section]({
+    "id": "nonlocal_games__conclusion", 
+    "title": "Conclusion" 
+})
+
+Congratulations! In this kata you learned how to communicate using quantum entanglement in nonlocal quantum games.