Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities

TL;DR

This paper proposes a scalable quantum circuit that implements a hyper-parallel Toffoli gate on a three-photon system using multiple degrees of freedom, reducing decoherence and resource requirements.

Contribution

It introduces a compact, deterministic hyper-parallel controlled-controlled-phase-flip gate on three photons utilizing polarization and spatial degrees of freedom, enhancing efficiency and scalability.

Findings

Reduces quantum resource requirements by half.

Feasible implementation with current technology.

Operates two independent gates simultaneously.

Abstract

Encoding qubits in multiple degrees of freedom (DOFs) of a quantum system allows less-decoherence quantum information processing with much less quantum resources. We present a compact and scalable quantum circuit to determinately implement a hyper-parallel controlled-controlled-phase-flip (hyper-$\rm{C^2PF}$) gate on a three-photon system in both the polarization and spatial DOFs. In contrast with the one with many qubits encoding in one DOF only, our hyper-$\rm{C^2PF}$ gate operating two independent $\rm{C^2PF}$ gates on a three-photon system with less decoherence, and reduces the quantum resources required in quantum information processing by a half. Additional photons, necessary for many approaches, are not required in the present scheme. Our calculation shows that this hyper-$\rm{C^2PF}$ gate is feasible in experiment.