  With the exponentially faster computation for certain problems, quantum
computing has garnered significant attention in recent years. Variational
quantum algorithms are crucial methods to implement quantum computing, and an
appropriate task-specific quantum circuit ansatz can effectively enhance the
quantum advantage of VQAs. However, the vast search space makes it challenging
to find the optimal task-specific ansatz. Expressibility, quantifying the
diversity of quantum circuit ansatz states to explore the Hilbert space
effectively, can be used to evaluate whether one ansatz is superior to another.
In this work, we propose using a transformer model to predict the
expressibility of quantum circuit ansatze. We construct a dataset containing
random PQCs generated by the gatewise pipeline, with varying numbers of qubits
and gates. The expressibility of the circuits is calculated using three
measures: KL divergence, relative KL divergence, and maximum mean discrepancy.
A transformer model is trained on the dataset to capture the intricate
relationships between circuit characteristics and expressibility. Four
evaluation metrics are employed to assess the performance of the transformer.
Numerical results demonstrate that the trained model achieves high performance
and robustness across various expressibility measures. This research can
enhance the understanding of the expressibility of quantum circuit ansatze and
advance quantum architecture search algorithms.
