Quantum Chebyshev probabilistic models for fragmentation functions

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. Quantum computing holds great promise for advancing data analysis in science, including high-energy physics. This work presents a quantum protocol for learning and sampling multivariate distributions, using Chebyshev polynomials and quantum Chebyshev transforms to study fragmentation functions and energy-momentum correlations in hadron production.