Pechukas-Yukawa formalism for Landau-Zener transitions in the presence of external noise

TL;DR

This paper applies the Pechukas-Yukawa formalism to analyze how external noise affects Landau-Zener transitions in quantum systems, providing insights into decoherence in quantum computers.

Contribution

It introduces a novel application of the Pechukas-Yukawa formalism to model noise effects on quantum level dynamics and Landau-Zener transitions.

Findings

Noise influences level dynamics and transition probabilities.

The formalism aligns with classical Landau-Zener results under linearization.

External fluctuations impact adiabatic evolution in quantum systems.

Abstract

Quantum systems are prone to decoherence due to both intrinsic interactions as well as random fluctuations from the environment. Using the Pechukas-Yukawa formalism, we investigate the influence of noise on the dynamics of an adiabatically evolving Hamiltonian which can describe a quantum computer. Under this description, the level dynamics of a parametrically perturbed quantum Hamiltonian are mapped to the dynamics of 1D classical gas. We show that our framework coincides with the results of the classical Landau-Zener transitions upon linearisation. Furthermore, we determine the effects of external noise on the level dynamics and its impact on Landau-Zener transitions.