From e988358acb00bbd2456536a1e7fd5056ba833211 Mon Sep 17 00:00:00 2001 From: VVA2024 Date: Tue, 17 Dec 2024 23:23:23 -0500 Subject: [PATCH] refs --- codes/quantum/properties/approximate_qecc.yml | 2 +- .../stabilizer/topological/surface/2d_surface/surface.yml | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/codes/quantum/properties/approximate_qecc.yml b/codes/quantum/properties/approximate_qecc.yml index a7bc6b2ca..8fef91cc0 100644 --- a/codes/quantum/properties/approximate_qecc.yml +++ b/codes/quantum/properties/approximate_qecc.yml @@ -150,7 +150,7 @@ features: - 'The \textit{Petz recovery map} a.k.a. the \textit{transpose map} \cite{doi:10.1007/BF01212345,doi:10.1093/qmath/39.1.97,arxiv:1810.03150}, a quantum channel determined by the codespace and noise channel, yields an infidelity of recovery that is at most twice away from the infidelity of the best possible recovery \cite{arxiv:quant-ph/0004088}. The fidelity can be expressed exactly as a function of the \term{Knill-Laflamme conditions} \cite[Thm. 1]{arxiv:2401.02022}, and it can be used to derive a generalization of the \term{Knill-Laflamme conditions} for approximate QECCs \cite{arxiv:0909.0931}. Satisfaction of the \term{Knill-Laflamme conditions} is sufficient but not necessary for the Petz recovery map to be the optimal recovery, and a necessary and sufficient condition has been derived \cite{arxiv:2410.23622}. - The infidelity of a modified Petz recovery map under erasure can be bounded using the conditional mutual information \cite{arxiv:1410.0664,arxiv:1509.07127,arxiv:1610.06169}. + The infidelity of a modified Petz recovery map under erasure can be bounded using the conditional mutual information via the \textit{approximate Petz theorem} \cite{arxiv:1410.0664,arxiv:1509.07127,arxiv:1610.06169}. In the case of topological codes, the Petz infidelity is related to the topological entanglement entropy \cite{arxiv:2408.00857}. Modifications include the Petz-like decoder \cite{arxiv:2405.06051}.' - 'The Yoshida-Kitaev decoder for the Hayden-Preskill protocol \cite{arxiv:1710.03363} can be extended to general QECCs \cite{arxiv:2405.06051}.' diff --git a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml index 1565f4774..ce099d914 100644 --- a/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml +++ b/codes/quantum/qubits/stabilizer/topological/surface/2d_surface/surface.yml @@ -121,7 +121,7 @@ features: - 'A color-code decoder can be used for the surface code \cite{arxiv:2306.16476}.' - 'Progressive-Proximity Bit-Flipping (PPBF) decoder \cite{arxiv:2402.15924}.' - 'Collision clustering decoder \cite{arxiv:2309.05558}.' - - 'Quasi-local decoder \cite{arxiv:2404.07251}.' + - 'Quasi-local Lindbladian decoder based on the approximate Petz theorem \cite{arxiv:2404.07251}.' - 'Exclusive decoder family incorporating post-selection on decoding instances deemed not too difficult \cite{arxiv:2405.03766}.' threshold: