Floquet-engineered holonomic gates in an atomic spin system

Holonomic gates consist of loops in some control-parameter space that produce non-Abelian geometric phases, which may couple states within a degenerate manifold. As an approach to universal quantum computing, there have been many successful demonstrations, yet large scale implementations remain elusive in part because of the required robust degeneracies. 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. We characterize these gates by their fidelities and by measurement of the gauge-invariant Wilson-loop, and discuss the various pros and cons of the control scheme as applied to universal quantum computing.