带纠缠辅助的非二元准循环低密度奇偶校验码
Non-Binary Quasi-Cyclic LDPC Codes with Entanglement Assistance
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中文总结 AI 辅助
该研究在任意有限域上构造两类带纠缠辅助的非二元准循环量子低密度奇偶校验码，通过图设计平衡纠错性能与纠缠消耗，为高效实现这类码提供实用方法。
中文摘要 AI 辅助
我们在任意有限域上构造了两类非二元纠缠辅助（EA）准循环（QC）量子低密度奇偶校验（QLDPC）码，每类都具有精确确定的码率。第一类由一对非二元经典QC-LDPC码推导而来，设计时使得所得EA-QC-QLDPC码整体Tanner图的无辅助部分无4环。第二类则由一个本身无4环的非二元经典QC-LDPC码构造而成。在开发第一类码时，我们采用单个贝尔对建立收发端间的纠缠，从而最小化所需纠缠资源。此外，这些构造表明，精心的基于图的设计可有效平衡纠错性能与纠缠消耗，为实现高效非二元EA-QC-QLDPC码提供了实用方法。
英文摘要
We construct two families of non-binary entanglement assisted (EA) quasi-cyclic (QC) quantum low-density parity-check (QLDPC) codes over arbitrary finite fields, each possessing a precisely determined code rate. The first family is derived from a pair of non-binary classical QC-LDPC codes, designed such that the unassisted portion of the overall Tanner graph of the resulting EA-QC-QLDPC code is free of 4-cycles. The second family, on the other hand, is constructed from a single non-binary classical QC-LDPC code whose Tanner graph itself is 4-cycle-free. In developing the codes belonging to the first family, we employ a \emph{single Bell pair} to establish entanglement between the transmitter and the receiver, thereby minimizing the required entanglement resources. Furthermore, these constructions demonstrate that careful graph-based design can effectively balance error-correction performance with entanglement consumption, providing a practical approach for realizing efficient non-binary EA-QC-QLDPC codes.
