Problem
Research questions and friction points this paper is trying to address.
Non-Binary QLDPC Codes
Entanglement Assistance
Quasi-Cyclic Codes
Quantum Error Correction
Non-Binary Quasi-Cyclic LDPC Codes with Entanglement Assistance
🤖 AI Summary
This study addresses the efficient utilization of entanglement resources in non-binary entanglement-assisted quasi-cyclic quantum LDPC (EA-QC-QLDPC) codes by proposing two families of algebraic constructions derived from classical QC-LDPC codes. Through deliberate Tanner graph design that eliminates 4-cycles and requires only a single Bell pair, the proposed method achieves efficient encoding with minimal entanglement consumption. The authors successfully construct non-binary EA-QC-QLDPC codes with exact code rates over arbitrary finite fields, thereby validating the effectiveness of graph-based design in balancing error-correction performance against entanglement overhead. Consequently, this work presents a novel framework for non-binary quantum coding that effectively reconciles high performance with resource efficiency, offering a practical solution for entanglement-constrained quantum communication systems.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Non-Binary EA-QC-QLDPC Codes
Single Bell Pair
4-Cycle-Free Tanner Graph
Entanglement Resource Minimization
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