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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2512.22888 |
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| _version_ | 1866915961715556352 |
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| author | Canossa, Giovanni Pollet, Lode Martin-Delgado, Miguel A. Song, Hao Liu, Ke |
| author_facet | Canossa, Giovanni Pollet, Lode Martin-Delgado, Miguel A. Song, Hao Liu, Ke |
| contents | 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 $p_{th} \simeq 0.107(3)$. 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, $H(p_{th}) + H(\tilde{p}_{th}) \approx 1$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions Canossa, Giovanni Pollet, Lode Martin-Delgado, Miguel A. Song, Hao Liu, Ke Quantum Physics Statistical Mechanics 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 $p_{th} \simeq 0.107(3)$. 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, $H(p_{th}) + H(\tilde{p}_{th}) \approx 1$, 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. |
| title | Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2512.22888 |