Adaptive fusion of training-free proxies for quantum architecture search

Training-free quantum architecture search (QAS) has shown substantial promise in automating quantum circuit design for variational quantum algorithms (VQAs) with minimal computational expense. However, various VQA tasks and search spaces often favor specific training-free proxies. Furthermore, circuit performance is influenced by multiple factors, such as expressibility, trainability, and circuit topology, making it challenging for a single proxy to assess circuit performance accurately. To address these limitations, we propose an adaptive QAS framework that dynamically integrates multiple training-free proxies, combining their strengths and mitigating individual biases. This framework uses a mixture-of-experts (MoE) model that adapts to different VQA tasks and search spaces. Specifically, we develop an expert model for each training-free proxy, where each expert focuses on a distinct feature, such as expressibility, trainability, or topology. A gating network then assigns weights to each expert based on the specific VQA task and search space. Our proposed QAS framework consistently outperforms state-of-the-art QAS algorithms across diverse VQAs, including variational quantum eigensolvers (VQEs) and quantum neural networks (QNNs), as well as multiple search spaces, such as gatewise, layerwise, and blockwise constructions. Moreover, our approach demonstrates transferability across different VQA tasks and search spaces.