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

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-${\mathrm{C}}^2\mathrm{PF}$) 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-${\mathrm{C}}^2\mathrm{PF}$ gate operating two independent ${\mathrm{C}}^2\mathrm{PF}$ 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-${\mathrm{C}}^2\mathrm{PF}$ gate is feasible in experiment.

arXiv comment13 page, 3 figures

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