Targeted Clifford logical gates for hypergraph product codes

Adway Patra; Alexander Barg

doi:10.22331/q-2025-08-29-1842

Targeted Clifford logical gates for hypergraph product codes

Department of ECE and Institute for Systems Research, University of Maryland, College Park, MD 20742

Published:	2025-08-29, volume 9, page 1842
Editor:	Joschka Roffe
Eprint:	arXiv:2411.17050v3
Doi:	https://doi.org/10.22331/q-2025-08-29-1842
Citation:	Quantum 9, 1842 (2025).

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Updated after initial publication: This publication was updated to version v3 after the initial publication. The authors left the following comment on the arXiv:

Final version, 46pp

Abstract

Starting with an explicit framework for designing logical Clifford circuits for CSS codes, we construct logical gates for Hypergraph Product Codes. We first derive symplectic matrices for CNOT, CZ, Phase, and Hadamard operators, which together generate the Clifford group. This enables us to design explicit transformations that result in targeted logical gates for arbitrary codes in this family. As a concrete example, we give logical circuits for the $[[18,2,3]]$ toric code.

► BibTeX data

@article{Patra2025targetedclifford,
  doi = {10.22331/q-2025-08-29-1842},
  url = {https://doi.org/10.22331/q-2025-08-29-1842},
  title = {Targeted {C}lifford logical gates for hypergraph product codes},
  author = {Patra, Adway and Barg, Alexander},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1842},
  month = aug,
  year = {2025}
}

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Cited by

[1] Jérôme Guyot and Samuel Jaques, "On the Addressability Problem on CSS Codes", Quantum 10, 2145 (2026).

[2] Zhuangzhuang Chen, Jack Owen Weinberg, and Narayanan Rengaswamy, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 158 (2025) ISBN:979-8-3315-5736-2.

[3] Victor V. Albert and Philippe Faist, "Handbook of Error-Correcting Codes", arXiv:2606.11484, (2026).

[4] Yiming Li, Zimu Li, Zi-Wen Liu, and Quynh T. Nguyen, "Poincaré Duality and Multiplicative Structures on Quantum Codes", arXiv:2512.21922, (2025).

[5] Zhuangzhuang Chen, Jack Owen Weinberg, and Narayanan Rengaswamy, "Fault Tolerant Quantum Simulation via Symplectic Transvections", arXiv:2504.11444, (2025).

[6] Asit Kumar Pradhan, Nithin Raveendran, Narayanan Rengaswamy, and Bane Vasić, "Linear Time Iterative Decoders for Hypergraph-Product and Lifted-Product Codes", arXiv:2504.01728, (2025).

[7] Hayato Goto, "Optimized Many-Hypercube Codes toward Lower Logical Error Rates and Earlier Realization", arXiv:2512.00561, (2025).

[8] Asit Kumar Pradhan, Nithin Raveendran, Narayanan Rengaswamy, and Bane Vasić, "Linear Time Iterative Decoders for Hypergraph-Product and Lifted-Product Codes", IEEE Transactions on Information Theory 72 7, 4618 (2026).

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