RT Journal Article
T1 Error resilience of fracton codes and near saturation of code-capacity threshold in three dimensions
A1 Canossa, Giovanni
A1 Pollet, Lode
A1 Martín-Delgado Alcántara, Miguel Ángel
A1 Song, Hao
A1 Liu, Ke
AB Fracton codes have been intensively studied as novel topological states of matter, yet their fault-tolerant properties remain largely unexplored. Here, we investigate the optimal thresholds of self-dual fracton codes, in particular, the checkerboard code, against stochastic Pauli noise. By utilizing a statistical-mechanical mapping combined with large-scale parallel tempering Monte Carlo simulations, we calculate the optimal code-capacity threshold of the checkerboard code to be 𝑝th≃0.107⁢(3). This value is the highest among known three-dimensional codes and nearly saturates the theoretical limit for topological codes. Our results further validate the generalized entropy relation for two mutually dual models, 𝐻⁡(𝑝th)+𝐻⁡(˜𝑝th)≈1, and extend its applicability beyond standard topological codes. This verification indicates the Haah's code also possesses a code-capacity threshold near the theoretical limit 𝑝th≈0.11. These findings highlight fracton codes as highly resilient quantum memory and demonstrate the utility of duality techniques in analyzing intricate error-correcting codes.
PB American Physical Society
SN 2469-9950
YR 2026
FD 2026-03-27
LK https://hdl.handle.net/20.500.14352/136473
UL https://hdl.handle.net/20.500.14352/136473
LA eng
NO G. Canossa, L. Pollet, M. A. Martin-Delgado, H. Song, and K. Liu, Error resilience of fracton codes and near saturation of code-capacity threshold in three dimensions, Phys. Rev. B 113, 104204 (2026).
NO German Research Foundation
NO European Commission
NO Ministerio de Ciencia e Investigación (España)
NO Agencia Estatal de Investigación (España)
NO Comunidad de Madrid
NO National Natural Science Foundation of China
NO Agence Nationale de la Recherche (France)
NO Bavarian State Government
DS Docta Complutense
RD 14 jun 2026