arXiv:2603.03045

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

Inhoe Koo, Hyunho Cha, Jungwoo Lee

quant-phcs.AISubmitted Mar 3, 2026• Announced Mar 4, 2026• 0 citations• Revised Mar 4, 2026 (v2)

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.

Comments: 7 pages, 6 figures, IEEE International Conference on Quantum Communications, Networking, and Computing (QCNC 2026)

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