Nonstabilizerness Estimation using Graph Neural Networks

2025-11-28

AI Summary

This work addresses the efficient estimation of nonstabilizerness—a key resource underlying quantum advantage—in quantum circuits. We propose the first graph neural network (GNN)-based multi-task learning framework, modeling quantum circuits as structured graphs and jointly optimizing Clifford discrimination (classification) and stabilized Rényi entropy (SRE) prediction (regression). The method generalizes across random, structured (e.g., transverse-field Ising model), and large-scale circuits. Crucially, it is the first to integrate hardware noise models with circuit topology. Empirical evaluation demonstrates superior performance across distribution shifts, large qubit counts (≥50), deep circuits, and noisy simulations—outperforming state-of-the-art approaches with up to 42% reduction in SRE prediction error. Our framework establishes a scalable, hardware-aware paradigm for real-time quantification and assessment of quantum advantage resources.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

This article proposes a Graph Neural Network (GNN) approach to estimate nonstabilizerness in quantum circuits, measured by the stabilizer Rényi 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 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.

Problem

• Estimating nonstabilizerness in quantum circuits using Graph Neural Networks
• Addressing classification and regression tasks for stabilizer Rényi entropy
• Improving generalization across diverse quantum circuit scenarios

Innovation

• Graph Neural Network estimates quantum nonstabilizerness
• Supervised learning from classification to regression tasks
• Graph representation integrates hardware-specific noise information