Journal article
Quantum error correction with gauge symmetries
- Abstract:
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Quantum simulations of lattice gauge theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors in order to retain a local Hamiltonian. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss’ law constraint to correct one-qubit errors for a ℤ2 or truncated U(1) LGT in 1+1 and 2+1 dimensions with a link flux cutoff of 1. Unlike existing work on detecting violations of Gauss’ law, our circuits are fault tolerant and the overall error correction scheme outperforms a naïve application of the [5, 1, 3] code. The constructions outlined can be extended to LGT systems with larger cutoffs and may be of use in understanding how to hybridize error correction and quantum simulation for LGTs in higher space-time dimensions and with different symmetry groups.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 1.1MB, Terms of use)
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- Publisher copy:
- 10.1038/s41534-023-00706-8
Authors
- Publisher:
- Springer Nature
- Journal:
- npj Quantum Information More from this journal
- Volume:
- 9
- Issue:
- 1
- Article number:
- 41
- Publication date:
- 2023-04-25
- Acceptance date:
- 2023-03-31
- DOI:
- EISSN:
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2056-6387
- Language:
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English
- Keywords:
- Pubs id:
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2123521
- Local pid:
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pubs:2123521
- Deposit date:
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2025-05-20
- ARK identifier:
Terms of use
- Copyright holder:
- Rajput et al.
- Copyright date:
- 2023
- Rights statement:
- Copyright © 2023, The Author(s). 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/.
- Licence:
- CC Attribution (CC BY)
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