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Parameterized Quantum Circuits (PQCs) are essential to quantum machinelearning and optimization algorithms. The expressibility of PQCs, whichmeasures their ability to represent a wide range of quantum states, is acritical factor influencing their efficacy in solving quantum problems.However, the existing technique for computing expressibility relies onstatistically estimating it through classical simulations, which requires manysamples. In this work, we propose a novel method based on Graph Neural Networks(GNNs) for predicting the expressibility of PQCs. By leveraging the graph-basedrepresentation of PQCs, our GNN-based model captures intricate relationshipsbetween circuit parameters and their resulting expressibility. We train the GNNmodel on a comprehensive dataset of PQCs annotated with their expressibilityvalues. Experimental evaluation on a four thousand random PQC dataset and IBMQiskit's hardware efficient ansatz sets demonstrates the superior performanceof our approach, achieving a root mean square error (RMSE) of 0.03 and 0.06,respectively.

Predicting Expressibility of Parameterized Quantum Circuits using Graph Neural Network