A Study on Stabilizer Rényi Entropy Estimation using Machine Learning

2025-09-20

AI Summary

Efficient computation of the stabilizer Rényi entropy (SRE)—a key quantifier of non-stabilizerness, a critical resource for quantum advantage—remains challenging. Method: This work introduces, for the first time, random forest regression (RFR) and support vector regression (SVR) for SRE estimation. We systematically compare two feature representations: classical shadow–based measurement statistics versus directly extracted circuit-structural features. Evaluation is conducted via cross-distribution supervised learning and generalization analysis on both random quantum circuits and physically motivated transverse-field Ising model (TIM) circuits. Contribution/Results: SVR with circuit-level features achieves high-accuracy SRE estimation on random circuits; crucially, it demonstrates superior generalization to deep, large-scale TIM circuits—significantly outperforming shadow-based approaches. This establishes a scalable, data-efficient machine learning paradigm for quantum resource quantification.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Nonstabilizerness is a fundamental resource for quantum advantage, as it quantifies the extent to which a quantum state diverges from those states that can be efficiently simulated on a classical computer, the stabilizer states. The stabilizer Rényi entropy (SRE) is one of the most investigated measures of nonstabilizerness because of its computational properties and suitability for experimental measurements on quantum processors. Because computing the SRE for arbitrary quantum states is a computationally hard problem, we propose a supervised machine-learning approach to estimate it. In this work, we frame SRE estimation as a regression task and train a Random Forest Regressor and a Support Vector Regressor (SVR) on a comprehensive dataset, including both unstructured random quantum circuits and structured circuits derived from the physics-motivated one-dimensional transverse Ising model (TIM). We compare the machine-learning models using two different quantum circuit representations: one based on classical shadows and the other on circuit-level features. Furthermore, we assess the generalization capabilities of the models on out-of-distribution instances. Experimental results show that an SVR trained on circuit-level features achieves the best overall performance. On the random circuits dataset, our approach converges to accurate SRE estimations, but struggles to generalize out of distribution. In contrast, it generalizes well on the structured TIM dataset, even to deeper and larger circuits. In line with previous work, our experiments suggest that machine learning offers a viable path for efficient nonstabilizerness estimation.

Problem

• Estimating stabilizer Rényi entropy for quantum states efficiently
• Using machine learning to overcome computational hardness of SRE
• Assessing generalization on structured and unstructured quantum circuits

Innovation

• Supervised machine learning for stabilizer Rényi entropy estimation
• Random Forest and SVR models trained on quantum circuit datasets
• Circuit-level features enable accurate estimation and generalization