Quantum Chebyshev probabilistic models for fragmentation functions

Abstract

Quantum generative modeling is emerging as a powerful tool for advancing data analysis in high-energy physics, where complex multivariate distributions are common. However, efficiently learning and sampling these distributions remains challenging. We propose a quantum protocol for a bivariate probabilistic model based on shifted Chebyshev polynomials, trained as a circuit-based representation of two correlated variables, with sampling performed via quantum Chebyshev transforms. As a key application, we study fragmentation functions (FFs) of charged pions and kaons from single-inclusive hadron production in electron-positron annihilation. We learn the joint distribution of momentum fraction z and energy scale Q, and infer their correlations from the entanglement structure. Building on the generalization capabilities of the quantum model and extended register architecture, we perform fine-grid multivariate sampling for FF dataset augmentation. Our results highlight the growing potential of quantum generative modeling to advance data analysis and scientific discovery in high-energy physics.

Metadata

Item Type:	Article
Authors/Creators:	Martínez de Lejarza, J.J. https://orcid.org/0000-0002-3866-3825 Wu, H.-Y. https://orcid.org/0000-0001-8201-4286 Kyriienko, O. https://orcid.org/0000-0002-6259-6570 Rodrigo, G. https://orcid.org/0000-0003-0451-0529 Grossi, M. https://orcid.org/0000-0003-1718-1314
Copyright, Publisher and Additional Information:	© The Author(s) 2025. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/bync-nd/4.0/.
Keywords:	Phenomenology; Quantum information
Dates:	7 April 2025 Accepted: 8 October 2025 Published (online): 19 November 2025 Published: 1 December 2025
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences
Date Deposited:	27 Jan 2026 14:11
Last Modified:	27 Jan 2026 14:11
Status:	Published
Publisher:	Springer Science and Business Media LLC
Refereed:	Yes
Identification Number:	10.1038/s42005-025-02361-1
Related URLs:	Dataset Software or Code
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:236851