Analysis of coupled quantum parametric harmonic oscillators by classical nonlinear modeling

Quantum-dot and ion-trap technologies are applied to implementation of quantum computers. Quantum mechanical systems constructed by the technologies are considered as networks of charged particles. In this paper, we present first that the networks are described by coupled quantum parametric harmonic oscillators (CQPHOs). Second, the CQPHOs are modeled by a system of nonlinear stochastic ordinary differential equations (NSODEs). The NSODEs consist of a deterministic drift term and a probabilistic fluctuation term. The drift term is derived by substituting a quantum probability density function and a quantum current density for the classical counterparts in a drift term of the Fokker-Planck equation. Third, we integrate numerically the system of the NSODEs from which probabilistic fluctuation term is removed. As a result of the integral, we find that the system behaves chaotically when the amplitude and the frequency of the time-varying parameter of the CQPHOs are in specific ranges. This implies that quantum computers may behave irregularly because not only of intrinsic probabilistic nature of quantum mechanics but also of deterministically chaotic nature.