From 7b7c8d675bf58743b72796292c756a65018e0c8b Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Mon, 12 Aug 2024 16:07:54 -0400 Subject: [PATCH] qldpc ref --- codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml b/codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml index c7807f98b..ad4cde0af 100644 --- a/codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml +++ b/codes/quantum/properties/stabilizer/qldpc/good_qldpc.yml @@ -30,12 +30,17 @@ description: | See \cite[Fig. 12]{arxiv:2402.16831} for more relationships between the constructions. +features: + rate: 'The codes'' rate and distance are both separated from zero as block length goes to infinity. AEL distance amplification can be used to construct asymptotically good QLDPC codes that approach the quantum Singleton bound \cite[Corr. 5.3]{arxiv:2212.09935}.' + relations: parents: - code_id: qldpc cousins: - code_id: translationally_invariant_stabilizer detail: 'Chain complexes describing some good QLDPC codes can be ''lifted'' into higher-dimensional manifolds admitting some notion of geometric locality \cite{arxiv:2012.02249,arxiv:2309.16104}. Applying this procedure to good QLDPC codes yiels \([[n,n^{1-2/D},n^{1-1/D}]]\) lattice stabilizer codes in \(D\) spatial dimensions that saturate the \hyperref[topic:bpt-bound]{BPT bound}, up to corrections poly-logarithmic in \(n\) \cite{arxiv:2303.06755}.' + - code_id: quantum_mds + detail: 'AEL distance amplification can be used to construct asymptotically good QLDPC codes that approach the quantum Singleton bound \cite[Corr. 5.3]{arxiv:2212.09935}.' # Begin Entry Meta Information