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

• URL: http://arxiv.org/abs/2507.12589v1
• Date: Wed, 16 Jul 2025 19:16:49 GMT
• Title: Efficient Qudit Circuit for Quench Dynamics of $2+1$D Quantum Link Electrodynamics
• Abstract summary: We propose a resource-efficient method for simulating $2+1$D spin-$S$ $mathrmU(1)$ quantum link lattice gauge theories with dynamical matter.<n>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.<n>Our framework significantly reduces the number of quantum resources and gate count.
• Score: 0.565395466029518
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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