Learning the expressibility of quantum circuit ansatz using transformer

TL;DR

This work addresses the challenge of selecting task-specific quantum circuit ansätze in variational quantum algorithms by predicting circuit expressibility from graph-encoded PQCs. It proposes a transformer-based predictor trained on a large DAG-based PQC dataset to estimate four expressibility measures, including both noiseless and noisy scenarios. The authors demonstrate strong predictive performance across RMSE, $R^2$, and correlation metrics, and show robustness to noise, enabling faster exploration of quantum architectures. By open-sourcing the dataset and model, the approach supports scalable quantum architecture search and can be extended to other quantum properties beyond expressibility.

Abstract

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.

Figures (11)

• Figure 1: Framework of the proposed expressibility estimation method. The method comprises three phases: (1) graph encoding of the PQC, (2) ground-truth expressibility calculation, and (3) transformer model training.
• Figure 2: Relationship between various expressibility measures and circuit properties.
• Figure 3: Transformer architecture.
• Figure 4: The RMSE of $Exp_1$ prediction across various transformer structures.
• Figure 5: Scatter plots of the relationship between the predicted and ground-truth $Exp_1$.