Qudit Gate Decomposition Dependence for Lattice Gauge Theories

TL;DR

This paper compares different qudit gate decomposition methods for lattice gauge theories on superconducting quantum computers, highlighting how basis choice affects gate efficiency, speed, and robustness, with optimal control often outperforming others for small dimensions.

Contribution

It systematically analyzes the dependence of qudit gate decomposition on basis choice and demonstrates the advantages of optimal control in reducing gate times and improving robustness.

Findings

ECD & $R_p( heta)$ decomposition scales as $ ext{O}(d^2)$

SNAP & Displacement scales at worst as $ ext{O}(d)

Optimal control outperforms other methods for small $d$ by a factor of 2-12

Abstract

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 & Displacement gates, ECD & single-qubit rotations $R(\theta,\phi)$, and optimal pulse control. For all three decompositions, implementing the necessary sequence of rotations concurrently rather then sequentially can reduce the primitive gate run time. The number of blocks required for the faster ECD & $R_p(\theta)$ is found to scale $\mathcal{O}(d^2)$, while slower SNAP & Displacement set scales at worst $\mathcal{O}(d)$. For qudits with $d<10$, the resulting gate times for the decompositions is similar, but strongly-dependent on experimental design choices. Optimal control can outperforms both decompositions for small $d$ by a factor of 2-12 at the cost of higher classical resources. Lastly, we find that SNAP & Displacement are slightly more robust to a simplified noise model.