A new method, called GFlowQEC, is the first use of a generative flow network (GFlowNet) to design quantum low‑density parity check (LDPC) codes. It is a causal transformer that builds a lifted‑product code one group element at a time. The network is trained with a trajectory‑balance objective so that it proposes each code with a probability proportional to a power of its distance‑based score. Once the policy is frozen, it can generate many code candidates in a single pass.

In a benchmark on 180‑qubit lifted‑product codes, the frozen GFlowQEC policy was run for 1 000 paid oracle evaluations. On average it discovered 313 certified top‑scoring codes for a positive noise bias (γ = +1) and 317 for a negative bias (γ = −1). These numbers exceed those from tuned parallel tempering, supervised screening, and soft Q‑learning in the same evaluation budget.

When counts are normalized per paid call, GFlowQEC finds more than twice as many inequivalent novel top‑scoring codes as tuned parallel tempering, and more than three and a half times as many as a supervised screen that ranks ten uniform random candidates. These gains are measured in terms of new high‑distance codes, not merely lower‑length examples.

However, the advantage fades under certain conditions. If each oracle call is inexpensive, if good codes are not extremely rare, or if the CPU time to evaluate a code dominates the budget, the lead disappears when measured per CPU second of exact ladder evaluation. In that regime a simple Bayesian optimisation or reinforcement‑learning approach can match or surpass GFlowQEC.

The authors also note that for the 180‑qubit family studied, no code better than those already found by Bayesian optimisation, reinforcement learning, or LLM‑guided searches was produced by GFlowQEC. Uniform sampling alone found roughly ten top‑scoring codes per 1 000 paid calls, showing that a trained policy is not strictly necessary for this size.