Nonstabilizerness Estimation using Graph Neural Networks

TL;DR

This paper introduces a Graph Neural Network approach to estimate nonstabilizerness in quantum circuits, enabling accurate, generalizable, and hardware-aware SRE predictions crucial for quantum advantage applications.

Contribution

The paper presents a novel GNN-based method for estimating nonstabilizerness, improving accuracy and generalization over existing techniques, and incorporating hardware-specific information.

Findings

GNN effectively captures features for robust SRE estimation.

Significant improvement in out-of-distribution circuit predictions.

Potential for hardware-aware quantum circuit analysis.

Abstract

This article proposes a Graph Neural Network (GNN) approach to estimate nonstabilizerness in quantum circuits, measured by the stabilizer R\'enyi entropy (SRE). Nonstabilizerness is a fundamental resource for quantum advantage, and efficient SRE estimations are highly beneficial in practical applications. We address the nonstabilizerness estimation problem through three supervised learning formulations starting from easier classification tasks to the more challenging regression task. Experimental results show that the proposed GNN manages to capture meaningful features from the graph-based circuit representation, resulting in robust generalization performances achieved across diverse scenarios. In classification tasks, the GNN is trained on product states and generalizes on circuits evolved under Clifford operations, entangled states, and circuits with higher number of qubits. In the regression task, the GNN significantly improves the SRE estimation on out-of-distribution circuits with higher number of qubits and gate counts compared to previous work, for both unstructured random quantum circuits and structured circuits derived from the transverse-field Ising model. Moreover, the graph representation of quantum circuits naturally integrates hardware-specific information. Simulations on noisy quantum hardware highlight the potential of the proposed GNN to predict the SRE measured on quantum devices.