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Trapped Ion Quantum Computing

Construction of a Family of Quantum Codes Using Sub-exceding Functions via the Hypergraph Product and the Generalized Shor Construction

arXiv
Authors: Luc Rabefihavanana, Harinaivo Andriatahiny, Randriamiarampanahy Ferdinand

Year

2026

Paper ID

28608

Status

Preprint

Abstract Read

~2 min

Abstract Words

116

Citations

N/A

Abstract

In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes Lk and Lk+, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in minimum distance, decoding efficiency, and structural simplicity. By combining the hypergraph product framework with a generalized Shor construction, we obtain a scalable class of quantum codes with parameters \[[6k2, k2, d\]]. The resulting quantum codes exhibit a rich combinatorial structure and promising properties, particularly in terms of locality, low-density parity-check (LDPC) structure, and asymptotic behavior. The minimum distance satisfies d=3 for k=3 and d=4 for kge4, establishing a new framework for structured quantum LDPC code design and optimization.

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  • This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes Lk and Lk^+, defined via sub-exceding functions.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.08213 [2] arXiv https://arxiv.org/abs/2603.08213 [3] Publisher https://arxiv.org/abs/2603.08213

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