# Multiple multi-control unitary operations: implementation and applications

## TL;DR

This paper introduces an efficient method for implementing multiple multi-control unitary operations in quantum computing, significantly reducing resource requirements and enabling large-scale quantum computations.

## Contribution

The paper presents a direct implementation approach for multi-control unitaries that avoids decomposition into basic gates, reducing complexity from cubic to linear in the number of qubits.

## Key findings

- Reduces two-photon operation complexity from O(n^3) to O(n).
- Facilitates large-scale quantum computation with fewer resources.
- Proposes application to hypergraph state generation.

## Abstract

How to implement a computation task efficiently is the central problem in quantum computation science. For a quantum circuit, the multi-control unitary operations are the very important components. We present an extremely efficient approach to implement multiple multi-control unitary operations directly without any decompositions to CNOT gates and single-photon gates. The necessary two-photon operations could be reduced from $\mathcal{O}(n^3)$ with the traditional decomposition approach to $\mathcal{O}(n)$ with the present approach, which will greatly relax the requirement resources and make this approach much feasible for large scale quantum computation. Moreover, the potential application to the ($n$-$k$)-uniform hypergraph state generation is proposed.