FlowQC: Conditional Flow Matching for Efficient and Robust Quantum Circuit Synthesis

Quantum circuit synthesis is crucial for near-term quantum computing, yet existing generative models built on diffusion models suffer from slow iterative sampling, limited conditional controllability, and high sensitivity to sampling steps and the guidance scales. To address these challenges, we propose flowQC, a conditional flow matching framework for efficient quantum circuit generation. To improve conditional generation quality, we introduce the Prompt-Aware Quantum Transformer (PAQ-former), which employs adaLN-Zero modulation and sigmoid residual gating to control the conditional signal dynamically in the generation trajectory. For dataset generation and verification, We firstly replace Qiskit's DensityMatrix representation with its Statevector implementation, enabling dataset generation to scale up to 12 qubits for large-scale training and evaluation. Experiments on conditional circuit generation tasks demonstrate that flowQC improves sampling efficiency and circuit quality over diffusion-based baselines. For SRV-conditioned circuit generation, flowQC achieves 4.74$\times$ inference acceleration and reduces generated circuit gate operations by 35.5% on average. Moreover, across varying numbers of sampling steps from 20 to 5 and guidance scales from 5 to 1, flowQC maintains more stable accuracy than the diffusion-based baseline. For unitary-conditioned generation, flowQC produces diverse candidate circuits validated by phase-invariant unitary equivalence evaluation. These results establish flowQC as an efficient and robust conditional generative framework for quantum circuit synthesis.