Non-Abelian Geometric Quantum Gates in Triangular Systems

This paper proposes a novel method for creating quantum gates using the geometric phases of vibrational modes in a three-body system. The use of shape space and the derivation of an SU(2) holonomy group for single-qubit control is a significant contribution. The paper also outlines a method for creating entangling gates and provides a concrete physical implementation using Rydberg trimers. The focus on experimental verification through interferometric protocols adds to the paper's value.