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arXiv:2606.22602

Quantum Simulation of Generalized Parton Distributions in the Schwinger Model

Tianyin Li, Hongxi Xing

Published Jun 21, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2606.22602

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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 ε\varepsilonε. 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.
Generalized Parton Distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED2), within the Hamiltonian formulation of lattice field theory. Quasi-distributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasi-parton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.
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We present a systematic quantum algorithm, which integrates both the hadronic state preparation and the evaluation of real-time light-front correlators, to study parton distribution functions (PDFs). As a proof of concept, we demonstrate the first direct simulation of the PDFs in the 1+11+11+1 dimensional Nambu-Jona-Lasinio model. We show the results obtained by exact diagonalization and by quantum computation using classical hardware. The agreement between these two distinct methods and the qualitative consistency with QCD PDFs validate the proposed quantum algorithm. Our work suggests the encouraging prospects of calculating QCD PDFs on current and near-term quantum devices. The presented quantum algorithm is expected to have many applications in high energy particle and nuclear physics.
Parton distribution functions (PDFs) describe the inner, nonperturbative structure of hadrons. Their computation involves matrix elements with a Wilson line along a direction on the light cone, posing significant challenges in Euclidean lattice calculations, where the time direction is not directly accessible. We propose implementing the light-front Wilson line within the Hamiltonian formalism using tensor network techniques. The approach is demonstrated in the massive Schwinger model (quantum electrodynamics in 1 + 1 dimensions), a toy model that shares key features with quantum chromodynamics. We present accurate continuum results for the fermion PDF of the vector meson at varying fermion masses, obtained from first-principle calculations directly in Minkowski space. Our strategy also provides a useful path for quantum simulations and quantum computing.
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