Optimizing Quantum LDPC Codes over the Quantum Erasure Channel Using Machine Learning

Quantum Error Correction (QEC) is essential for realizing fault-tolerant quantum computing. Among the various QEC codes, quantum Low-Density Parity-Check (qLDPC) codes are particularly promising due to their constant encoding-rate and scalability properties, which make them suitable for large-scale quantum computation. This work focuses on optimizing qLDPC codes derived from the hypergraph product (HGP) construction over the quantum erasure channel. We reduce this optimization problem to a search over classical Tanner graphs and we employ Simulated Annealing, as well as Machine Learning techniques such as Projective Simulation, to traverse the space of Tanner graphs. Our results show that these methods significantly outperform traditional techniques like the Progressive Edge-Growth algorithm, achieving a reduction in logical error rates of about one order of magnitude.