Continuous-time quantum walks on dynamical percolation graphs

¹ Quantum Technology Lab, Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano I-20133 Milano, Italy
² QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku - FI-20014 Turun Yliopisto, Finland

^(a) claudia.benedetti@unimi.it
^(b) matteo.rossi@utu.fi
^(c) matteo.paris@fisica.unimi.it

Received: 3 December 2018
Accepted: 14 December 2018

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.