Predicting Expressibility of Parameterized Quantum Circuits using Graph Neural Network

TL;DR

This paper introduces a graph neural network approach to predict the expressibility of parameterized quantum circuits, significantly reducing the computational effort compared to traditional simulation-based methods.

Contribution

The paper presents a novel GNN-based method for predicting PQC expressibility, leveraging graph representations to improve accuracy and efficiency.

Findings

Achieved RMSE of 0.03 on a large PQC dataset.

Achieved RMSE of 0.06 on IBM Qiskit's ansatz sets.

Outperformed existing estimation techniques in accuracy.

Abstract

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