  Lattice gauge theories are fundamental to various fields, including particle
physics, condensed matter, and quantum information theory. Recent progress in
the control of quantum systems allows for studying Abelian lattice gauge
theories in table-top experiments. However, several challenges remain, such as
implementing dynamical fermions in higher spatial dimensions and magnetic field
terms. Here, we map D-dimensional U(1) Abelian lattice gauge theories onto
qudit systems with local interactions for arbitrary D. We propose a variational
quantum simulation scheme for the qudit system with a local Hamiltonian, that
can be implemented on a universal qudit quantum device as the one developed in
[Nat. Phys. 18, 1053-1057 (2022)]. We describe how to implement the variational
imaginary-time evolution protocol for ground state preparation as well as the
variational real-time evolution protocol to simulate non-equilibrium physics on
universal qudit quantum computers, supplemented with numerical simulations. Our
proposal can serve as a way of simulating lattice gauge theories, particularly
in higher spatial dimensions, with minimal resources, regarding both system
sizes and gate count.
