Gottesman code corr + ref

codes/classical/analog/analog.yml

@@ -33,7 +33,7 @@ protection: |
   Defining a density for infinite constellations can be done using a limit \cite[pg. 349]{preset:EricZin}.
 
   The Kabatiansky-Levenshtein bound \cite{manual:{G. A. Kabatiansky, V. I. Levenshtein, “On Bounds for Packings on a Sphere and in Space”, Probl. Peredachi Inf., 14:1 (1978), 3–25; Problems Inform. Transmission, 14:1 (1978), 1–17}} says that any sphere packing must satistfy \(\frac{1}{n}\log_{2}\Delta\lesssim-0.5990\) asymptotically with dimension \(n\).
-  Other bounds include the Rogers bound \cite{doi:10.1112/plms/s3-8.4.609}.
+  Other bounds include the Rogers bound \cite{doi:10.1112/plms/s3-8.4.609} and its recent improvement \cite{arxiv:2312.10026}.
   For more details, see \cite[Ch. 10.4]{preset:EricZin}\cite[Ch. 1]{doi:10.1007/978-1-4757-6568-7}.
 
   The \textit{covering problem} asks how one can cover all of space by overlapping spheres in the most efficient way.

codes/quantum/qubits/small_distance/quantum_hamming.yml

@@ -7,14 +7,16 @@ code_id: quantum_hamming
 physical: qubits
 logical: qubits
 
-name: 'Gottesman code'
+name: '\([[2^r, 2^r-r-2, 3]]\) Gottesman code'
 short_name: '\([[2^r, 2^r-r-2, 3]]\)'
 introduced: '\cite{arXiv:quant-ph/9604038}'
 
 alternative_names:
   - '\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code'
 
-description: 'A family of stabilizer codes of distance \(3\) that saturate the asymptotic quantum Hamming bound. Can be obtained from the CSS construction with a \([2^r,r+1,2^{r-1}] = C_2^{\perp}\) RM code and a \([2^r,2^r-1,2] = C_1\) even-weight code \cite{arxiv:quant-ph/9605021}.'
+description: 'A family of non-CSS stabilizer codes of distance \(3\) that saturate the asymptotic quantum Hamming bound.'
+
+# Can be obtained from the CSS construction with a \([2^r,r+1,2^{r-1}] = C_2^{\perp}\) RM code and a \([2^r,2^r-1,2] = C_1\) even-weight code \cite{arxiv:quant-ph/9605021}.
 
 protection: 'Protects against any single qubit error.'
 
@@ -25,11 +27,12 @@ relations:
     - code_id: small_distance_quantum
   cousins:
     - code_id: quantum_perfect
-      detail: 'Quantum Hamming codes saturate the asymptotic quantum Hamming bound.'
+      detail: '\([[2^r, 2^r-r-2, 3]]\) Gottesman codes saturate the asymptotic quantum Hamming bound.'
     - code_id: hamming
-      detail: '\([[2^r, 2^r-r-2, 3]]\) quantum Hamming codes are analogues of Hamming codes in that they saturate the asymptotic Hamming bound.'
-    - code_id: reed_muller
-      detail: '\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code can be obtained from the CSS construction using a first-order \([2^r,r+1,2^{r-1}]\) RM code and a \([2^r,2^r-1,2]\) even-weight code \cite{arxiv:quant-ph/9605021}.'
+      detail: '\([[2^r, 2^r-r-2, 3]]\) Gottesman codes are analogues of Hamming codes in that they saturate the asymptotic Hamming bound.'
+
+# - code_id: reed_muller
+#   detail: 'Gottesman codes can be obtained from the CSS construction using a first-order \([2^r,r+1,2^{r-1}]\) RM code and a \([2^r,2^r-1,2]\) even-weight code \cite{arxiv:quant-ph/9605021}.'
 
 
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