Quantum Simulation of Generalized Parton Distributions in the Schwinger Model

Abstract

We present a quantum algorithm for simulating Generalized Parton Distributions (GPDs) in the Schwinger model. Unlike the staggered fermions widely utilized in current quantum simulations, we employ Wilson fermions for lattice discretization. This choice is critical for the quantum computation of GPDs due to their strict preservation of charge conjugation symmetry. We construct a comprehensive algorithmic framework that includes the preparation of hadronic states with non-zero momentum and the measurement of light-cone correlation functions incorporating Wilson lines. We provide a complexity analysis, demonstrating that the resources required for our algorithm scale polynomially with both the number of qubits and the desired precision $\varepsilon$. Finally, we benchmark our approach using exact diagonalization, extracting mass spectra and GPDs (also parton distribution functions) that are consistent with theoretical expectations and fundamental physical constraints.