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Bulletin of the Russian Academy of Sciences Physics

A Quantum Control NOT Gate Based on Four-Wave Mixing in a Cavity for Photonic Qubits with Orbital Angular Momentum

S. N. Andrianov, А. А. Калачев, O. P. Shindyaev, A. V. Shkalikov

Published Mar 1, 2020• 3 citations
Publisher

Abstract

Abstract Photonic qubits with angular momentum states interacting in a medium with Kerr-type nonlinearity in a cavity are considered. The use of a quantum logic gate (a controlled NOT gate) in the process of four-wave mixing on such qubits is considered. A theory of the functioning of this gate is constructed using the input/output formalism. The conditions for matching the parameters that must be realized for the effective operation of the gate are obtained.

DOI
10.3103/s1062873820030041

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Abstract Photonic qubits with angular momentum states interacting in a medium with Kerr-type nonlinearity in a cavity are considered. The use of a quantum logic gate (a controlled NOT gate) in the process of four-wave mixing on such qubits is considered. A theory of the functioning of this gate is constructed using the input/output formalism. The conditions for matching the parameters that must be realized for the effective operation of the gate are obtained.
We propose and experimentally demonstrate a controlled-not gate with light beams carrying orbital angular momentum (OAM) through a degenerate four-wave mixing process via a photonic band gap structure satisfying the phase-matching condition. By employing the different topological charges of a Laguerre-Gaussian beam as a qubit in this nonlinear process, the controlled-not gate with OAM can be realized. Moreover, we investigate the evolution of the controlled-not gate, which can be modulated by the frequency and the power of the incident beam, i.e. , under electromagnetically induced transparency conditions. The study results are useful for applications in quantum communication and information storage.
Natural language processing is efficient using quantum neural networks including multiqubit controlled NOT gates with multiple control qubits and a single target qubit. We propose here a photonic miltiqubit controlled NOT gate based on a multi-wave mixing process in a cavity. Theory of such a multiqubit gate is constructed using input-output formalism. Parameters matching condition is found that must be fulfilled for successful gate operation. Recommendations are given for the construction of quantum neural networks that are able to solve various practical problems of natural language processing.
Abstract By employing the different topological charges of a Laguerre–Gaussian beam as a qubit, we experimentally demonstrate a controlled-NOT (CNOT) gate with light beams carrying orbital angular momentum via a photonic band gap structure in a hot atomic ensemble. Through a degenerate four-wave mixing process, the spatial distribution of the CNOT gate including splitting and spatial shift can be affected by the Kerr nonlinear effect in multilevel atomic systems. Moreover, the intensity variations of the CNOT gate can be controlled by the relative phase modulation. This research can be useful for applications in quantum information processing.