Distance-preserving stabilizer measurements in hypergraph product codes

Argyris Giannisis Manes; Jahan Claes

doi:10.22331/q-2025-01-30-1618

Distance-preserving stabilizer measurements in hypergraph product codes

Argyris Giannisis Manes and Jahan Claes

Departments of Physics and Applied Physics, Yale University, New Haven, CT 06520, USA Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA

Published:	2025-01-30, volume 9, page 1618
Editor:	Tom Gur
Eprint:	arXiv:2308.15520v2
Doi:	https://doi.org/10.22331/q-2025-01-30-1618
Citation:	Quantum 9, 1618 (2025).

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Abstract

Unlike the surface code, quantum low-density parity-check (QLDPC) codes can have a finite encoding rate, potentially lowering the error correction overhead. However, finite-rate QLDPC codes have nonlocal stabilizers, making it difficult to design stabilizer measurement circuits that are low-depth and do not decrease the effective distance. Here, we demonstrate that a popular family of finite-rate QLDPC codes, hypergraph product codes, has the convenient property of distance-robustness: any stabilizer measurement circuit preserves the effective distance. In particular, we prove the depth-optimal circuit in [Tremblay et al, PRL 129, 050504 (2022)] is also optimal in terms of effective distance.

Featured image: Example logical operators in a hypergraph product code.

► BibTeX data

@article{Manes2025distancepreserving,
  doi = {10.22331/q-2025-01-30-1618},
  url = {https://doi.org/10.22331/q-2025-01-30-1618},
  title = {Distance-preserving stabilizer measurements in hypergraph product codes},
  author = {Manes, Argyris Giannisis and Claes, Jahan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1618},
  month = jan,
  year = {2025}
}

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