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Cited by 8Quantum Computing Algorithms and ArchitectureCoding theory and cryptographyQuantum Information and Cryptography

Transversal Clifford and T -Gate Codes of Short Length and High Distance

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Jain, Shubham P., Albert, Victor V.·2025·IEEE Journal on Selected Areas in Information Theory
DOI 10.1109/jsait.2025.3570832
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Abstract

The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will soon be realizable, it is important to construct stabilizer codes that, for a given code distance, admit fault-tolerant implementations of logical gates with the fewest number of physical qubits. To this aim, we construct three kinds of codes encoding a single logical qubit for distances up to 31. First, we construct the smallest known doubly even codes, all of which admit a transversal implementation of the Clifford group. Applying a doubling procedure arXiv:1509.03239 to such codes yields the smallest known weak triply even codes for the same distances and number of encoded qubits. This second family of codes admit a transversal implementation of the logical T-gate. Relaxing the triply even property, we obtain our third family of triorthogonal codes with an even lower overhead at the cost of requiring additional Clifford gates to achieve the same logical operation. To our knowledge, these are the smallest known triorthogonal codes for their respective distances. While not qLDPC, the stabilizer generator weights of the code families with transversal T-gates scale roughly as the square root of their lengths.

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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 [117]

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Authors
Jain, S. P., & Albert, V. V.
Affiliations
Joint Center for Quantum Information and Computer Science (US)
ORCID
Venue
IEEE Journal on Selected Areas in Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2025
Volume
6
Pages
127-137
ISSN
2641-8770 (ISSN-L)
DOI
10.1109/jsait.2025.3570832
OpenAlex
W4410427697
Cited by
8
References
6
Citations by year
2026: 3 · 2025: 5
FWCI
2.61
Type
journal article
Language
en
Open access
Licence
Locations
  • IEEE Journal on Selected Areas in Information Theory (publishedVersion)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • arXiv (Cornell University) (cc-by)
Funders
  • NSF (OMA-2120757 (QLCI), CIF-2330909)
  • Institute for Mathematical and Statistical Innovation
  • National Science Foundation (DMS-1929348)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
stabilizer codes, doubly-even codes, nonlocal interactions, fault-tolerant quantum computing, logical qubit encoding, code distance, code length, qLDPC codes

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