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Author: valbert4

codes/quantum/qubits/small_distance/small/4/css_4_1_2/css_4_1_2.svg

@@ -25,6 +25,17 @@ description: |
     Z & Z & Z & Z
   \end{array}~.
   \end{align}
+  The code is depicted in \ref{figure:css-412-operators}.
+  \begin{figure}
+    \includegraphics{css_4_1_2}
+    \caption{
+    Stabilizer generators of the \([[4,1,2]]\) LNCY code.
+    The 4 data qubits (circles) are arranged on a \(2\times 2\) rotated surface code lattice with open boundaries.
+    The bulk generator is a weight-four (four-body) \(Z\) operator and the two boundary generators are weight-two (two-body) \(X\) operators.
+    Red regions correspond to \(X\) operators while blue regions correspond to \(Z\) operators.}
+    \label{figure:css-412-operators}
+  \end{figure}
+
   The code admits the following basis of codewords,
   \begin{align}
     \begin{split}

…its/small_distance/small/4/css_4_1_2.yml …distance/small/4/css_4_1_2/css_4_1_2.ymlcodes/quantum/qubits/small_distance/small/4/css_4_1_2.yml renamed to codes/quantum/qubits/small_distance/small/4/css_4_1_2/css_4_1_2.yml codes/quantum/qubits/small_distance/small/4/css_4_1_2.yml renamed to codes/quantum/qubits/small_distance/small/4/css_4_1_2/css_4_1_2.yml

@@ -25,13 +25,14 @@ description: |
   \end{align}
   The above stabilizer tableau is equivalent to \cite[ID 646]{preset:qiskit} by applying \(H\) to qubits 1 and 2 and \(SH\) (with \(H\) applied first) to qubits 3 and 4, followed by the qubit relabeling \((1,2,3,4,5,6,7)\to(5,6,1,3,7,2,4)\).
 
-  The stabilizer group of the \([[7,2,2]]\) QETC, together with the logical-\(Z\) operator on the first logical qubit, generates the stabilizer group of one of the sixteen distinct indecomposable \([[7,1,3]]\) codes \cite{arxiv:0709.1780}.
-
 
 relations:
   parents:
     - code_id: small_distance_qubit_stabilizer
     - code_id: qetc
+  cousins:
+    - code_id: bare_7_1_3
+      detail: 'The stabilizer group of the \([[7,2,2]]\) QETC, together with the logical-\(Z\) operator on the first logical qubit, generates the stabilizer group of a \([[7,1,3]]\) code \cite{arxiv:2310.10278} equivalent to the bare \([[7,1,3]]\) code \cite{manual:{V. V. Albert, private communication, 2026}}.'
 
 
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