Nonstabilizerness Estimation using Graph Neural Networks

TL;DR

<1-2 sentence problem statement> The paper tackles estimating nonstabilizerness, quantified by stabilizer Rényi entropy $M_2$, in quantum circuits with a graph-based representation. <2-3 sentence method> It introduces a Graph Neural Network architecture with a graph-processing Transformer and a parallel global-feature path, to address three supervised tasks: stabilizer-state classification, SRE-based classification, and SRE estimation, backed by a large, publicly released dataset and hardware-noise considerations. <1-2 sentence findings> The approach achieves strong generalization across circuit sizes and entanglement structures, outperforms SVR baselines on extrapolation tasks, and demonstrates hardware-aware SRE prediction capabilities, with ablations confirming the value of the graph representation. <1 sentence significance> This work provides a scalable, structure-aware framework for nonstabilizerness estimation, with practical implications for quantum-device benchmarking and architecture search.

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.

Figures (15)

• Figure 1: Overview of the quantum circuit composition in the dataset designed for the stabilizer state classification problem and the respective $M_2$ values.
• Figure 2: $M_2$ value distribution in datasets of product states.
• Figure 3: Overview of the distribution of the $M_2$ values across the quantum circuits in the dataset designed for the SRE estimation problem.
• Figure 4: SRE value distributions of quantum circuits grouped by qubit number in the RQC and TIM noisy datasets are shown in Figure \ref{['fig:random_noise']} and \ref{['fig:tim_noise']}, respectively. The $M_2$ values are computed under simulated noise using the IBM FakeOslo backend.
• Figure 5: Overview of the GNN approach to nonstabilizerness estimation. Box A summarizes the three different problem formulations, box B illustrates the process to translate a quantum circuit in our graph-based representation, and box C illustrates the GNN architecture.