# Continuous-time quantum walks on dynamical percolation graphs

## TL;DR

This paper investigates how continuous-time quantum walks behave under dynamical percolation noise, revealing effects on quantum search efficiency and potential for network defect detection.

## Contribution

It introduces a model for quantum walks with time- and space-dependent noise and explores its implications on quantum search and network analysis.

## Key findings

- Noise affects quantum walk dynamics and search performance.
- Quantum walks can be used to probe network defects.
- Model extension to many-particle systems is discussed.

## Abstract

We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of the walker. In order to illustrate the general features of the model, we review recent results on two paradigmatic examples: the dynamics of quantum walks on the line and the effects of noise on the performances of quantum spatial search on the complete and the star graph. We also discuss future perspectives, including extension to many-particle quantum walk, to noise model for on-site energies and to the analysis of different noise spectra. Finally, we address the use of quantum walks as a quantum probe to characterize defects and perturbations occurring in complex, classical and quantum, networks.