Optimizing hypergraph product codes with random walks, simulated annealing and reinforcement learning

Abstract: Hypergraph products are quantum low-density parity-check (LDPC) codes constructed from two classical LDPC codes. Although their dimension and distance depend only on the parameters of the underlying classical codes, optimizing their performance against various noise channels remains challenging. This difficulty partly stems from the complexity of decoding in the quantum setting. The standard, ad hoc approach typically involves selecting classical LDPC codes with large girth. In this work, we focus on optimizing performance against the quantum erasure channel. A key advantage of this channel is the existence of an efficient maximum-likelihood decoder, which enables us to employ optimization techniques based on sampling random codes, such as Reinforcement Learning (RL) and Simulated Annealing (SA). Our results indicate that these techniques improve performance relative to the state-of-the-art.