delete typo

exercises/Exercise1.ipynb

@@ -87,7 +87,7 @@
     "Consider the controlled-$Z$ gate\n",
     "\n",
     "$$\n",
-    "CZ = |1\\rangle \\langle 1 | \\otimes I + |0\\rangle \\langle 0 | \\otimes Z,\n",
+    "CZ = |0\\rangle \\langle 0 | \\otimes I + |1\\rangle \\langle 1 | \\otimes Z,\n",
     "$$\n",
     "\n",
     "and the following two families of states.\n",
@@ -101,106 +101,6 @@
     "\n",
     "* (b) Apply the $CZ$ gate to the first two qubits of the three qubit state $|a\\rangle \\otimes |\\Phi^+\\rangle$. Again find the reduced density matrices, and their eigenvalues and vectors. Are the eigenvalues of both qubits still the same?"
    ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Hints\n",
-    "\n",
-    "### 1\n",
-    "\n",
-    "The truth table is reversable, so it would be possible to create a solution using only three qubits. But it would also be hard. In the solution I present the least elegant solution that uses 6 qubits in all. They should know that such non-elegant solutions are an option.\n",
-    "\n",
-    "### 2\n",
-    "\n",
-    "Looking at Hello Qiskit (or otherwise looking up Bell tests) and using the mentioned example should be enough to set them on the right path.\n",
-    "\n",
-    "### 3 and 4\n",
-    "\n",
-    "Just some matrix stuff. Maybe doing some partial trace examples with them would be good, though."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Solutions"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Solution 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from qiskit import QuantumCircuit\n",
-    "from qiskit_aer import AerSimulator\n",
-    "from qiskit.circuit.library.standard_gates import XGate\n",
-    "\n",
-    "# create a controlled-controlled-controlled-X gate\n",
-    "# This performs an X on the target qubit if the three controls are all |1>\n",
-    "cccx = XGate().control(3)\n",
-    "\n",
-    "def boolean_gate(abc):\n",
-    "\n",
-    "    qc = QuantumCircuit(6,3)\n",
-    "\n",
-    "    # encode a, b and c in qubits 0, 1 and 2, respectively\n",
-    "    if abc[0]=='1':\n",
-    "        qc.x(0)\n",
-    "    if abc[1]=='1':\n",
-    "        qc.x(1)\n",
-    "    if abc[2]=='1':\n",
-    "        qc.x(2)\n",
-    "\n",
-    "    # we'll encode d, e and f in qubits 3, 4 and 5, respectively\n",
-    "    # for each input we'll do the following process\n",
-    "    #     1 - rotate that input to 111\n",
-    "    #     2 - implement cccxs whose targets are any output bits that should be 1\n",
-    "    #     3 - undo step 1\n",
-    "    # This will then prepare the correct outputs (although in a needlessly long way)\n",
-    "\n",
-    "    # 000 -> 010\n",
-    "    if abc == '000':\n",
-    "        qc.x([0,1,2])\n",
-    "        qc.append(cccx, [0,1,2, 4])\n",
-    "        qc.x([0,1,2])\n",
-    "\n",
-    "    # 001 -> 110\n",
-    "    if abc == '001':\n",
-    "        qc.x([0,1])\n",
-    "        qc.append(cccx, [0,1,2, 3])\n",
-    "        qc.append(cccx, [0,1,2, 4])\n",
-    "        qc.x([0,1])\n",
-    "\n",
-    "    # 010 -> 001\n",
-    "    if abc == '010':\n",
-    "        qc.x([0,2])\n",
-    "        qc.append(cccx, [0,1,2, 5])\n",
-    "        qc.x([0,2])\n",
-    "\n",
-    "    # and so on for the other inputs that I can't be bothered to do\n",
-    "\n",
-    "    # finally we measure the output bits to get the output\n",
-    "    qc.measure([3,4,5], [2,1,0])\n",
-    "\n",
-    "    return AerSimulator().run(qc, shots=1, memory=True).result().get_memory()[0]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {