In this work we investigate the effect of decomposition basis on primitive qudit gates on superconducting radio-frequency cavity-based quantum computers with applications to lattice gauge theory. Three approaches are tested: snap and displacement gates, ecd and single-qubit rotations $R(\theta ,\varphi )$, and optimal pulse control. For all three decompositions, implementing the necessary sequence of rotations concurrently rather than sequentially can reduce the primitive gate run time. The number of blocks required for the faster ecd and $R_p\left(\theta \right)$ is found to scale as $O\left(d^2\right)$, while the slower snap and displacement set scales sublinearly with $d$ on the permutation gates relevant for lattice gauge theory. For qudits with $d<10$, the resulting gate times for the two decompositions are similar, though strongly dependent on experimental design choices. Optimal control can outperform both decompositions for small $d$ by a factor of 2 to 12 at the cost of higher classical resources. Lastly, we find that snap and displacement are slightly more robust to a simplified noise model.

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• Lattice QCD
• Quantum algorithms
• Quantum simulation
• Qudits