A generative flow network (GFlowNet) model called GFlowQEC has managed to propose high-quality quantum LDPC codes with fewer simulated evaluations than conventional search methods. It is, according to its authors, the first GFlowNet applied to quantum code design. The system builds each code by adding one group element at a time and learns to suggest candidates with a probability proportional to a power of their score.

Choosing a quantum error-correcting code for a real device means scoring candidates with circuit-level simulations so slow that only a few hundred can be run. So every evaluation counts, and a search is judged by how many good codes it finds per paid evaluation. Quantum LDPC codes built from a few group elements protect many logical qubits, but good ones are rare in a huge space.

GFlowQEC is trained once on scores from earlier searches, frozen, and then proposes lifted-product codes with 180 physical qubits, scored by their distances. Ranking ten of its draws per paid call, it finds more than twice as many new top-scoring codes (inequivalent to any it was trained on) as tuned parallel tempering, even when tempering starts from GFlowQEC's training codes. It finds more than three and a half times as many as a supervised screen ranking ten random candidates per call.

When both rank a hundred candidates, the supervised screen beats GFlowQEC and does best ranking GFlowQEC's own draws. In addition, soft Q-learning, which shares the GFlowNet's optimal policy, matches its performance at one noise bias and does better at the other, indicating that the gain does not depend on the GFlowNet's training loss. Taken together, the authors conclude that a trained proposer can make a budget of expensive evaluations go further when good codes are rare.