Several small improvements in presentation (#53)

* Add detailed hint to the first task in Measurements
* Add explanations to several solutions in JointMeasurements and marked task complexity

JointMeasurements/ReferenceImplementation.qs

@@ -31,25 +31,32 @@ namespace Quantum.Kata.JointMeasurements {
     
     // Task 3. |0000⟩ + |1111⟩ or |0011⟩ + |1100⟩ ?
     operation GHZOrGHZWithX_Reference (qs : Qubit[]) : Int {
+        // Considering only the two middle qubits of the array, their parity for the first state is 0,
+        // so the first state belongs to the +1 eigenspace of operator Z ⊗ Z on these qubits;
+        // their parity for the second state is 1, so the second state belongs to the -1 eigenspace.
         return Measure([PauliZ, PauliZ], qs[1 .. 2]) == Zero ? 0 | 1;
     }
     
     
     // Task 4. |0..0⟩ + |1..1⟩ or W state ?
     operation GHZOrWState_Reference (qs : Qubit[]) : Int {
+        // Since the number of qubits in qs is even, the parity of both |0..0⟩ and |1..1⟩ basis states is 0,
+        // so both of them belong to the +1 eigenspace of operator Z ⊗ Z ⊗ ... ⊗ Z. 
+        // All basis vectors in W state have parity 1 and belong to the -1 eigenspace of this operator.
         return MeasureAllZ(qs) == Zero ? 0 | 1;
     }
     
     
-    // Task 5. Parity measurement in different basis
+    // Task 5*. Parity measurement in different basis
     operation DifferentBasis_Reference (qs : Qubit[]) : Int {
-        // The first state is a superposition of |++⟩ and |--⟩,
-        // the second one - of |+-⟩ and |-+⟩
+        // The first state is a superposition of the states |++⟩ and |--⟩, 
+        // which belong to the +1 eigenspace of the operator X ⊗ X;
+        // the second one is a superposition of |+-⟩ and |-+⟩, which belong to the -1 eigenspace.
         return Measure([PauliX, PauliX], qs) == Zero ? 0 | 1;
     }
     
     
-    // Task 6. Controlled X gate with |0⟩ target
+    // Task 6*. Controlled X gate with |0⟩ target
     operation ControlledX_Reference (qs : Qubit[]) : Unit {
         H(qs[1]);
         if (Measure([PauliZ, PauliZ], qs) == One) {
@@ -58,7 +65,7 @@ namespace Quantum.Kata.JointMeasurements {
     }
     
     
-    // Task 7*. Controlled X gate with arbitrary target
+    // Task 7**. Controlled X gate with arbitrary target
     operation ControlledX_General_Reference (qs : Qubit[]) : Unit {
         
         body (...) {

JointMeasurements/Tasks.qs

@@ -79,7 +79,7 @@ namespace Quantum.Kata.JointMeasurements {
     }
     
     
-    // Task 5. Parity measurement in different basis
+    // Task 5*. Parity measurement in different basis
     // Input: Two qubits (stored in an array) which are guaranteed to be
     //        either in superposition α|00⟩ + β|01⟩ + β|10⟩ + α|11⟩
     //        or in superposition α|00⟩ - β|01⟩ + β|10⟩ - α|11⟩.
@@ -92,10 +92,10 @@ namespace Quantum.Kata.JointMeasurements {
     }
     
     
-    // Task 6. Controlled X gate with |0⟩ target
+    // Task 6*. Controlled X gate with |0⟩ target
     // Input: Two unentangled qubits (stored in an array of length 2).
     //        The first qubit will be in state |ψ⟩ = α |0⟩ + β |1⟩, the second - in state |0⟩
-    //        (this can be written as two-qubit state (α|0⟩ + β|1⟩) ⊕ |0⟩).
+    //        (this can be written as two-qubit state (α|0⟩ + β|1⟩) ⊗ |0⟩).
     // Goal:  Change the two-qubit state to α |00⟩ + β |11⟩ using only single-qubit gates and joint measurements.
     //        Do not use two-qubit gates.
     // You do not need to allocate extra qubits.
@@ -104,7 +104,7 @@ namespace Quantum.Kata.JointMeasurements {
     }
     
     
-    // Task 7*. Controlled X gate with arbitrary target
+    // Task 7**. Controlled X gate with arbitrary target
     // Input: Two qubits (stored in an array of length 2) in an arbitrary
     //        two-qubit state α|00⟩ + β|01⟩ + γ|10⟩ + δ|11⟩.
     // Goal:  Change the two-qubit state to α|00⟩ + β|01⟩ + δ|10⟩ + γ|11⟩ using only single-qubit gates and joint measurements.

Measurements/Tasks.qs

@@ -35,7 +35,14 @@ namespace Quantum.Kata.Measurements {
     // Output: true if qubit was in |1⟩ state, or false if it was in |0⟩ state.
     // The state of the qubit at the end of the operation does not matter.
     operation IsQubitOne (q : Qubit) : Bool {
-        // ...
+        // The operation M will measure a qubit in the Z basis (|0⟩ and |1⟩ basis)
+        // and return Zero if the observed state was |0⟩ or One if the state was |1⟩.
+        // To answer the question, you need to perform the measurement and check whether the result
+        // equals One - either directly or using library function IsResultOne.
+        //
+        // Replace the returned expression with (M(q) == One)
+        // Then rebuild the project and rerun the tests - T101_IsQubitOne_Test should now pass!
+
         return false;
     }
     

Superposition/ReferenceImplementation.qs

@@ -357,8 +357,8 @@ namespace Quantum.Kata.Superposition {
                 WState_PowerOfTwo_Reference(qs);
             } else {
                 // allocate extra qubits
-                using (ans = Qubit[P - N]) {
-                    let all_qubits = qs + ans;
+                using (anc = Qubit[P - N]) {
+                    let all_qubits = qs + anc;
                     
                     repeat {
                         // prepare state W_P on original + ancilla qubits
@@ -367,12 +367,12 @@ namespace Quantum.Kata.Superposition {
                         // measure ancilla qubits; if all of the results are Zero, we get the right state on main qubits
                         mutable allZeros = true;
                         for (i in 0 .. (P - N) - 1) {
-                            set allZeros = allZeros && IsResultZero(M(ans[i]));
+                            set allZeros = allZeros && IsResultZero(M(anc[i]));
                         }
                     }
                     until (allZeros)
                     fixup {
-                        ResetAll(ans);
+                        ResetAll(anc);
                     }
                 }
             }