Q3SAT-GPT: A Generative Model for Discovering Quantum Circuits for the 3-SAT Problem

Abstract

This work introduces Q3SAT-GPT, a generative model for discovering quantum circuits for the Max-E3-SAT problem. Our method learns from high-performing QAOA-style ans\"atze to directly generate candidate circuits. To create high-quality supervision, we also introduce Mosaic Adaptive QAOA (MosaicADAPT-QAOA), an adaptive strategy for constructing low-depth QAOA circuits by selecting subsets of mixer operators in each step, rather than inserting operators sequentially. The resulting circuits serve as training data for the generative model, allowing it to learn effective circuit design patterns while eliminating the need for costly variational optimization at inference time. Experiments show that our framework attains strong solution quality with shallow circuits and scales significantly better than both our adaptive construction procedure and conventional variational baselines. Our results establish generative modeling as a high-performance route toward the scalable discovery of quantum optimization circuits, demonstrating that these models can effectively internalize circuit logic while providing a foundation for future, instance-aware inductive biases. Reproducibility: The source code is available at https://github.com/pratimugale/Q3SAT-GPT.