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

• URL: http://arxiv.org/abs/2603.03045v2
• Date: Wed, 04 Mar 2026 09:29:40 GMT
• Title: QFlowNet: Fast, Diverse, and Efficient Unitary Synthesis with Generative Flow Networks
• Abstract summary: Unitary synthesis is a fundamental challenge in quantum compilation.<n>We propose QFlowNet, a framework that learns efficiently from sparse signals by pairing a Generative Flow Network (GFlowNet) with Transformers.
• Score: 5.077782193180541
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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