Efficient Qudit Circuit for Quench Dynamics of $2+1$D Quantum Link Electrodynamics

TL;DR

This paper introduces a resource-efficient qudit-based quantum simulation method for 2+1D lattice gauge theories, enabling scalable and accurate studies of quench dynamics with reduced resource overhead on current quantum hardware.

Contribution

It develops a novel qudit encoding framework for 2+1D U(1) lattice gauge theories, eliminating ancillary qubits and demonstrating effective simulation of quench dynamics.

Findings

Explicit circuits for spin-1/2 case constructed and validated.

Numerical simulations show accurate dynamics capture with realistic noise.

Method extends to higher-spin representations with general coupling circuits.

Abstract

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-$S$ $\mathrm{U}(1)$ 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.