# Implementations of two-photon four-qubit Toffoli and Fredkin gates assisted by nitrogen-vacancy centers

## TL;DR

This paper presents efficient, resource-saving quantum circuits for four-qubit Toffoli and Fredkin gates using single photons and nitrogen-vacancy centers, promising practical implementation with current technology.

## Contribution

The paper introduces two compact quantum circuits for deterministic four-qubit gates utilizing polarization and spatial degrees of freedom in photons, enhanced by NV centers.

## Key findings

- High fidelities and efficiencies predicted for the gates.
- Implementation feasible with current quantum technology.
- Reduced quantum resource requirements compared to previous methods.

## Abstract

It is desirable to implement an efficient quantum information process demanding fewer quantum resources. We designed two compact quantum circuits for determinately implementing four-qubit Toffoli and Fredkin gates on single-photon systems in both the polarization and spatial degrees of freedom (DoFs) via diamond nitrogen-vacancy (NV) centers in resonators. The gates are heralded by the electron spins associated with the diamond NV centers. In contrast to the ones with one DoF, our implementations reduce the quantum resource and are robust against the decoherence. Evaluations of fidelities and efficiencies of our gates show that our schemes may be implemented with current technology.