Code conversion with the quantum Golay code for a universal transversal gate set
Open accessAbstract
The [[7,1,3]] Steane code and [[23,1,7]] quantum Golay code have been identified as good candidates for fault-tolerant quantum computing via code concatenation. These two codes have transversal implementations of all Clifford gates but require some other scheme for fault-tolerant $T$ gates. Using magic states, Clifford operations, and measurements is one common scheme, but magic-state distillation can have a large overhead. Code conversion is one avenue for implementing a universal gate set fault tolerantly without the use of magic-state distillation. Analogously to how the [[7,1,3]] Steane code can be fault tolerantly converted to and from the [[15,1,3]] Reed-Muller code which has a transversal $T$ gate, the [[23,1,7]] Golay code can be converted to a [[95,1,7]] triorthogonal code with a transversal $T$ gate. A crucial ingredient of this procedure is the [[49,1,5]] triorthogonal code, which can itself be seen as being related to the self-dual [[17,1,5]] two-dimensional color code. Additionally, a method for code conversion based on a transversal cnot between the codes, rather than stabilizer measurements, is described.
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Similar code-switching principles apply to other families, such as the doubled color codes and quadratic residue codes.
“Similar code-switching principles apply to other families, such as the doubled color codes [115] and quadratic residue codes [116, 117].”
From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [116]
The General Code-Doubling Procedure (Section II) describes code conversion beyond the Golay code, and the Introduction identifies related methods for doubled color codes. Our copy does not identify the quantum Golay code as a quadratic residue code or explicitly apply the procedure to quadratic residue codes, so that part of the citing sentence is not established by this source. (LLM, conf=0.78)
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Quantum error correction and fault tolerance: A comprehensive tutorial
Spencer, D. J., Jain, S. P., Tanggara, A., Sun, Z., Haug, T., Khu, D., & Bharti, K. (2026) · arXiv
- Authors
- Sullivan, M.
- Affiliations
- Brookhaven National Laboratory (US)
- Corresponding author
- Sullivan, Matthew
- ORCID
- Sullivan, Matthew
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2024-04-18
- Volume
- 109
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W4394916791
- Cited by
- 7
- References
- 3
- Citations by year
- 2026: 3 · 2025: 4
- FWCI
- 0.91
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (DE-SC0012704)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Keywords
- program translation, Steane code, fault-tolerant quantum computing, universal gate set, magic state distillation, color codes, concatenated codes
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