Optimizing compilation of lattice gauge theory quantum simulation with qudits

Recent developments in mapping lattice QCD to digital quantum computers have shown a scalable path with well-defined quantum compilation challenges toward the continuum. Though demonstrations have commonly employed lowest truncation and few-plaquette lattices, fully decomposed quantum circuits of higher complexity situations are needed to assess quantum resource requirements in anticipated domains of quantum advantage for nuclear and particle physics. In this work, we develop a custom quantum circuit implementation of the SU(2) plaquette operator using qudits to encode a higher truncation of the digitized gauge field, and provide an optimized end-to-end quantum resource estimate. We demonstrate the optimized plaquette operator implementation by simulating the real-time dynamics of SU(2) non-Abelian gauge fields on a lattice system with many plaquettes, where we employ parallelization opportunities like those that will arise in the repeated application of the plaquette operator in higher-dimensional lattice volumes. Such quantum resource estimates will aid in analyzing how costs scale with truncation level and lattice system complexity. The circuits presented also offer an ambitious executable for future qudit hardware platforms.