From c7f8e9b4a88e718d059ec1de88216f4198add0d3 Mon Sep 17 00:00:00 2001
From: quantumjim <decodoku@gmail.com>
Date: Tue, 12 Nov 2024 13:01:40 +0100
Subject: [PATCH] ex4

---
 exercises/Exercise4.ipynb | 23 ++++++++++++++++-------
 1 file changed, 16 insertions(+), 7 deletions(-)

diff --git a/exercises/Exercise4.ipynb b/exercises/Exercise4.ipynb
index a507a94..ad34513 100644
--- a/exercises/Exercise4.ipynb
+++ b/exercises/Exercise4.ipynb
@@ -84,17 +84,26 @@
     "boundary conditions. Then the code would be translationally invariant, and all $A_s$\n",
     "and $B_p$ stabilizers would be four qubit operators.\n",
     "\n",
-    "* (a) The parameter $L$ counts the number of plaquettes along each direction. Show that\n",
+    "a) The parameter $L$ counts the number of plaquettes along each direction. Show that\n",
     "$n = 2L^2$, where $n$ is the number of qubits.\n",
-    "* (b) Show that the number of plaquette operators is $L^2$, but that the number of independent plaquette operators is $L^2-1$. Show the same thing for the vertex operators.\n",
-    "* (c) How many logical qubits, $k$, can be stored in the stabilizer space?\n",
-    "* (d) Define logical $X$ and $Z$ operators for these logical qubits. Note that these are not\n",
+    "\n",
+    "b) Show that the number of plaquette operators is $L^2$, but that the number of independent plaquette operators is $L^2-1$. Show the same thing for the vertex operators.\n",
+    "\n",
+    "c) How many logical qubits, $k$, can be stored in the stabilizer space?\n",
+    "\n",
+    "d) Define logical $X$ and $Z$ operators for these logical qubits. Note that these are not\n",
     "uniquely defined. However, as with any stabilizer code, you will know that your logical\n",
     "operators are a valid choice if they satisfy the following conditions.\n",
-    "    1. Logical Pauli operators must commute with all stabilizers.\n",
-    "    2. Logical Pauli operators for the same logical qubit anticommute: $\\left[ X_j, Z_j \\right] = 0$.\n",
-    "    3. Logical Pauli operators for different logical qubits commute: $\\{ X_j, Z_j \\} = 0$."
+    "\n",
+    "1. Logical Pauli operators must commute with all stabilizers.\n",
+    "2. Logical Pauli operators for the same logical qubit anticommute: $\\left[ X_j, Z_j \\right] = 0$.\n",
+    "3. Logical Pauli operators for different logical qubits commute: $\\{ X_j, Z_j \\} = 0$."
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": []
   }
  ],
  "metadata": {