Added teleportation tasks 2.1 to 2.3 (#1619)

Added teleportation tasks 2.1 to 2.3

---------

Co-authored-by: Mariia Mykhailova <[email protected]>
Co-authored-by: Mariia Mykhailova <[email protected]>

katas/content/teleportation/index.md

@@ -86,7 +86,7 @@ We split the teleportation protocol into several steps:
 
 @[section]({
     "id": "teleportation__testing_standard_teleportation",
-    "title": "Testing standard quantum teleportation"
+    "title": "Testing Quantum Teleportation"
 })
 
 In this lesson, your goal is to put together the code from the previous exercises to teleport the states $\ket{0}$ and $\ket{1}$, as well as superposition states $\frac{1}{2}(\ket{0}+\ket{1})$, $\frac{1}{2}(\ket{0}-\ket{1})$, $\frac{1}{2}(\ket{0}+i\ket{1})$ and $\frac{1}{2}(\ket{0}-i\ket{1})$, and to verify that teleportation succeeds each time.
@@ -98,6 +98,54 @@ In this lesson, your goal is to put together the code from the previous exercise
     "codePath": "./examples/TestingStandardTeleportation.qs"
 })
 
+
+@[section]({
+    "id": "teleportation__different_entanglement_pair",
+    "title": "Teleportation Using Different Entangled Pair"
+})
+
+In this lesson we will take a look at the changes in the reconstruction process (Bob's task) if the qubits shared between Alice and Bob are entangled in a different state. Alice's part of the protocol remains the same in all exercises.
+
+As a reminder, the standard teleportation protocol requires shared qubits in state $\ket{\Phi^{+}} = \frac{1}{\sqrt{2}}(\ket{00} + \ket{11})$.
+
+In each exercise, the inputs are:
+
+1. Bob's part of the entangled pair of qubits `qBob`.
+2. The tuple of classical bits received from Alice, in the format used in `SendMessage` exercise.
+
+The goal is to transform Bob's qubit `qBob` into the state in which the message qubit had been originally.
+
+@[exercise]({
+    "id": "teleportation__reconstruct_message_phi_minus",
+    "title": "Reconstruct Message with |Φ⁻⟩",
+    "path": "./reconstruct_message_phi_minus",
+    "qsDependencies": [
+        "../KatasLibrary.qs",
+        "./Common.qs"
+    ]
+})
+
+@[exercise]({
+    "id": "teleportation__reconstruct_message_psi_plus",
+    "title": "Reconstruct Message with |Ψ⁺⟩",
+    "path": "./reconstruct_message_psi_plus",
+    "qsDependencies": [
+        "../KatasLibrary.qs",
+        "./Common.qs"
+    ]
+})
+
+@[exercise]({
+    "id": "teleportation__reconstruct_message_psi_minus",
+    "title": "Reconstruct Message with |Ψ⁻⟩",
+    "path": "./reconstruct_message_psi_minus",
+    "qsDependencies": [
+        "../KatasLibrary.qs",
+        "./Common.qs"
+    ]
+})
+
+
 @[section]({
     "id": "teleportation__three_parties",
     "title": "Teleportation with Three Parties"
@@ -116,4 +164,4 @@ There are multiple variants of teleportation protocol that involve more than two
         "../KatasLibrary.qs",
         "./Common.qs"
     ]
-})
+})

katas/content/teleportation/reconstruct_message_phi_minus/Placeholder.qs

@@ -0,0 +1,5 @@
+namespace Kata {
+    operation ReconstructMessage_PhiMinus(qBob : Qubit, (b1 : Bool, b2 : Bool)) : Unit {
+        // Implement your solution here...
+    }
+}

katas/content/teleportation/reconstruct_message_phi_minus/Solution.qs

@@ -0,0 +1,10 @@
+namespace Kata {
+    operation ReconstructMessage_PhiMinus(qBob : Qubit, (b1 : Bool, b2 : Bool)) : Unit {
+        if not b1 {
+            Z(qBob);
+        }
+        if b2 {
+            X(qBob);
+        }
+    }
+}

katas/content/teleportation/reconstruct_message_phi_minus/Verification.qs

@@ -0,0 +1,10 @@
+namespace Kata.Verification {
+    open Microsoft.Quantum.Diagnostics;
+    open Microsoft.Quantum.Katas;
+
+    @EntryPoint()
+    operation CheckSolution() : Bool {
+        let teleport = ComposeTeleportation(StatePrep_BellState(_, _, 1), SendMessage_Reference, Kata.ReconstructMessage_PhiMinus, _, _, _);
+        return TeleportTestLoop(teleport);  
+    }
+}

katas/content/teleportation/reconstruct_message_phi_minus/index.md

@@ -0,0 +1,2 @@
+**Goal:** 
+Transform Bob's qubit `qBob` into the state in which the message qubit had been originally. It is given that `qAlice` and `qBob` were initially entangled in $\ket{\Phi ^{-}} = \frac{1}{\sqrt{2}}(\ket{00}-\ket{11})$ state.

katas/content/teleportation/reconstruct_message_phi_minus/solution.md

@@ -0,0 +1,15 @@
+Bob's side of this protocol can actually be represented as a sequence of two steps:
+
+ 1. Transform the Bell pair he shares with Alice back to $\ket{\Phi ^+}$. This can be done by applying the $Z$ gate to Bob's qubit.
+ 2. Apply the standard teleportation protocol.
+
+The final set of corrections we need is the $Z$ gate, followed by the standard teleportation corrections:
+- For 00, only Z correction is required.
+- For 01, no change is required.
+- For 10, both Z and X correction is required.
+- For 11, only X correction is requried.
+
+@[solution]({
+    "id": "teleportation__reconstruct_message_phi_minus_solution",
+    "codePath": "./Solution.qs"
+})

katas/content/teleportation/reconstruct_message_psi_minus/Placeholder.qs

@@ -0,0 +1,5 @@
+namespace Kata {
+    operation ReconstructMessage_PsiMinus(qBob : Qubit, (b1 : Bool, b2 : Bool)) : Unit {
+        // Implement your solution here...
+    }
+}

katas/content/teleportation/reconstruct_message_psi_minus/Solution.qs

@@ -0,0 +1,10 @@
+namespace Kata {
+    operation ReconstructMessage_PsiMinus(qBob : Qubit, (b1 : Bool, b2 : Bool)) : Unit {
+        if not b1 {
+            Z(qBob);
+        }
+        if not b2 {
+            X(qBob);
+        }
+    }
+}

katas/content/teleportation/reconstruct_message_psi_minus/Verification.qs

@@ -0,0 +1,10 @@
+namespace Kata.Verification {
+    open Microsoft.Quantum.Diagnostics;
+    open Microsoft.Quantum.Katas;
+
+    @EntryPoint()
+    operation CheckSolution() : Bool {
+        let teleport = ComposeTeleportation(StatePrep_BellState(_, _, 3), SendMessage_Reference, Kata.ReconstructMessage_PsiMinus, _, _, _);
+        return TeleportTestLoop(teleport);  
+    }
+}

katas/content/teleportation/reconstruct_message_psi_minus/index.md

@@ -0,0 +1,2 @@
+**Goal:** 
+Transform Bob's qubit `qBob` into the state in which the message qubit had been originally. It is given that `qAlice` and `qBob` were initially entangled in $\ket{\Psi ^{-}} = \frac{1}{\sqrt{2}}(\ket{01}-\ket{10})$ state.

katas/content/teleportation/reconstruct_message_psi_minus/solution.md

@@ -0,0 +1,14 @@
+Bob's side of this protocol can be represented as a sequence of two steps:
+ 1. Transform the Bell pair he shares with Alice back to $\ket{\Phi ^+}$. This can be done by applying the $Z$ and $X$ gates to Bob's qubit.
+ 2. Apply the standard teleportation protocol.
+
+The final set of corrections we need is the $Z$ and $X$ gates, followed by the standard teleportation corrections:
+- For 00, both Z and X correction is required.
+- For 01, only X correction is required.
+- For 10, only Z correction is required.
+- For 11, no change is requried.
+
+@[solution]({
+    "id": "teleportation__reconstruct_message_psi_minus_solution",
+    "codePath": "./Solution.qs"
+})

katas/content/teleportation/reconstruct_message_psi_plus/Placeholder.qs

@@ -0,0 +1,5 @@
+namespace Kata {
+    operation ReconstructMessage_PsiPlus(qBob : Qubit, (b1 : Bool, b2 : Bool)) : Unit {
+        // Implement your solution here...
+    }
+}

katas/content/teleportation/reconstruct_message_psi_plus/Solution.qs

@@ -0,0 +1,10 @@
+namespace Kata {
+    operation ReconstructMessage_PsiPlus(qBob : Qubit, (b1 : Bool, b2 : Bool)) : Unit {
+        if b1 {
+            Z(qBob);
+        }
+        if not b2 {
+            X(qBob);
+        }
+    }
+}

katas/content/teleportation/reconstruct_message_psi_plus/Verification.qs

@@ -0,0 +1,10 @@
+namespace Kata.Verification {
+    open Microsoft.Quantum.Diagnostics;
+    open Microsoft.Quantum.Katas;
+
+    @EntryPoint()
+    operation CheckSolution() : Bool {
+        let teleport = ComposeTeleportation(StatePrep_BellState(_, _, 2), SendMessage_Reference, Kata.ReconstructMessage_PsiPlus, _, _, _);
+        return TeleportTestLoop(teleport);  
+    }
+}

katas/content/teleportation/reconstruct_message_psi_plus/index.md

@@ -0,0 +1,2 @@
+**Goal:** 
+Transform Bob's qubit `qBob` into the state in which the message qubit had been originally. It is given that `qAlice` and `qBob` were initially entangled in $\ket{\Psi ^{+}} = \frac{1}{\sqrt{2}}(\ket{00}+\ket{11})$ state.

katas/content/teleportation/reconstruct_message_psi_plus/solution.md

@@ -0,0 +1,14 @@
+Bob's side of this protocol can be represented as a sequence of two steps:
+ 1. Transform the Bell pair he shares with Alice back to $\ket{\Phi ^+}$. This can be done by applying the $X$ gate to Bob's qubit.
+ 2. Apply the standard teleportation protocol.
+
+The final set of corrections we need is the $X$ gate, followed by the standard teleportation corrections:
+- For 00, only X correction is required.
+- For 01, both Z and X correction is required.
+- For 10, no change is required.
+- For 11, only Z correction is requried.
+
+@[solution]({
+    "id": "teleportation__reconstruct_message_psi_plus_solution",
+    "codePath": "./Solution.qs"
+})