Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead

Oscar Higgott, Nikolas P. Breuckmann

Research output: Contribution to journalArticle (Academic Journal)peer-review

26 Citations (Scopus)


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 depolarising 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 LDPC 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 depolarising error rates as high as $0.2\%$, where they have a qubit overhead that is $4.3\times$ lower than the most efficient version of the surface code and $5.1\times$ lower than the subsystem toric code. Their threshold and pseudo-threshold exceeds $0.42\%$ for circuit-level depolarising noise, increasing to $2.4\%$ under infinite bias using gauge fixing.
Original languageEnglish
Article number031039
Number of pages30
JournalPhysical Review X
Issue number3
Early online date19 Sept 2021
Publication statusPublished - Sept 2021

Bibliographical note

Funding Information:
N. P. B. would like to thank Steve Flammia for pointing out Ref. . The authors would like to thank Andrew Landahl, Lingling Lao, and Michael Newman for helpful discussions. We would also like to thank Dan Browne for feedback on our manuscript. O. H. acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) (Grant No. EP/L015242/1). N. P. B. is supported by a UCLQ Fellowship. The authors also acknowledge the use of the UCL Myriad High Performance Computing Facility (Myriad@UCL), and associated support services in the completion of this work.

Publisher Copyright:
© 2021 authors. Published by the American Physical Society.


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