DOI 10.15507/2079-6900.23.202104.433–443

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 78M35 78M20

Simulation of switchers for CNOT-gates based on optical waveguide interaction with coupled mode theory

A. A. Lytaev, I. Yu. Popov

National Research University ITMO (Saint Petersburg, Russian Federation)

Abstract. The paper is devoted to simulation of interactions in the system of two symmetrical slab optical waveguides, that guide exactly two guided modes with the aim to use the directional coupler as a switcher for CNOT gate in the waveguide model of quantum-like computations. The coupling mode theory is used to solve the system of Maxwell equations. The asymptotic analysis is applied to simplify the system of differential equations, so an approximate analytic solution can be found. The solution obtained is used for the quick directional coupler parameters adjusting algorithm, so the power exchange in the system occurs as that of correctly working CNOT-gate switcher. Moreover, the finite difference method is used to solve the stricter system of equations, that additionally takes into account the process of power exchange between different order guided modes, so the computational error of the device can be estimated. It was obtained, that the possible size of the device may not exceed 1 mm in the largest dimension, while the computational error does not exceed 3%.

Key Words: optical quantum computations, CNOT-gate, Maxwell equations, optical waveguides, theory of coupled modes, finite difference method

For citation: A. A. Lytaev, I. Yu. Popov. Simulation of switchers for CNOT-gates based on optical waveguide interaction with coupled mode theory. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 23:4(2021), 433–443. DOI: https://doi.org/10.15507/2079-6900.23.202104.433–443

Submitted: 05.07.2021; Revised: 07.08.2021; Accepted: 25.08.2021

Information about the authors:

Aleksandr A. Lytaev, Graduate Student, National Research University ITMO (49 Kronverskiy Av., Saint Petersburg 197101, Russia), ORCID: https://orcid.org/0000-0003-1976-3350, sas-lyt@ya.ru

Igor Yu. Popov, leading professor, National Research University ITMO (49 Kronverskiy Av., Saint Petersburg 197101, Russia), D. Sci. (Mathematics and Physics), ORCID: https://orcid.org/0000-0002-5251-5327, popov1955@gmail.com

All authors have read and approved the final manuscript.

Conflict of interest: The authors declare no conflict of interest.

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