Geodesic
Simulation of switchers for CNOT-gates based on optical waveguide interaction with coupled mode theory
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 23 (2021) no. 4, pp. 433-443.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 %.
Keywords: optical quantum computations, CNOT-gate, Maxwell equations, optical waveguides, theory of coupled modes, finite difference method. 
@article{SVMO_2021_23_4_a5,
     author = {A. A. Lytaev and I. Yu. Popov},
     title = {Simulation of switchers for {CNOT-gates} based on optical waveguide interaction with coupled mode theory},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {433--443},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2021_23_4_a5/}
}
TY  - JOUR
AU  - A. A. Lytaev
AU  - I. Yu. Popov
TI  - Simulation of switchers for CNOT-gates based on optical waveguide interaction with coupled mode theory
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2021
SP  - 433
EP  - 443
VL  - 23
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2021_23_4_a5/
LA  - ru
ID  - SVMO_2021_23_4_a5
ER  - 
%0 Journal Article
%A A. A. Lytaev
%A I. Yu. Popov
%T Simulation of switchers for CNOT-gates based on optical waveguide interaction with coupled mode theory
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2021
%P 433-443
%V 23
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2021_23_4_a5/
%G ru
%F SVMO_2021_23_4_a5
A. A. Lytaev; I. Yu. Popov. Simulation of switchers for CNOT-gates based on optical waveguide interaction with coupled mode theory. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 23 (2021) no. 4, pp. 433-443. http://geodesic.mathdoc.fr/item/SVMO_2021_23_4_a5/

[1] J. Cirac, P. Zoller, “Quantum computations with cold trapped ions”, Physical Review Letters, 74:20 (1995), 4091-4094 | DOI

[2] A. Blais, R. S. Huang, A. Wallraff, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation”, Physical Review A, 69:6 (2004) | DOI

[3] D. G. Cory, A. F. Fahmy, T. F. Havel, “Ensemble quantum computing by NMR-spectroscopy”, Proceedings of the National Academy of Sciences, 94:5 (1997), 1634–1639 | DOI

[4] E. Knill, R. Laflamme, G. J. Milburn, “A scheme for efficient quantum computation with linear optics”, Nature, 409:6816 (2001), 249–257 | DOI

[5] G. P. Miroshnichenko, “Linear optical quantum computing”, Nanosystems: Physics, Chemistry, Mathematics, 3:4 (2012), 36–53 (In Russ.)

[6] G. J. Milburn, “Quantum optical Fredkin gate”, Physical Review Letters, 62:18 (1989), 2124–2127 | DOI

[7] J. Fu, T. Shaofang, “Quantum Computations with Transverse Modes of an Optical Field Propagating in Waveguides”, Chinese Physics Letters, 20:9 (2003), 1426–1429 | DOI

[8] M. P. Faleeva, I. Y. Popov, “On quantum bit coding by Gaussian beam modes for the quantum key distribution”, Nanosystems: Physics, Chemistry, Mathematics, 11:6 (2020), 651–658 | DOI

[9] D. Gloge, D. Marcuse, “Formal Quantum Theory of Light Rays”, Journal of the Optical Society of America, 59:12 (1969), 1629–1631 | DOI

[10] J. Fu, T. Shaofang, J. Deng, “Classical simulation of quantum entanglement using optical transverse modes in multimode waveguides”, Physical Review A, 70:4 (2005) | DOI

[11] D. Marcuse, Light transmission optics, Van Nostrand Reinhold, New-York, 1982, 534 pp.