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International Journal of Theoretical Physics

A Performance Analysis of Quantum Low-Density Parity-Check Codes for Correcting Correlated Errors

Jihao Fan

Published Oct 20, 2020• 1 citation
Publisher
DOI
10.1007/s10773-020-04630-x

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With the development of quantum error correction techniques, many counterparts of classical error correction coding techniques have been found in quantum area. As the quantum counterpart of a good error correction code in classical communications, quantum low density parity check code becomes a promising coding technique in quantum error correction area. In this paper, a construction method of quantum low density parity check code (quantum LDPC) based on Projective Geometry is proposed, and the quantum code QLDPC [21,6] is selected as an example to illustrate the whole construction procedures. By numerical simulation, the error correction performance of QLDPC [21,6] is discussed over the bit-flipping channel. It is shown that this method is available and has some advantages.
Quantum low density parity check (QLDPC) codes are useful primitives for quantum information processing because they can be encoded and decoded efficiently. Besides, the error correcting capability of a few QLDPC codes exceeds the quantum Gilbert-Varshamov bound. Here, we report a numerical performance analysis of an adaptive entanglement distillation scheme using QLDPC codes. In particular, we find that the expected yield of our adaptive distillation scheme to combat depolarization errors exceed that of Leung and Shor whenever the error probability is less than about 0.07 or greater than about 0.28. This finding illustrates the effectiveness of using QLDPC codes in entanglement distillation.