Graph Neural Networks for Parameterized Quantum Circuits Expressibility Estimation

TL;DR

This paper presents a novel Graph Neural Network-based method for efficiently estimating the expressibility of parameterized quantum circuits, significantly reducing computational costs compared to traditional statistical techniques.

Contribution

It introduces a GNN model that accurately predicts PQC expressibility, including in noisy and out-of-range scenarios, with minimal training data and high efficiency.

Findings

GNN model achieves RMSE of 0.05 on noiseless data

Model accurately predicts expressibility on noisy quantum hardware

Exhibits strong extrapolation capabilities to larger circuits

Abstract

Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness the full potential of the quantum state space. It is thus a crucial guidepost to know when selecting a particular PQC ansatz. However, the existing technique for expressibility computation through statistical estimation requires a large number of samples, which poses significant challenges due to time and computational resource constraints. This paper introduces a novel approach for expressibility estimation of PQCs using Graph Neural Networks (GNNs). We demonstrate the predictive power of our GNN model with a dataset consisting of 25,000 samples from the noiseless IBM QASM Simulator and 12,000 samples from three distinct noisy quantum backends. The model accurately estimates expressibility, with root mean square errors (RMSE) of 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare our model's predictions with reference circuits [Sim and others, QuTe'2019] and IBM Qiskit's hardware-efficient ansatz sets to further evaluate our model's performance. Our experimental evaluation in noiseless and noisy scenarios reveals a close alignment with ground truth expressibility values, highlighting the model's efficacy. Moreover, our model exhibits promising extrapolation capabilities, predicting expressibility values with low RMSE for out-of-range qubit circuits trained solely on only up to 5-qubit circuit sets. This work thus provides a reliable means of efficiently evaluating the expressibility of diverse PQCs on noiseless simulators and hardware.