Optimal Threshold for Fracton Codes and Nearly Saturated Code Capacity in Three Dimensions
- URL: http://arxiv.org/abs/2512.22888v1
- Date: Sun, 28 Dec 2025 11:36:07 GMT
- Title: Optimal Threshold for Fracton Codes and Nearly Saturated Code Capacity in Three Dimensions
- Authors: Giovanni Canossa, Lode Pollet, Miguel A. Martin-Delgado, Hao Song, Ke Liu,
- Abstract summary: We find the optimal code capacity of the checkerboard code to be $p_th simeq 0.108(2)$.<n>This value is the highest among known three-dimensional codes and nearly saturates the theoretical limit for topological codes.<n>These findings highlight fracton codes as highly resilient quantum memory and demonstrate the utility of duality techniques in analyzing intricate quantum error-correcting codes.
- Score: 2.9154861336115765
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 $p_{th} \simeq 0.108(2)$. 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, $H(p_{th}) + H(\tilde{p}_{th}) \approx 1$, and extend its applicability beyond standard topological codes. This verification indicates the Haah's code also possesses a code capacity near the theoretical limit $p_{th} \approx 0.11$. These findings highlight fracton codes as highly resilient quantum memory and demonstrate the utility of duality techniques in analyzing intricate quantum error-correcting codes.
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