Efficient Qudit Circuit for Quench Dynamics of \(2+1D\) Quantum Link Electrodynamics
A major challenge in the burgeoning field of quantum simulation for high-energy physics is the realization of scalable \(2+1\)D lattice gauge theories on state-of-the-art quantum hardware, which is an essential step towards the overarching goal of probing \(3+1\)D quantum chromodynamics on a quantum computer. Despite great progress, current experimental implementations of \(2+1\)D lattice gauge theories are mostly restricted to relatively small system sizes and two-level representations of the gauge and electric fields. Here, we propose a resource-efficient method for quantum simulating \(2+1\)D spin-\(S\)\(U(1)\) quantum link lattice gauge theories with dynamical matter using qudit-based quantum processors. By integrating out the matter fields through Gauss's law, we reformulate the quantum link model in a purely spin picture compatible with qudit encoding across arbitrary spatial dimensions, eliminating the need for ancillary qubits and reducing resource overhead. Focusing first on the spin-\(1/2\) case, we construct explicit circuits for the full Hamiltonian and demonstrate through numerical simulations that the first-order Trotterized circuits accurately capture the quench dynamics even in the presence of realistic noise levels. Additionally, we introduce a general method for constructing coupling-term circuits for higher-spin representations \(S > 1/2\). Compared to conventional qubit encodings, our framework significantly reduces the number of quantum resources and gate count. Our approach significantly enhances scalability and fidelity for probing nonequilibrium phenomena in higher-dimensional lattice gauge theories, and is readily amenable to implementation on state-of-the-art qudit platforms.