Single-shot preparation of hypergraph product codes via dimension jump

Yifan Hong

doi:10.22331/q-2025-10-07-1879

Single-shot preparation of hypergraph product codes via dimension jump

Yifan Hong

Joint Quantum Institute & Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD 20742, USA

Published:	2025-10-07, volume 9, page 1879
Editor:	Felix Huber
Eprint:	arXiv:2410.05171v2
Doi:	https://doi.org/10.22331/q-2025-10-07-1879
Citation:	Quantum 9, 1879 (2025).

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Abstract

Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for encoding quantum low-density parity-check codes is transversal initialization, where one begins in a product state and measures a set of stabilizer generators. In the presence of measurement errors however, this procedure is generically not fault-tolerant, and so one typically needs to repeat the measurements many times, resulting in a deep initialization circuit. We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with $O(\sqrt{n})$ spatial overhead, and we show that the protocol is robust even in the presence of measurement errors. Our construction is inspired by dimension-jumping in topological codes and leverages two properties that arise from the homological product of codes. We provide some improvements to lower the spatial overhead and discuss applications to fault-tolerant architectures.

► BibTeX data

@article{Hong2025singleshot,
  doi = {10.22331/q-2025-10-07-1879},
  url = {https://doi.org/10.22331/q-2025-10-07-1879},
  title = {Single-shot preparation of hypergraph product codes via dimension jump},
  author = {Hong, Yifan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1879},
  month = oct,
  year = {2025}
}

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