Improved energy barrier in higher-dimensional hypergraph product codes
Phys. Rev. A 113, 012440 – Published 28 January, 2026
DOI: https://doi.org/10.1103/b9r5-xhcp
Abstract
Single-shot error correction outperforms conventional approaches by requiring only one round of stabilizer measurements for decoding, even in the presence of measurement errors. This capability relates to the soundness and confinement property of codes, which provides an energy barrier lower bound. Earlier research established a confinement property for three-dimensional (3D) hypergraph product codes [A. O. Quintavalle et al., PRX Quantum 2, 020340 (2021)], yielding an energy barrier lower bound for these codes. In this work, by analyzing the structure of logical operators, we show an improved energy barrier lower bound for higher-dimensional hypergraph product (HHGP) codes with low-density parity check (LDPC) property. Our bound exceeds results derived from soundness and confinement, and unlike standard hypergraph product codes, these higher-dimensional variants can possess macroscopic energy barriers even when the underlying classical codes lack this property. Specifically, our results show that the energy barrier of LDPC HHGP codes is lower bounded by the distance of the underlying classical codes. This bound is tight if the underlying classical codes exhibit system size-dependent distances but constant energy barriers, like 3D and 4D toric codes.
