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Abstract

Quantum computers are expected to efficiently simulate lattice gauge theory in the non-perturbative regime, which is a notoriously difficult set of simulations for classical computers. Recent works on representing lattice gauge theory on digital quantum computers have found scalable paths toward large-scale quantum simulations. However, many quantum compilation challenges must be overcome for such simulations to be feasible on a practical scale. As an entry point to these challenges, we address the simulation of SU(2) lattice gauge theory. Using qudits to encode the digitized gauge field at an arbitrarily high truncation level, we compile the target simulation into elementary qudit gates. The search for efficient compilation methods inspired improvements to uniformly-controlled rotations for qudits that nearly halves the two-qudit gate count compared to previously known implementations. Since uniformly-controlled rotations are useful for synthesizing generic unitary operators, this optimization may be widely applied to general quantum computing applications. Additionally, we found that the present simulation benefits from qudits with a mix of different dimensions. Accordingly, we generalized the previous technique to this scenario. Finally, we formalize a technique, Subspace Gating, which is useful for embedding lower-dimensional qudit circuits (including qudits with differing dimensions) in higher dimensional ones. Demonstrating these compilation techniques, we perform an end-to-end simulation of real-time, qutrit-digitized SU(2) gauge field dynamics on a cube. This simulation is more complex in lattice size and gauge field truncation level than prior Non-Abelian lattice gauge theory simulations while still being within the realm of feasibility for near-term quantum hardware. By explicit decomposition into elementary qudit gates, we provide exact resource counts as well as precise resource scaling with increasing gauge field truncation level. We also parallelize the evolution of opposing cube 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 co-developing strategies between lattice gauge theory simulation and quantum compilation. Ultimately, it provides insight on how future quantum field theory simulations might be orchestrated on powerful quantum computers.