2026-06-28T09:46:38Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1364732026-05-01T00:08:39Zcom_20.500.14352_14col_20.500.14352_15

Error resilience of fracton codes and near saturation of code-capacity threshold in three dimensions Canossa, Giovanni Pollet, Lode Martín-Delgado Alcántara, Miguel Ángel Song, Hao Liu, Ke 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. 2026-04-30T18:07:13Z 2026-04-30T18:07:13Z 2026-04-30T18:07:13Z 2026-03-27 journal article https://hdl.handle.net/20.500.14352/136473 2469-9950 10.1103/2y2z-hgfn 2469-9969 eng 390814868 info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-122547NB-I00/ES/TECNOLOGIAS CLAVE PARA COMPUTACION CUANTICA/ 23PDI0006/MadQuantum-CM TEC-2024/COM-84/QUITEMAD-CM 12522502 12474145 12447101 ANR-23-CE30-0018 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). http://creativecommons.org/licenses/by/4.0/ open access Attribution 4.0 International American Physical Society