Balanced Product Quantum Codes

Nikolas P. Breuckmann, Jens N. Eberhardt · 2020 · IEEE Trans. Inf. Theory (2021)

| 编号 QE118 | 主题 qLDPC 码 | 链接 arXiv:2012.09271 |

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。

This work provides the first explicit and non-random family of $[[N,K,D]]$ LDPC quantum codes which encode $K\in \Theta (N^{\frac{4}{5}})$ logical qubits with distance $D\in \Omega (N^{\frac{3}{5}})$. The family is constructed by amalgamating classical codes and Ramanujan graphs via an operation called balanced product. Recently, Hastings-Haah-O’Donnell and Panteleev-Kalachev were the first to show that there exist families of LDPC quantum codes which break the $\mathrm{polylog}(N)\sqrt{N}$ distance barrier. However, their constructions are based on probabilistic arguments which only guarantee the code parameters with high probability whereas our bounds hold unconditionally. Further, balanced produc

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