Realization of nonadiabatic holonomic multiqubit controlled gates with Rydberg atoms

Abstract

Nonadiabatic holonomic gates provide an effective means to perform high-speed and error-resilient manipulation of quantum states. It is practically important to realize nonadiabatic holonomic multiqubit controlled gates since multiqubit controlled gates are widely used in quantum information processing. Rydberg atoms are an appealing physical system for the realization of nonadiabatic holonomic multiqubit controlled gates as the Rydberg-mediated interaction is beneficial to couple two qubits. In this paper, we put forward a scheme for the realization of nonadiabatic holonomic multiqubit controlled gates based on Rydberg atoms, where an $(n+1)$-qubit controlled-$(\mathrm{n}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{\ensuremath{\sigma}})$ gate can be realized by $(2n\ensuremath{-}1)$ basic operations. Moreover, the effective coupling between two qubits is in the first-order strength of Rabi frequencies, which allows for the implementation of quantum gates within a short duration.