Design and Analysis of Quantum Dual-Containing CSS LDPC Codes based on Quasi-Dyadic Matrices
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917482843865088 |
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| author | Baldelli, Alessio Baldi, Marco Battaglioni, Massimo Chiaraluce, Franco Santini, Paolo |
| author_facet | Baldelli, Alessio Baldi, Marco Battaglioni, Massimo Chiaraluce, Franco Santini, Paolo |
| contents | Building scalable quantum computers requires quantum error-correcting codes that enable reliable operations in the presence of noise. Motivated by such need, this paper introduces two constructions of high-rate, quantum dual-containing (DC) Calderbank-Shor-Steane (CSS) low-density parity-check (LDPC) codes based on quasi-dyadic matrices. Their DC structure enables the transversal implementation of the Hadamard gate, and, jointly with the sparsity of their parity-check matrices enable low-complexity decoding via a standard binary belief-propagation algorithm. We provide several theoretical results concerning the cycle properties of these CSS codes. We also investigate their automorphism groups as well as their minimum distance. Furthermore, through numerical simulations, we show that the quantum CSS LDPC codes obtained through these constructions achieve better finite-length error rate performance than existing DC codes across different block lengths and code rates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_03631 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Design and Analysis of Quantum Dual-Containing CSS LDPC Codes based on Quasi-Dyadic Matrices Baldelli, Alessio Baldi, Marco Battaglioni, Massimo Chiaraluce, Franco Santini, Paolo Information Theory Quantum Physics Building scalable quantum computers requires quantum error-correcting codes that enable reliable operations in the presence of noise. Motivated by such need, this paper introduces two constructions of high-rate, quantum dual-containing (DC) Calderbank-Shor-Steane (CSS) low-density parity-check (LDPC) codes based on quasi-dyadic matrices. Their DC structure enables the transversal implementation of the Hadamard gate, and, jointly with the sparsity of their parity-check matrices enable low-complexity decoding via a standard binary belief-propagation algorithm. We provide several theoretical results concerning the cycle properties of these CSS codes. We also investigate their automorphism groups as well as their minimum distance. Furthermore, through numerical simulations, we show that the quantum CSS LDPC codes obtained through these constructions achieve better finite-length error rate performance than existing DC codes across different block lengths and code rates. |
| title | Design and Analysis of Quantum Dual-Containing CSS LDPC Codes based on Quasi-Dyadic Matrices |
| topic | Information Theory Quantum Physics |
| url | https://arxiv.org/abs/2605.03631 |