Designing Codes around Interactions: The Case of a Spin
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I present a new approach for designing quantum error-correcting codes guaranteeing a physically natural implementation of Clifford operations. Inspired by the scheme put forward by Gottesman, Kitaev, and Preskill for encoding a qubit in an oscillator in which Clifford operations may be performed via Gaussian unitaries, this approach yields new schemes for encoding a qubit in a large spin in which single-qubit Clifford operations may be performed via spatial rotations. I construct all possible examples of such codes, provide universal-gate-set implementations using quadratic angular-momentum Hamiltonians, and derive criteria for when these codes exactly correct physically relevant errors.
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By embedding a logical qubit within a bosonic logical qudit, multiple layers of error correction can be implemented inside a single oscillator.
“By embedding a logical qubit within a bosonic logical qudit20,56–58, multiple layers of error correction can be implemented inside a single oscillator.”
From Quantum error correction of qudits beyond break-even (2025) · cites this paper as [57]
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- Authors
- Gross, J. A.
- Affiliations
- Université de Sherbrooke (CA)
- Corresponding author
- Gross, Jonathan A.
- ORCID
- Gross, Jonathan A.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2021-07-02
- Volume
- 127
- Issue
- 1
- Pages
- 010504-010504
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W3026839285
- Cited by
- 63
- References
- 24
- Citations by year
- 2026: 17 · 2025: 19 · 2024: 15 · 2023: 7 · 2022: 1 · 2021: 4
- FWCI
- 2.39
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Natural Sciences and Engineering Research Council of Canada
- Canada First Research Excellence Fund
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum error-correcting codes, Clifford operations, spatial rotation, universal gate set
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