# 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.

## Key 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.