Solitonic Fixed Point Attractors in the Complex Ginzburg–Landau Equation for Associative Memories

Abstract

It was recently shown [V.V. Cherny, T. Byrnes, A.N. Pyrkov, Adv. Quantum Technol. 2019 2, 1800087] that the nonlinear Schrodinger equation with a simplified dissipative perturbation of special kind features a zero-velocity solitonic solution of non-zero amplitude which can be used in analogy to attractors of Hopfield's associative memory. In this work, we consider a more complex dissipative perturbation adding the effect of two-photon absorption and the quintic gain/loss effects that yields formally the complex Ginzburg-Landau equation (CGLE). We construct a perturbation theory for the CGLE with a small dissipative perturbation and define the behavior of the solitonic solutions with parameters of the system and compare the solution with numerical simulations of the CGLE. We show that similarly to the nonlinear Schrodinger equation with a simplified dissipation term, a zero-velocity solitonic solution of non-zero amplitude appears as an attractor for the CGLE. In this case the amplitude and velocity of the solitonic fixed point attractor does not depend on the quintic gain/loss effects. Furthermore, the effect of two-photon absorption leads to an increase in the strength of the solitonic fixed point attractor.

Solitonic attractors in the coupled nonlinear Schrödinger equations with weak dissipations

“…When the dissipation term ratios are different, there are solitonic attractors for both components. It should be noted that the solitonic solutions may become unstable if the condition |ò| = 1 is not well satisfied [45]. It would be interesting to explore the cases with g ≠ 1, more dissipation effects [39], and high-order effects [46,47], which may lead to more diverse soliton attractor patterns.…”

Hybrid quantum-classical unsupervised data clustering based on the Self-Organizing Feature Map

“…For the problem of classification which is closely connected to the problem of clusterization, a protocol of quantum classification, tested on the MNIST dataset, via slow feature analysis based on the use of quantum Frobenius distance was proposed [46]. Furthermore, many other hybrid and quantum protocols inspired classical neural networks were developed [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61].…”