From 8f287cc266d49ca0fc464a945f9b331484479507 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Mon, 21 Oct 2024 23:29:38 -0400 Subject: [PATCH] ~ --- codes/quantum/properties/qecc.yml | 1 + codes/quantum/qudits/stabilizer/qudit_stabilizer.yml | 2 +- 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/codes/quantum/properties/qecc.yml b/codes/quantum/properties/qecc.yml index 4ae43478b..ae8114f4f 100644 --- a/codes/quantum/properties/qecc.yml +++ b/codes/quantum/properties/qecc.yml @@ -58,6 +58,7 @@ features: decoders: - 'The effect of an error is a mapping of the code subspace into another, potentially overlapping, subspace. To determine, or diagnose, the effect of the error in what is known as \textit{syndrome-based decoding}, one can measure one or more operators called \textit{check operators}, which resolve code and error spaces without collapsing the quantum information inside the spaces. The eigenvalues of check operators are called \textit{error syndromes}. One \textit{round} or \textit{cycle} of quantum error correction proceeds by extracting syndromes and performing correcting operations to map the error space containing the logical information back into the codespace. For some codes, correcting operations are not necessary because one can instead track which error space contains the logical information.' + notes: - 'See Refs. \cite{arxiv:quant-ph/9712048,doi:10.1090/gsm/047,doi:10.1017/CBO9780511976667,arxiv:0904.2557,arxiv:0905.2794,arxiv:1302.3428,doi:10.1103/RevModPhys.88.041001,doi:10.1002/9783527805785.ch1,arxiv:1907.11157,preset:PreskillNotes,arxiv:1910.03672,doi:10.1002/9781119790327.ch10,arxiv:2407.12737} for overviews of quantum error correction.' - 'See Refs. \cite{doi:10.1017/CBO9781139034807,doi:10.1201/b15868,preset:GottesmanBook} for books on quantum error correction.' diff --git a/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml b/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml index 67bf6faf1..4ebb79c29 100644 --- a/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml +++ b/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml @@ -30,7 +30,7 @@ description: | One can switch between stabilizer codes by appending another Abelian subgroup of the \hyperref[topic:qudit-pauli]{modular-qudit Pauli group} to the stabilizer group and taking the center of the resulting larger group. - \begin{defterm}{Code switching, code deformation, or stabilizer update rule} + \begin{defterm}{Stabilizer code switching, code deformation, or update rule} \label{topic:code-switching} Code switching is a map between stabilizer codes that is done using a stabilizer group \(\mathsf{F}\) of the \(n\)-\hyperref[topic:qudit-pauli]{modular-qudit Pauli group}, \begin{align}