Quantum Architecture Search with Neural Predictor Based on Graph Measures

Quantum architecture search (QAS) has attracted increasing attention owing to its remarkable ability to automate the design of quantum circuits for variational quantum algorithms (VQAs). However, evaluating the performance of numerous quantum circuits is essential to provide feedback for the search strategy, which inevitably renders QAS computationally expensive. Performance predictors have emerged as highly efficient evaluation methods to mitigate this challenge. However, the performance predictor faces a critical challenge in reducing the required number of circuit-performance pairs for training. This study encodes circuit architecture by representing a quantum circuit as a relational graph that emphasizes message exchange. Subsequently, valuable information about circuit architecture is extracted through three types of graph measures, including distance-based, degree-based, and cluster-based measures. The graph measures define a smooth space related to circuit performance, facilitating the training of the performance predictor. The effectiveness of the proposed method is assessed across three tasks within variational quantum eigensolvers (VQE): identifying the ground states of the Transverse Field Ising Model (TFIM), the Heisenberg model, and the ${\text{BeH}}_2$ molecule. The simulation results demonstrate notable enhancements in predictive accuracy achieved by our method, coupled with a substantial reduction in the required number of training samples for the predictor.