The Performance of Long Quantum LDPC Codes Based on the Hypergraph Product
Quantum low-density parity-check (LDPC) codes based on the hypergraph product (HGP) provide a promising approach to achieving fault-tolerant quantum computation with small overheads. In this work, we investigate the performance of long HGP codes whose component codes are classical LDPC codes. We focus on the quantum erasure channel and consider both maximum-likelihood decoding and iterative decoding. For sufficiently long codes, we clearly observe a threshold behavior for the tested codes as the block length increases. Moreover, we find that the performance curves of long LDPC HGP codes exhibit both a waterfall region near the threshold and an error floor region as the channel quality increases. These observations provide some new insights about the design of LDPC HGP codes.
