Quantum LDPC Codes With Almost Linear Minimum Distance

P. Panteleev and G. Kalachev · 2020 · IEEE Transactions on Information Theory

| 编号 QE020 | 主题 基础理论 | 链接 arXiv:2012.04068 |

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。

We give a construction of quantum LDPC codes of dimension $\Theta (\log N)$ and distance $\Theta (N/\log N)$ as the code length $N\to \infty $ . Using a product of chain complexes this construction also provides a family of quantum LDPC codes of distance $\Omega (N^{1-\alpha /2}/\log N)$ and dimension $\Omega (N^\alpha \log N)$ , where $0 \le \alpha . We also introduce and study a new operation called lifted product, which naturally generalizes the product operations for quantum codes and chain complexes. Moreover, as a simple byproduct of our results on quantum codes, we obtain a new result on classical codes. We show that for any fixed $R there exists an asymptotically go

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