2025/12/28 by Giovanni Canossa, Canossa, Giovanni, Lode Pollet +7
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.2512.22888
openalex publication_date 2025/12/28 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28
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 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 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 quantum error-correcting codes.