Error-detected three-photon hyperparallel Toffoli gate with state-selective reflection

TL;DR

This paper proposes an error-detected hyperparallel Toffoli gate for three-photon systems that operates on multiple degrees of freedom simultaneously, achieving high fidelity and efficiency with current technology.

Contribution

It introduces a novel hyper-Toffoli gate design utilizing state-selective reflection and heralding, enabling simultaneous operations on polarization and spatial modes with improved robustness.

Findings

Near-unit fidelity achievable with current technology

Enhanced efficiency through procedure recycling

Feasible implementation with existing experimental parameters

Abstract

We present an error-detected hyperparallel Toffoli (hyper-Toffoli) gate for a three-photon system based on the interface between polarized photon and cavity-nitrogen-vacancy(NV) center system. This hyper-Toffoli gate can be used to perform double Toffoli gate operations simultaneously on both the polarization and spatial-mode degrees of freedom (DoFs) of a three-photon system with a low decoherence, shorten operation time, and less quantum resources required, in compared with those on two independent three-photon systems in one DoF only. As the imperfect cavity-NV-center interactions are transformed into the detectable failures rather than infidelity based on the heralding mechanism of detectors, a near-unit fidelity of the quantum hyper-Toffoli gate can be implemented. By recycling the procedures, the efficiency of our protocol for the hyper-Toffoli gate is improved further. Meanwhile, the evaluation of gate performance with achieved experiment parameters shows that it is feasible with current experimental technology and provides a promising building block for quantum compute.