Spatial overhead reduction for 2D hypergraph product codes
Abstract
The hypergraph product creates a quantum stabilizer code from two input classical linear codes; a paradigmatic example being the surface code as a hypergraph product of two classical repetition codes. Many properties of the hypergraph product code can be inherited from those of the classical codes such as the code dimension, minimum distance and certain fault-tolerant gadgets. We investigate ways to reduce the number of physical qubits in hypergraph product codes while maintaining some of their useful properties for fault tolerance. We show that the code dimension, canonical logical basis, and minimum distances of the hypergraph product code are preserved through this reduction. We also provide syndrome-measurement schedules that preserve the effective distance as well as examples of reduced hypergraph product codes with parameter improvements such as [ [610,64,6] ] → [ [441,64,6] ] and [ [1225,49,11] ] → [ [931,49,11] ]. In memory simulations with circuit-level depolarizing noise, the reduced codes can exhibit logical error rates comparable to their unreduced versions at the sampled low physical-error rates, while using fewer physical qubits. Finally, we show how overhead reduction can be compatible with homomorphic measurement gadgets, fold-transversal gates and automorphisms, which extends the savings to logical computation.
Related
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- 2 Fast 2 Surgery: Fast surgery on QLDPC codes with Õ(n(k + d)) space overhead
- Algorithmic Construction of Gapped Boundaries for Topological Stabilizer Codes: A Route to Low-Overhead Planar qLDPC Codes
BibTeX
@misc{pabla2026spatial,
title = {{Spatial overhead reduction for 2D hypergraph product codes}},
author = {Aarav Pabla and Yu-Xin Wang and Yifan Hong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.11318},
eprint = {2605.11318},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.11318},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spatial overhead reduction for 2D hypergraph product codes
AU - Aarav Pabla
AU - Yu-Xin Wang
AU - Yifan Hong
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2605.11318
UR - https://arxiv.org/abs/2605.11318
AB - The hypergraph product creates a quantum stabilizer code from two input classical linear codes; a paradigmatic example being the surface code as a hypergraph product of two classical repetition codes. Many properties of the hypergraph product code can be inherited from those of the classical codes such as the code dimension, minimum distance and certain fault-tolerant gadgets. We investigate ways to reduce the number of physical qubits in hypergraph product codes while maintaining some of their useful properties for fault tolerance. We show that the code dimension, canonical logical basis, and minimum distances of the hypergraph product code are preserved through this reduction. We also provide syndrome-measurement schedules that preserve the effective distance as well as examples of reduced hypergraph product codes with parameter improvements such as [ [610,64,6] ] → [ [441,64,6] ] and [ [1225,49,11] ] → [ [931,49,11] ]. In memory simulations with circuit-level depolarizing noise, the reduced codes can exhibit logical error rates comparable to their unreduced versions at the sampled low physical-error rates, while using fewer physical qubits. Finally, we show how overhead reduction can be compatible with homomorphic measurement gadgets, fold-transversal gates and automorphisms, which extends the savings to logical computation.
ER -