Kubica, Aleksander and Vasmer, Michael (2022) Single-shot quantum error correction with the three-dimensional subsystem toric code. Nature Communications, 13 . Art. No. 6272. ISSN 2041-1723. PMCID PMC9586949. doi:10.1038/s41467-022-33923-4. https://resolver.caltech.edu/CaltechAUTHORS:20221103-651740800.11
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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.
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| Additional Information: | 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. | |||||||||
| Group: | AWS Center for Quantum Computing | |||||||||
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| PubMed Central ID: | PMC9586949 | |||||||||
| DOI: | 10.1038/s41467-022-33923-4 | |||||||||
| Record Number: | CaltechAUTHORS:20221103-651740800.11 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20221103-651740800.11 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 117696 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Research Services Depository | |||||||||
| Deposited On: | 15 Nov 2022 16:37 | |||||||||
| Last Modified: | 15 Nov 2022 19:05 |
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