# Nonstabilizerness Estimation using Graph Neural Networks

arXiv: https://arxiv.org/abs/2511.23224 · HTML: https://mlsanity.com/paper/2511.23224/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 59 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 11 of 11)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Quantum Circuit Optimization with AlphaTensor](https://mlsanity.com/paper/2402.14396/) (2024)
- [Topological Quantum Compiling with Reinforcement Learning](https://mlsanity.com/paper/2004.04743/) (2020)
- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [Machine Learning for Practical Quantum Error Mitigation](https://mlsanity.com/paper/2309.17368/) (2023)
- [QuEst: Graph Transformer for Quantum Circuit Reliability Estimation](https://mlsanity.com/paper/2210.16724/) (2022)
- [Quantum Circuit Design using a Progressive Widening Enhanced Monte Carlo Tree Search](https://mlsanity.com/paper/2502.03962/) (2025)
- [Graph Neural Networks for Parameterized Quantum Circuits Expressibility Estimation](https://mlsanity.com/paper/2405.08100/) (2024)
- [Fast algorithms for classical specifications of stabiliser states and Clifford gates](https://mlsanity.com/paper/2311.10357/) (2023)

## Built on by (most cited first, 1 of 1)

- [Magic-Informed Quantum Architecture Search](https://mlsanity.com/paper/2605.03932/) (2026)

## Abstract (arXiv)

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.