| 1. | Kuba Chmielewski, Krzysztof Grygiel, Karol Bartkiewicz Stability Analysis of Three Coupled Kerr Oscillators: Implications for Quantum Computing CMST, 31 (1–3), pp. 33–47, 2025, ISSN: 1505-0602. Abstract | Links | BibTeX @article{kuba_stability_2025,
title = {Stability Analysis of Three Coupled Kerr Oscillators: Implications for Quantum Computing},
author = {Kuba Chmielewski and Krzysztof Grygiel and Karol Bartkiewicz },
url = {https://cmst.eu/articles/stability-analysis-of-three-coupled-kerr-oscillators-implications-for-quantum-computing/},
doi = {10.12921/cmst.2025.0000012},
issn = {1505-0602},
year = {2025},
date = {2025-08-18},
urldate = {2025-08-22},
journal = {CMST},
volume = {31},
number = {1–3},
pages = {33--47},
abstract = {We investigate the classical dynamics of optical nonlinear Kerr couplers, focusing on their potential relevance to
quantum computing applications. The system consists of three Kerr-type nonlinear oscillators arranged in two configurations:
a triangular arrangement, where each oscillator is coupled to the others, and a sandwich arrangement, where only the
middle oscillator interacts with the two outer ones. The system is driven by an external periodic field and subject to dissipative
processes. Its evolution is governed by six non-autonomous differential equations derived from a Kerr Hamiltonian with
nonlinear coupling terms. We demonstrate that even for identical Kerr media, the interplay between nonlinear couplings
and mismatched fundamental and pump frequencies gives rise to rich and complex dynamics, including the emergence of
multiple stable attractors. These attractors are highly sensitive to both the coupling configuration and initial conditions.
A key contribution of this work is a detailed stability analysis based on numerical calculation of Lyapunov exponents, revealing
transitions from regular to chaotic dynamics as damping is reduced. We identify critical damping thresholds for the
onset of chaos and characterize phenomena such as chaotic beats. These findings offer insights for potential experimental
realizations and are directly relevant to emerging quantum technologies, where Kerr parametric oscillators play a central
role in quantum gates, error correction protocols, and quantum neural network architectures.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate the classical dynamics of optical nonlinear Kerr couplers, focusing on their potential relevance to
quantum computing applications. The system consists of three Kerr-type nonlinear oscillators arranged in two configurations:
a triangular arrangement, where each oscillator is coupled to the others, and a sandwich arrangement, where only the
middle oscillator interacts with the two outer ones. The system is driven by an external periodic field and subject to dissipative
processes. Its evolution is governed by six non-autonomous differential equations derived from a Kerr Hamiltonian with
nonlinear coupling terms. We demonstrate that even for identical Kerr media, the interplay between nonlinear couplings
and mismatched fundamental and pump frequencies gives rise to rich and complex dynamics, including the emergence of
multiple stable attractors. These attractors are highly sensitive to both the coupling configuration and initial conditions.
A key contribution of this work is a detailed stability analysis based on numerical calculation of Lyapunov exponents, revealing
transitions from regular to chaotic dynamics as damping is reduced. We identify critical damping thresholds for the
onset of chaos and characterize phenomena such as chaotic beats. These findings offer insights for potential experimental
realizations and are directly relevant to emerging quantum technologies, where Kerr parametric oscillators play a central
role in quantum gates, error correction protocols, and quantum neural network architectures. |
