Non-Abelian dynamics on a cube: improving quantum compilation through qudit-based simulations

Abstract: Recent developments in mapping lattice gauge theories relevant to the Standard Model onto digital quantum computers identify scalable paths with well-defined quantum compilation challenges toward the continuum. As an entry point to these challenges, we address the simulation of SU(2) lattice gauge theory. Using qudit registers to encode the digitized gauge field, we provide quantum resource estimates, in terms of elementary qudit gates, for arbitrarily high local gauge field truncations. We then demonstrate an end-to-end simulation of real-time, qutrit-digitized SU(2) dynamics on a cube. Through optimizing the simulation, we improved circuit decompositions for uniformly-controlled qudit rotations, an algorithmic primitive for general applications of quantum computing. The decompositions also apply to mixed-dimensional qudit systems, which we found advantageous for compiling lattice gauge theory simulations. Furthermore, we parallelize the evolution of opposite faces in anticipation of similar opportunities arising in three-dimensional lattice volumes. This work details an ambitious executable for future qudit hardware and attests to the value of codesign strategies between lattice gauge theory simulation and quantum compilation.