~

codes/quantum/properties/stabilizer/qldpc/qldpc.yml

@@ -69,6 +69,7 @@ features:
     Conversely, a code with parameters \(k\) and \(d\) requires a graph with \(\Omega(d)\) edges of length \(\Omega(d/n^{1/D})\) \cite{arxiv:2109.10982}.
 
   decoders:
+    - 'Iterative error estimation based on the MIN-SUM and SUM-PRODUCT algorithms \cite{arxiv:quant-ph/0502086}.'
     - 'Belief-propagation (BP) decoder \cite{arxiv:0801.1241} is a quantum version of the classical BP decoder, but performance suffers due to degeneracy \cite{arxiv:2012.15297}.
     Various post-processing algorithms have been proposed (see below and also Ref. \cite{doi:10.1109/MILCOM58377.2023.10356284,doi:10.1109/ICASSP48485.2024.10446153}).'
     - 'BP-OSD decoder, scaling as \(O(n^3)\), adds a post-processing step based on ordered statistics decoding (OSD) to the belief propogation (BP) decoder \cite{arxiv:1904.02703}.

codes/quantum/qubits/small_distance/small/shor_nine.yml

@@ -62,7 +62,7 @@ relations:
     - code_id: quantum_parity
       detail: 'The Shor code is part of the sub-family of \([[m^2,1,m]]\) QPCs.'
     - code_id: real_projective_plane
-      detail: 'The Shor code is the smallest surface code defined on the projective plane \(\mathbb{R}P^2\) \cite[Fig. 4]{arxiv:quant-ph/9810055}.'
+      detail: 'The Shor code is one of the nine-qubit surface codes defined on the projective plane \(\mathbb{R}P^2\) \cite[Fig. 4]{arxiv:quant-ph/9810055}.'
     - code_id: stab_9_1_3
       detail: 'The \([[9,1,3]]_{\mathbb{Z}_q}\) modular-qudit code for \(q=2\) reduces to the \([[9,1,3]]\) Shor code.'
   cousins:

codes/quantum/qubits/stabilizer/hermitian/hermitian_qldpc.yml

@@ -13,6 +13,9 @@ introduced: '\cite{arxiv:quant-ph/0502086}'
 description: |
   A Hermitian qubit QLDPC code whose stabilizer generator matrix is constructed using two nested subgroups of \(GF(4)^n\).
 
+features:
+  rate: 'Two families with rate of one-half are provided.'
+
 relations:
   parents:
     - code_id: stabilizer_over_gf4