Do some minor cleanup

microsoft · tcNickolas · Oct 5, 2019 · Oct 2, 2019 · Oct 2, 2019 · Oct 2, 2019
commit 8872146830eb5161bf28ceb30c6a2246e2ac2f96
diff --git a/BasicGates/BasicGates.ipynb b/BasicGates/BasicGates.ipynb
@@ -85,7 +85,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 101. State flip: $|0\\rangle$ to $|1\\rangle$ and vice versa\n",
+    "### Task 1.1. State flip: $|0\\rangle$ to $|1\\rangle$ and vice versa\n",
     "\n",
     "**Input:** A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
     "\n",
@@ -122,7 +122,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 102. Basis change: $|0\\rangle$ to $|+\\rangle$ and $|1\\rangle$ to $|-\\rangle$ (and vice versa)\n",
+    "### Task 1.2. Basis change: $|0\\rangle$ to $|+\\rangle$ and $|1\\rangle$ to $|-\\rangle$ (and vice versa)\n",
     "\n",
     "**Input**: A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
     "\n",
@@ -153,7 +153,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 103. Sign flip: $|+\\rangle$  to $|-\\rangle$  and vice versa.\n",
+    "### Task 1.3. Sign flip: $|+\\rangle$  to $|-\\rangle$  and vice versa.\n",
     "\n",
     "**Input**: A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
     "\n",
@@ -177,7 +177,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 104. Amplitude change: $|0\\rangle$ to $\\cos{α} |0\\rangle + \\sin{α} |1\\rangle$.\n",
+    "### Task 1.4. Amplitude change: $|0\\rangle$ to $\\cos{α} |0\\rangle + \\sin{α} |1\\rangle$.\n",
     "\n",
     "**Inputs:**\n",
     "\n",
@@ -210,7 +210,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 105. Phase flip\n",
+    "### Task 1.5. Phase flip\n",
     "\n",
     "**Input:** A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
     "\n",
@@ -234,7 +234,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 106. Phase change\n",
+    "### Task 1.6. Phase change\n",
     "\n",
     "**Inputs:**\n",
     "\n",
@@ -264,12 +264,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 107. Global Phase Change",
+    "### Task 1.7. Global phase change\n",
+    "**Input:** A qubit in state $|\\psi\\rangle = \\beta |0\\rangle + \\gamma |1\\rangle$.\n",
     "\n",
-    "**Input:** \n",
-    "1) A qubit in state $|\\psi\\rangle = \\beta |0\\rangle + \\gamma |1\\rangle$.\n",
+    "**Goal**: Change the state of the qubit to $- \\beta |0\\rangle - \\gamma |1\\rangle$.\n",
     "\n",
-    "**Goal**: Change the state of the qubit to - $|\\psi\\rangle$.\n"
+    "> Note: this change on its own is not observable - there is no experiment you can do on a standalone qubit to figure out whether it acquired the global phase or not. \n",
+    "> However, you can use a controlled version of this operation to observe the global phase it introduces. \n",
+    "> This is used in later katas as part of more complicated tasks."
    ]
   },
   {
@@ -280,7 +282,7 @@
    "source": [
     "%kata T107_GlobalPhaseChange_Test\n",
     "\n",
-    "operation GlobalPhaseChange (q : Qubit[]) : Unit is Adj+Ctl {\n",
+    "operation GlobalPhaseChange (q : Qubit) : Unit is Adj+Ctl {\n",
     "    // ...\n",
     "}"
    ]
@@ -289,7 +291,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 108. Bell state change - 1\n",
+    "### Task 1.8. Bell state change - 1\n",
     "\n",
     "**Input:** Two entangled qubits in Bell state $|\\Phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|00\\rangle + |11\\rangle\\big)$.\n",
     "\n",
@@ -313,7 +315,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 109. Bell state change - 2\n",
+    "### Task 1.9. Bell state change - 2\n",
     "\n",
     "**Input:** Two entangled qubits in Bell state $|\\Phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|00\\rangle + |11\\rangle\\big)$.\n",
     "\n",
@@ -337,7 +339,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 110. Bell state change - 3\n",
+    "### Task 1.10. Bell state change - 3\n",
     "\n",
     "**Input:** Two entangled qubits in Bell state $|\\Phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|00\\rangle + |11\\rangle\\big)$.\n",
     "\n",
@@ -372,7 +374,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 201. Two-qubit gate - 1\n",
+    "### Task 2.1. Two-qubit gate - 1\n",
     "\n",
     "**Input:** Two unentangled qubits (stored in an array of length 2).\n",
     "The first qubit will be in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$, the second - in state $|0\\rangle$\n",
@@ -403,7 +405,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 202. Two-qubit gate - 2\n",
+    "### Task 2.2. Two-qubit gate - 2\n",
     "\n",
     "**Input:** Two unentangled qubits (stored in an array of length 2) in state $|+\\rangle \\otimes |+\\rangle = \\frac{1}{2} \\big( |00\\rangle + |01\\rangle + |10\\rangle \\color{blue}+ |11\\rangle \\big)$.\n",
     "\n",
@@ -431,7 +433,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 203. Two-qubit gate - 3\n",
+    "### Task 2.3. Two-qubit gate - 3\n",
     "\n",
     "**Input:** Two unentangled qubits (stored in an array of length 2) in an arbitrary two-qubit state $\\alpha |00\\rangle + \\color{blue}\\beta |01\\rangle + \\color{blue}\\gamma |10\\rangle + \\delta |11\\rangle$.\n",
     "\n",
@@ -458,7 +460,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 204. Toffoli gate\n",
+    "### Task 2.4. Toffoli gate\n",
     "\n",
     "**Input:** Three qubits (stored in an array of length 3) in an arbitrary three-qubit state \n",
     "$\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\zeta|101\\rangle + \\color{blue}\\eta|110\\rangle + \\color{blue}\\theta|111\\rangle$.\n",
@@ -483,7 +485,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Task 205. Fredkin gate\n",
+    "### Task 2.5. Fredkin gate\n",
     "\n",
     "**Input:** Three qubits (stored in an array of length 3) in an arbitrary three-qubit state \n",
     "$\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\color{blue}\\zeta|101\\rangle + \\color{blue}\\eta|110\\rangle + \\theta|111\\rangle$.\n",

diff --git a/BasicGates/ReferenceImplementation.qs b/BasicGates/ReferenceImplementation.qs
@@ -17,7 +17,7 @@ namespace Quantum.Kata.BasicGates {
     // Part I. Single-Qubit Gates
     //////////////////////////////////////////////////////////////////
 
-    // Task 101. State flip
+    // Task 1.1. State flip
     // Input: A qubit in state |ψ⟩ = α |0⟩ + β |1⟩.
     // Goal: Change the state of the qubit to α |1⟩ + β |0⟩.
     // Example:
@@ -28,7 +28,7 @@ namespace Quantum.Kata.BasicGates {
     }
 
 
-    // Task 102. Basis change: |0⟩ to |+⟩ and |1⟩ to |-⟩ (and vice versa)
+    // Task 1.2. Basis change: |0⟩ to |+⟩ and |1⟩ to |-⟩ (and vice versa)
     // Input: A qubit in state |ψ⟩ = α |0⟩ + β |1⟩.
     // Goal: Change the state of the qubit as follows:
     //     If the qubit is in state |0⟩, change its state to |+⟩ = (|0⟩ + |1⟩) / sqrt(2).
@@ -40,15 +40,15 @@ namespace Quantum.Kata.BasicGates {
     }
 
 
-    // Task 103. Sign flip: |+⟩ to |-⟩ and vice versa.
+    // Task 1.3. Sign flip: |+⟩ to |-⟩ and vice versa.
     // Inputs: A qubit in state |ψ⟩ = α |0⟩ + β |1⟩.
     // Goal: Change the qubit state to α |0⟩ - β |1⟩ (flip the sign of |1⟩ component of the superposition).
     operation SignFlip_Reference (q : Qubit) : Unit is Adj+Ctl {
         Z(q);
     }
 
 
-    // Task 104*. Amplitude change (|0⟩ to cos(alpha)*|0⟩ + sin(alpha)*|1⟩).
+    // Task 1.4*. Amplitude change (|0⟩ to cos(alpha)*|0⟩ + sin(alpha)*|1⟩).
     // Inputs:
     //     1) Angle alpha, in radians, represented as Double.
     //     2) A qubit in state β|0⟩ + γ|1⟩.
@@ -61,7 +61,7 @@ namespace Quantum.Kata.BasicGates {
     }
 
 
-    // Task 105. Phase flip
+    // Task 1.5. Phase flip
     // Input: A qubit in state |ψ⟩ = α |0⟩ + β |1⟩.
     // Goal:  Change the qubit state to α |0⟩ + iβ |1⟩ (flip the phase of |1⟩ component of the superposition).
     operation PhaseFlip_Reference (q : Qubit) : Unit is Adj+Ctl {
@@ -70,7 +70,7 @@ namespace Quantum.Kata.BasicGates {
     }
 
 
-    // Task 106*. Phase change
+    // Task 1.6*. Phase change
     // Inputs:
     //     1) Angle alpha, in radians, represented as Double.
     //     2) A qubit in state β|0⟩ + γ|1⟩.
@@ -82,17 +82,14 @@ namespace Quantum.Kata.BasicGates {
         R1(alpha, q);
     }
 
-    // Task 107. Global Phase Change
-    // Inputs:
-    //     1) Pauli operator (μ) represented as Pauli.
-    //     2) Angle alpha, in radians, represented as Double.
-    //     3) A qubit in state β|0⟩ + γ|1⟩.
+    // Task 1.7. Global Phase Change
+    // Input: A qubit in state β|0⟩ + γ|1⟩.
     // Goal: Change the state of the qubit to - β|0⟩ - γ|1⟩.
-    operation GlobalPhaseChange_Reference(q: Qubit) : Unit is Adj+Ctl{
-        R(PauliI,2.0*PI(),q);
+    operation GlobalPhaseChange_Reference (q: Qubit) : Unit is Adj+Ctl {
+        R(PauliI, 2.0 * PI(), q);
     }
 
-    // Task 108. Bell state change - 1
+    // Task 1.8. Bell state change - 1
     // Input: Two entangled qubits in Bell state |Φ⁺⟩ = (|00⟩ + |11⟩) / sqrt(2).
     // Goal:  Change the two-qubit state to |Φ⁻⟩ = (|00⟩ - |11⟩) / sqrt(2).
     operation BellStateChange1_Reference (qs : Qubit[]) : Unit is Adj+Ctl {
@@ -101,7 +98,7 @@ namespace Quantum.Kata.BasicGates {
     }
 
 
-    // Task 109. Bell state change - 2
+    // Task 1.9. Bell state change - 2
     // Input: Two entangled qubits in Bell state |Φ⁺⟩ = (|00⟩ + |11⟩) / sqrt(2).
     // Goal:  Change the two-qubit state to |Ψ⁺⟩ = (|01⟩ + |10⟩) / sqrt(2).
     operation BellStateChange2_Reference (qs : Qubit[]) : Unit is Adj+Ctl {
@@ -110,7 +107,7 @@ namespace Quantum.Kata.BasicGates {
     }
 
 
-    // Task 110 Bell state change - 3
+    // Task 1.10 Bell state change - 3
     // Input: Two entangled qubits in Bell state |Φ⁺⟩ = (|00⟩ + |11⟩) / sqrt(2).
     // Goal:  Change the two-qubit state to |Ψ⁻⟩ = (|01⟩ - |10⟩) / sqrt(2).
     operation BellStateChange3_Reference (qs : Qubit[]) : Unit is Adj+Ctl {
@@ -124,7 +121,7 @@ namespace Quantum.Kata.BasicGates {
     // Part II. Multi-Qubit Gates
     //////////////////////////////////////////////////////////////////
 
-    // Task 201. Two-qubit gate - 1
+    // Task 2.1. Two-qubit gate - 1
     // 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⟩).
@@ -137,7 +134,7 @@ namespace Quantum.Kata.BasicGates {
     }
 
 
-    // Task 202. Two-qubit gate - 2
+    // Task 2.2. Two-qubit gate - 2
     // Input: Two qubits (stored in an array of length 2)
     //        in state |+⟩ ⊗ |+⟩ = (|00⟩ + |01⟩ + |10⟩ + |11⟩) / 2.
     // Goal: Change the two-qubit state to (|00⟩ + |01⟩ + |10⟩ - |11⟩) / 2.
@@ -148,7 +145,7 @@ namespace Quantum.Kata.BasicGates {
         // alternatively: CZ(qs[0], qs[1]);
     }
 
-    // Task 203. Two-qubit gate - 3
+    // Task 2.3. Two-qubit gate - 3
     // 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⟩ + γ|01⟩ + β|10⟩ + δ|11⟩.
@@ -161,7 +158,7 @@ namespace Quantum.Kata.BasicGates {
     }
 
 
-    // Task 204. Toffoli gate
+    // Task 2.4. Toffoli gate
     // Input: Three qubits (stored in an array of length 3) in an arbitrary three-qubit state
     //        α|000⟩ + β|001⟩ + γ|010⟩ + δ|011⟩ + ε|100⟩ + ζ|101⟩ + η|110⟩ + θ|111⟩.
     // Goal:  Flip the state of the third qubit if the state of the first two is |11⟩:
@@ -172,7 +169,7 @@ namespace Quantum.Kata.BasicGates {
         // alternatively (Controlled X)(qs[0..1], qs[2]);
     }
 
-    // Task 205. Fredkin gate
+    // Task 2.5. Fredkin gate
     // Input: Three qubits (stored in an array of length 3) in an arbitrary three-qubit state
     //        α|000⟩ + β|001⟩ + γ|010⟩ + δ|011⟩ + ε|100⟩ + ζ|101⟩ + η|110⟩ + θ|111⟩.
     // Goal:  Swap the states of second and third qubit if and only if the state of the first qubit is |1⟩: