[BasicGates] Add task 1.10 to the workbook (#728)

BasicGates/BasicGates.ipynb

@@ -405,6 +405,13 @@
     "}"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.10.-Bell-state-change---3).*"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},

BasicGates/Workbook_BasicGates.ipynb

@@ -1066,6 +1066,51 @@
    "source": [
     "[Return to Task 1.9 of the Basic Gates kata](./BasicGates.ipynb#Task-1.9.-Bell-state-change---2)."
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 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",
+    "**Goal:**  Change the two-qubit state, without adding a global phase, to $|\\Psi^{-}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|01\\rangle - |10\\rangle\\big)$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Solution ##\n",
+    "We remember from Task 1.3 that the Pauli-Z gate leaves the sign of the $|0\\rangle$ component of the single qubit superposition unchanged but flips the sign of the $|1\\rangle$ component of the superposition. We have also just seen in Task 1.9 how to change our input state to the state $\\frac{1}{\\sqrt{2}} \\big(|01\\rangle + |10\\rangle\\big)$, which is almost our goal state (disregarding the phase change for the moment). So it would seem that a combination of these two gates wiill be what we need here. The remaining question is in what order to apply them, and to which qubit.\n",
+    "\n",
+    "First of all, which qubit? Looking back at Task 1.9, it seems clear that we need to use qubit `qs[0]`, like we did there.\n",
+    "\n",
+    "Second, in what order should we apply the gates? Remember that the Pauli-Z gate flips the phase of the $|1\\rangle$ component of the superposition and leaves the $|0\\rangle$ component alone.   \n",
+    "Let's experiment with applying X to `qs[0]` first. Looking at our \"halfway answer\" state $\\frac{1}{\\sqrt{2}} \\big(|01\\rangle + |10\\rangle\\big)$, we can see that if we apply the Z gate to `qs[0]`, it will leave the $|0_{A}\\rangle$ alone but flip the phase of $|1_{A}\\rangle$ to $-|1_{A}\\rangle$, thus flipping the phase of the $|11\\rangle$ component of our  Bell state.  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%kata T110_BellStateChange3\n",
+    "\n",
+    "operation BellStateChange3 (qs : Qubit[]) : Unit is Adj+Ctl {\n",
+    "    X(qs[0]);\n",
+    "    Z(qs[0]);\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[Return to Task 1.10 of the Basic Gates kata](./BasicGates.ipynb#Task-1.10.-Bell-state-change---3)."
+   ]
   }
  ],
  "metadata": {