Non-Binary Quasi-Cyclic LDPC Codes with Entanglement Assistance
2026-08-17 • Information Theory
Information Theory
AI summaryⓘ
The authors created two types of quantum error-correcting codes that work over general finite fields. The first type uses two classical codes combined so that the part of the code without entanglement avoids small loops, improving performance and needing only one entangled pair between sender and receiver. The second type builds from one classical code designed to have no small loops at all. Their work shows how to design quantum codes that balance error correction strength with low entanglement use.
Quantum error correctionEntanglement assisted codesQuasi-cyclic codesLow-density parity-check codesTanner graph4-cycleNon-binary codesFinite fieldsBell pairQuantum communication
Authors
Pavan Kumar, Shayan Srinivasa Garani
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.