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

TL;DR

QFlowNet introduces a novel method combining Generative Flow Networks and Transformers to efficiently synthesize diverse quantum circuits, significantly improving success rate and solution variety over traditional reinforcement learning approaches.

Contribution

The paper presents QFlowNet, a new framework that leverages GFlowNets and Transformers for fast, diverse, and efficient unitary synthesis in quantum compilation.

Findings

Achieved 99.7% success rate on 3-qubit benchmarks.

Discovered a diverse set of compact quantum circuits.

Outperformed traditional RL in solution diversity and inference speed.

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.