QFlowNet: Fast, Diverse, and Efficient Unitary Synthesis with Generative Flow Networks

Unitary Synthesis, the decomposition of a unitary matrix into a sequence of quantum gates, is a fundamental challenge in quantum compilation. Prevailing reinforcement learning (RL) approaches are often hampered by sparse reward signals, which necessitate complex reward shaping or long training times, and typically converge to a single policy, lacking solution diversity. In this work, we propose QFlowNet, a novel framework that learns efficiently from sparse signals by pairing a Generative Flow Network (GFlowNet) with Transformers. Our approach addresses two key challenges. First, the GFlowNet framework is fundamentally designed to learn a diverse policy that samples solutions proportional to their reward, overcoming the single-solution limitation of RL while offering faster inference than other generative models like diffusion. Second, the Transformers act as a powerful encoder, capturing the non-local structure of unitary matrices and compressing a high-dimensional state into a dense latent representation for the policy network. Our agent achieves an overall success rate of 99.7% on a 3-qubit benchmark(lengths 1-12) and discovers a diverse set of compact circuits, establishing QFlowNet as an efficient and diverse paradigm for unitary synthesis.