Qupeggio: Quantum Error-Correcting Code Discovery via Autoregressive Generation and Diffusion Repair

Quantum error-correcting (QEC) code discovery is essential for fault-tolerant quantum computation (FTQC), yet it remains largely driven by expert-designed constructions. Existing automated approaches based on reinforcement learning offer a promising alternative, but require enormous numbers of increasingly expensive code evaluations and have so far been limited to relatively small codes. Meanwhile, the field has accumulated millions of previously discovered QEC codes, raising a natural question: can this existing knowledge be reused to amortize code discovery across different design problems, rather than searching for every code from scratch? Moreover, can such learned knowledge help discover high-distance codes competitive with those already known? We introduce a generate-and-repair framework that learns reusable construction patterns from existing QEC codes, combining global construction from learned priors with targeted local refinement that preserves useful existing structure. An autoregressive model generates code constructions across different numbers of physical and logical qubits, while a diffusion model selectively repairs parts of promising constructions that limit their code performance. Across large and diverse code specifications, our framework generalizes to sparsely represented and unseen settings, and discovers SAT-certified codes whose distances extend beyond the frontier represented in the training data. These results show that generative modeling can amortize QEC code discovery across design problems while continuing to improve upon the constructions from which it learns.