Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases

Fuente: arXiv
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Autores principales: Negari, Amir-Reza, Ellison, Tyler D., Hsieh, Timothy H.
Formato: Preprint
Publicado: 2024
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author Negari, Amir-Reza
Ellison, Tyler D.
Hsieh, Timothy H.
author_facet Negari, Amir-Reza
Ellison, Tyler D.
Hsieh, Timothy H.
contents We establish a correspondence between the fault-tolerance of local stabilizer codes experiencing measurement and physical errors and the mixed-state phases of decohered resource states in one higher dimension. Drawing from recent developments in mixed-state phases of matter, this motivates a diagnostic of fault-tolerance, which we refer to as the spacetime Markov length. This is a length scale determined by the decay of the (classical) conditional mutual information of repeated syndrome measurement outcomes in spacetime. The diagnostic is independent of the decoder, and its divergence signals the intrinsic breakdown of fault tolerance. As a byproduct, we find that decoherence may be useful for exposing transitions from higher-form symmetry-protected topological phases driven by both incoherent and coherent perturbations.
format Preprint
id arxiv_https___arxiv_org_abs_2412_00193
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases
Negari, Amir-Reza
Ellison, Tyler D.
Hsieh, Timothy H.
Quantum Physics
Statistical Mechanics
Strongly Correlated Electrons
We establish a correspondence between the fault-tolerance of local stabilizer codes experiencing measurement and physical errors and the mixed-state phases of decohered resource states in one higher dimension. Drawing from recent developments in mixed-state phases of matter, this motivates a diagnostic of fault-tolerance, which we refer to as the spacetime Markov length. This is a length scale determined by the decay of the (classical) conditional mutual information of repeated syndrome measurement outcomes in spacetime. The diagnostic is independent of the decoder, and its divergence signals the intrinsic breakdown of fault tolerance. As a byproduct, we find that decoherence may be useful for exposing transitions from higher-form symmetry-protected topological phases driven by both incoherent and coherent perturbations.
title Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases
topic Quantum Physics
Statistical Mechanics
Strongly Correlated Electrons
url https://arxiv.org/abs/2412.00193