Diffusion Codes: Self-Correction from Small(er)-Set Expansion with Tunable Non-locality

Adithya Sriram, Vedika Khemani, Benedikt Placke · 2025 · arXiv 2025

| 编号 QE128 | 主题 qLDPC 码 | 链接 arXiv:2510.07179 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Optimal constructions of classical LDPC codes can be obtained by choosing the Tanner graph uniformly at random among biregular graphs. We introduce a class of codes that we call “diffusion codes”, defined by placing each edge connecting bits and checks on some graph, and acting on that graph with a random SWAP network. By tuning the depth of the SWAP network, we can tune a tradeoff between the amount of randomness — and hence the optimality of code parameters — and locality with respect to the underlying graph. For diffusion codes defined on the cycle graph, if the SWAP network has depth $\sim Tn$ with $T>n^{2\beta }$ for arbitrary $\beta >0$, then we prove that almost surely the Tanner graph is

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