Quantum approach to the dynamical systems modeling

TL;DR

This paper introduces a quantum-based framework for simulating classical dynamical systems, enabling analysis of complex and dissipative models with potential applications in scientific and practical fields.

Contribution

It develops a novel quantum extension approach for classical systems, applicable to various non-Hamiltonian and dissipative dynamical models.

Findings

Successfully applied to logistic, Van der Pol, Lorenz, R"ossler, and Rabinovich-Fabrikant systems.

Provides algorithms integrated into quantum simulators for complex system analysis.

Enables solving problems with scientific and practical significance using quantum methods.

Abstract

We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian) dissipative dynamical systems. As examples, we consider the logistic model, the Van der Pol oscillator, dynamical systems of Lorenz, R\"ossler (including R\"ossler hyperchaos) and Rabinovich-Fabrikant. Developed methods and algorithms integrated in quantum simulators will allow us to solve a wide range of problems with scientific and practical significance.