Holonomic Quantum Computing in Ultracold Neutral Atoms via Floquet Engineering

Holonomic quantum computing (QC) aims to be an intrinsically fault-tolerant alternative to conventional QC techniques; it utilizes non-Abelian geometric phases in highly degenerate systems to realize universal unitary transformations of states in the manifold. While there have been many successful implementations, a scalable platform remains elusive in large part because of the required degeneracy; recently, several proposals have shown that Floquet-engineering may be used to surpass this issue. We demonstrate this concept in a BEC of Floquet-engineered rubidium-87 atoms, where fast periodic driving results in the required degeneracies between atomic spin states and their subsequent holonomic evolution. In particular, we utilize Wilson loops to show that the geometric phase is non-Abelian in a fully gauge-invariant manner; this is required for the protocol to be truly holonomic. Our results for spin-1 transformations are shown along with numerical simulations, and we discuss the protocol's efficacy as a real-world QC model.