A quantum representation of $\pi$ fragmentation functions through variational quantum circuits

Abstract

We present a variational quantum-circuit model for fragmentation functions (FFs). Isospin and charge-conjugation symmetries are imposed to construct an independent six-flavor basis describing charged and neutral pion production, while physics-inspired Ans\"atze, including logarithmic feature maps and mass thresholds, encode the relevant kinematics. This quantum architecture substantially reduces the quantum circuit redundancies and improve optimization convergence. Using the DSS14 pion FF set as a benchmark, we first develop a one-dimensional variational representation (FF-VQR) in the momentum fraction at fixed energy scale, and show how entanglement between quark and gluon FFs yields a significant improvement, with accurate results already obtained using just two variational layers. A spectral analysis further demonstrates that the quantum model achieves high expressivity with a limited number of Fourier modes, supporting its use as a compact non-perturbative parametrization suitable for DGLAP evolution. We then extend the FF-VQR to two dimensions by incorporating the energy-scale dependence. By encoding all flavor channels within a single entangled quantum circuit, the quantum model provides a unified representation with higher accuracy than an independent encoding for each partonic species.