diff --git a/codes/quantum/properties/stabilizer/qldpc/qldpc.yml b/codes/quantum/properties/stabilizer/qldpc/qldpc.yml index 017ae2ed9..48d5952a9 100644 --- a/codes/quantum/properties/stabilizer/qldpc/qldpc.yml +++ b/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}. diff --git a/codes/quantum/qubits/small_distance/small/shor_nine.yml b/codes/quantum/qubits/small_distance/small/shor_nine.yml index 72b8e0305..e64c4e9fc 100644 --- a/codes/quantum/qubits/small_distance/small/shor_nine.yml +++ b/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: diff --git a/codes/quantum/qubits/stabilizer/hermitian/hermitian_qldpc.yml b/codes/quantum/qubits/stabilizer/hermitian/hermitian_qldpc.yml index 220d619ae..1c85fc313 100644 --- a/codes/quantum/qubits/stabilizer/hermitian/hermitian_qldpc.yml +++ b/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