Nonadiabatic holonomic multiqubit controlled gates

Abstract

Previous schemes of nonadiabatic holonomic quantum computation were focused mainly on realizing a universal set of elementary gates. Multiqubit controlled gates could be built by decomposing them into a series of the universal gates. In this article, we propose an approach for realizing nonadiabatic holonomic multiqubit controlled gates in which a $(n+1)$-qubit controlled-$(\mathrm{n}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{\ensuremath{\sigma}})$ gate is realized by $(2n\ensuremath{-}1)$-basic operations instead of decomposing it into the universal gates, whereas a $(n+1)$-qubit controlled arbitrary rotation gate can be obtained by combining only two such controlled-$(\mathrm{n}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{\ensuremath{\sigma}})$ gates. Our scheme greatly reduces the operations of nonadiabatic holonomic quantum computation.