Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead

We introduce a technique that uses gauge fixing to significantly improve the quantum-error-correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this...

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Autores principales:	Oscar Higgott, Nikolas P. Breuckmann
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/5219d68ce74b4240bc68f002e81b2d09
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spelling	oai:doaj.org-article:5219d68ce74b4240bc68f002e81b2d092021-12-02T17:04:31ZSubsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead10.1103/PhysRevX.11.0310392160-3308https://doaj.org/article/5219d68ce74b4240bc68f002e81b2d092021-08-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.031039http://doi.org/10.1103/PhysRevX.11.031039https://doaj.org/toc/2160-3308We introduce a technique that uses gauge fixing to significantly improve the quantum-error-correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this information to improve performance. Applied to the subsystem toric code with three-qubit check operators, we increase the threshold under circuit-level depolarizing noise from 0.67% to 0.81%. The threshold increases further under a circuit-level noise model with small finite bias, up to 2.22% for infinite bias. Furthermore, we construct families of finite-rate subsystem low-density parity-check codes with three-qubit check operators and optimal-depth parity-check measurement schedules. To the best of our knowledge, these finite-rate subsystem codes outperform all known codes at circuit-level depolarizing error rates as high as 0.2%, where they have a qubit overhead that is 4.3× lower than the most efficient version of the surface code and 5.1× lower than the subsystem toric code. Their threshold and pseudo-threshold exceeds 0.42% for circuit-level depolarizing noise, increasing to 2.4% under infinite bias using gauge fixing.Oscar HiggottNikolas P. BreuckmannAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 3, p 031039 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Oscar Higgott Nikolas P. Breuckmann Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead
description	We introduce a technique that uses gauge fixing to significantly improve the quantum-error-correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this information to improve performance. Applied to the subsystem toric code with three-qubit check operators, we increase the threshold under circuit-level depolarizing noise from 0.67% to 0.81%. The threshold increases further under a circuit-level noise model with small finite bias, up to 2.22% for infinite bias. Furthermore, we construct families of finite-rate subsystem low-density parity-check codes with three-qubit check operators and optimal-depth parity-check measurement schedules. To the best of our knowledge, these finite-rate subsystem codes outperform all known codes at circuit-level depolarizing error rates as high as 0.2%, where they have a qubit overhead that is 4.3× lower than the most efficient version of the surface code and 5.1× lower than the subsystem toric code. Their threshold and pseudo-threshold exceeds 0.42% for circuit-level depolarizing noise, increasing to 2.4% under infinite bias using gauge fixing.
format	article
author	Oscar Higgott Nikolas P. Breuckmann
author_facet	Oscar Higgott Nikolas P. Breuckmann
author_sort	Oscar Higgott
title	Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead
title_short	Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead
title_full	Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead
title_fullStr	Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead
title_full_unstemmed	Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead
title_sort	subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/5219d68ce74b4240bc68f002e81b2d09
work_keys_str_mv	AT oscarhiggott subsystemcodeswithhighthresholdsbygaugefixingandreducedqubitoverhead AT nikolaspbreuckmann subsystemcodeswithhighthresholdsbygaugefixingandreducedqubitoverhead
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Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead

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