Learning the expressibility of quantum circuit ansatz using transformer

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.