  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-$(\boldsymbol{\mathrm{n}\cdot \mathrm{\sigma}})$ gate is realized by
$(2n-1)$ basic operations instead of decomposing it into the universal gates,
whereas an $(n+1)$-qubit controlled arbitrary rotation gate can be obtained by
combining only two such controlled-$(\boldsymbol{\mathrm{n}\cdot
\mathrm{\sigma}})$ gates. Our scheme greatly reduces the operations of
nonadiabatic holonomic quantum computation.
