Single-shot quantum error correction with the three-dimensional subsystem toric code

Creators: Kubica, Aleksander; Vasmer, Michael

Abstract

Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to implement QEC is one of the most pressing challenges. Here, we introduce a new topological quantum error-correcting code, the three-dimensional subsystem toric code (3D STC). The 3D STC can be realized with geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions. We prove that one round of parity-check measurements suffices to perform reliable QEC with the 3D STC even in the presence of measurement errors. We also propose an efficient single-shot QEC decoding strategy for the 3D STC and numerically estimate the resulting storage threshold against independent bit-flip, phase-flip and measurement errors to be p_STC ≈ 1.045%. Such a high threshold together with local parity-check measurements make the 3D STC particularly appealing for realizing fault-tolerant quantum computing.

Additional Information

© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. A.K. thanks Héctor Bombín, Sergey Bravyi, Daniel Gottesman, Alexei Kitaev, and John Preskill for helpful discussions. M.V. thanks Dan Browne and Jacob Bridgeman for valuable discussions. A.K. acknowledges the funding provided by the Simons Foundation through the "It from Qubit" Collaboration. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. This work was completed prior to A.K. joining AWS Center for Quantum Computing. Author contributions. Concept conceived by both authors. Bulk model devised by M.V., lattice realizations of the model by A.K. Analytic proofs by A.K. Simulations designed and written by A.K. Data collected and analyzed by M.V. Manuscript prepared by both authors. Data availability. The data generated in this study have been deposited in the Zenodo database 10.5281/zenodo.7087715. Code availability. The code that supports the findings of this study is available from the corresponding author upon request. The authors declare no competing interests.

Attached Files

Published - 41467_2022_Article_33923.pdf

Supplemental Material - 41467_2022_33923_MOESM1_ESM.pdf

Files

41467_2022_33923_MOESM1_ESM.pdf

Files (3.9 MB)

Name	Size	Download all
41467_2022_33923_MOESM1_ESM.pdf md5:20a94835a7cfaaa7738e70697c523d24	1.2 MB	Preview Download
41467_2022_Article_33923.pdf md5:fba25d545cb1a577913c3ae85e86f3cd	2.7 MB	Preview Download

Additional details

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes