Genealogy-Conditioned Quantum Architecture Search with Synthetic Lineage Pretraining

Quantum architecture search (QAS) can automate the design of parameterized quantum circuits (PQCs), but testing an architecture typically requires an expensive inner-loop parameter optimization. Surrogate models can screen candidates before this evaluation, yet training the surrogate often requires the same quantum-evaluated architecture labels that it is meant to save. We introduce Genealogy-Conditioned Quantum Architecture Search (GCQAS), which pretrains a reusable offspring-ranking model without executing quantum circuits or collecting expert labels. GCQAS constructs synthetic lineages, assigns each family a different randomized scoring rule, and trains a contextual Transformer to infer how candidate structure, inheritance, and ancestral outcomes jointly determine local rankings. Because the rule differs across lineages, the model cannot memorize one and is forced to learn to infer the active rule from the ancestors' outcomes in its context. During a target search, the model remains frozen and uses the contextual information from candidate circuit's genealogy to predict the performance of each offspring in a genetic algorithm. We evaluate the same surrogate on distribution matching and variational quantum eigensolver under noiseless and noisy simulation, with target circuits of up to 16 qubits despite pretraining only on six-qubit lineages. GCQAS continues to guide search across this change in scale and objective, whereas a genetic algorithm with no surrogate, a genetic algorithm with in-context Bayesian optimization as a surrogate, and an online QAS surrogate do not achieve comparable solutions under the evaluation budget. GCQAS also improves on task-specific adaptive construction in the corresponding benchmark regimes. These results show that synthetic lineage pretraining can learn a transferable search strategy: task-general knowledge is stored in the model, while sparse target-specific evidence is supplied through the evolving context.