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 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 identified Floquet engineered systems of ultracold atoms as a potential candidate, where fast periodic driving results in the required degeneracies between atomic spin states and their subsequent holonomic evolution. With this promising outlook for holonomic QC in ultracold atomic systems, a full understanding requires us to consider the effects of interactions in these protocols. Here we present some recent theoretical and experimental progress towards implementing the Floquet-engineered holonomic QC scheme in a rubidium-87 BEC including the effects of mean-field interactions.