Nonadiabatic holonomic multiqubit controlled gates

TL;DR

This paper introduces a new method for implementing multiqubit controlled gates in nonadiabatic holonomic quantum computation, reducing the number of operations needed compared to traditional decomposition methods.

Contribution

The authors propose a direct approach to realize multiqubit controlled gates without decomposing into universal gates, significantly simplifying nonadiabatic holonomic quantum computation.

Findings

Reduces the number of operations for multiqubit controlled gates

Enables implementation of controlled arbitrary rotation gates with minimal steps

Simplifies the process of nonadiabatic holonomic quantum computation

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-$(\boldsymbol{\mathrm{n}\cdot \mathrm{\sigma}})$ 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.