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 -qubit controlled- gate is realized by basic operations instead of decomposing it into the universal gates, whereas an -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.