# Suppression of the Landau-Zener transition probability by a weak classical noise

## TL;DR

This paper demonstrates that weak classical noise can significantly suppress the Landau-Zener transition probability in a qubit, especially when the noise correlation time exceeds the transition time, with analytical treatment for Gaussian and telegraph noise.

## Contribution

It provides an analytical framework to understand how weak classical noise affects Landau-Zener transitions, highlighting the role of noise correlation time.

## Key findings

- Weak classical noise reduces the average Landau-Zener transition probability.
- Noise effects become negligible when correlation time exceeds transition time.
- Analytical results are obtained for Gaussian and telegraph noise.

## Abstract

When the drive which causes the level crossing in a qubit is slow, the probability, P_{LZ}, of the Landau-Zener transition is close to 1. We show that in this regime, which is most promising for applications, the noise due to the coupling to the environment, reduces the average P_{LZ}. At the same time, the survival probability, 1-P_{LZ}, which is exponentially small for a slow drive, can be completely dominated by noise-induced correction. Our main message is that the effect of a weak classical noise can be captured analytically by treating it as a perturbation in the Schroedinger equation. This allows us to study the dependence of the noise-induced correction to P_{LZ} on the correlation time of the noise. As this correlation time exceeds the bare Landau-Zener transition time, the effect of noise becomes negligible. We consider two conventional realizations of noise: Gaussian noise and telegraph noise.