Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions
By employing statistical-mechanical mapping and large-scale Monte Carlo simulations, this study determines that the checkerboard fracton code achieves an optimal code capacity threshold of approximately 10.7%, the highest among known three-dimensional codes and nearly saturating the theoretical limit, thereby validating generalized entropy relations and confirming the high error resilience of fracton codes as quantum memories.