# Quantum low-density parity-check codes

The distance of a quantum low-density parity-check code sets its error-correction capability, yet exact computation is NP-hard and heuristic search is slow, which limits screening of large code spaces. BB-Net turns distance estimation for bivariate bicycle (BB) codes into a learning task: an attention network trained on roughly 58,000 codes labeled with upper bounds from high-budget heuristic searches predicts distance directly from the sparse polynomial structure. On the test set, BB-Net reaches 96.39% accuracy against reference distances, above the 94.86% of the best heuristic in the same table, QDistEvol, and evaluates one code in 0.005 s.

The distance of a quantum low-density parity-check code sets its error-correction capability, yet exact computation is NP-hard and heuristic search is slow, which limits screening of large code spaces. BB-Net turns distance estimation for bivariate bicycle (BB) codes into a learning task: an attention network trained on roughly 58,000 codes labeled with upper bounds from high-budget heuristic searches predicts distance directly from the sparse polynomial structure. On the test set, BB-Net reaches 96.39% accuracy against reference distances, above the 94.86% of the best heuristic in the same table, QDistEvol, and evaluates one code in 0.005 s.