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

TL;DR

This paper explores advanced optimization techniques like reinforcement learning and simulated annealing to enhance hypergraph product quantum LDPC codes' performance against the quantum erasure channel, leveraging efficient decoding methods.

Contribution

It introduces the application of RL and SA for optimizing hypergraph product codes, demonstrating improved performance over existing methods.

Findings

RL and SA outperform traditional optimization approaches

Optimized codes show increased robustness against quantum erasure

Efficient decoding enables practical optimization of quantum codes

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.