Designing efficient quantum circuits is a central bottleneck to exploring the potential of quantum computing, particularly for noisy intermediate-scale quantum (NISQ) devices, where circuit efficiency and resilience to errors are paramount. The search space of gate sequences grows combinatorially, and handcrafted templates often waste scarce qubit and depth budgets. We introduce \textsc{FlowQ-Net} (Flow-based Quantum design Network), a generative framework for automated quantum circuit synthesis based on Generative Flow Networks (GFlowNets). This framework learns a stochastic policy to construct circuits sequentially, sampling them in proportion to a flexible, user-defined reward function that can encode multiple design objectives such as performance, depth, and gate count. This approach uniquely enables the generation of a diverse ensemble of high-quality circuits, moving beyond single-solution optimization. We demonstrate the efficacy of \textsc{FlowQ-Net} through an extensive set of simulations. We apply our method to Variational Quantum Algorithm (VQA) ansatz design for molecular ground state estimation, Max-Cut, and image classification, key challenges in near-term quantum computing. Circuits designed by \textsc{FlowQ-Net} achieve significant improvements, yielding circuits that are 10$\times$-30$\times$ more compact in terms of parameters, gates, and depth compared to commonly used unitary baselines, without compromising accuracy. This trend holds even when subjected to error profiles from real-world quantum devices. Our results underline the potential of generative models as a general-purpose methodology for automated quantum circuit design, offering a promising path towards more efficient quantum algorithms and accelerating scientific discovery in the quantum domain.

翻译：设计高效的量子电路是探索量子计算潜力的核心瓶颈，尤其对于噪声中等规模量子（NISQ）设备而言，电路效率和抗误差能力至关重要。门序列的搜索空间呈组合式增长，手工设计的模板往往浪费稀缺的量子比特和深度资源。我们提出\\textsc{FlowQ-Net}（基于流的量子设计网络），这是一种基于生成流网络（GFlowNets）的自动化量子电路综合生成框架。该框架学习一种随机策略以顺序构建电路，根据灵活的、用户定义的奖励函数按比例采样电路，该函数可编码多种设计目标，如性能、深度和门数量。这种方法独特地实现了高质量电路多样化集合的生成，超越了单解优化。我们通过大量仿真验证了\\textsc{FlowQ-Net}的有效性。我们将该方法应用于变分量子算法（VQA）的拟设设计，用于分子基态估计、最大割问题和图像分类——这些是近期量子计算中的关键挑战。\\textsc{FlowQ-Net}设计的电路取得了显著改进，与常用酉基线相比，在参数、门数量和深度方面实现了10倍至30倍的压缩，且不牺牲精度。即使在面对真实量子设备的误差分布时，这一趋势依然成立。我们的结果凸显了生成模型作为自动化量子电路设计通用方法的潜力，为开发更高效的量子算法和加速量子领域的科学发现提供了一条有前景的路径。