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Discrete-Time Quantum Walk on Multilayer Networks
Mahesh N Jayakody1, Priodyuti Pradhan2, Dana Ben Porath1
1Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel.
Abstract:
A Multilayer network is a potent platform that paves the way for the study of the interactions among entities in various networks with multiple types of relationships. This study explores the dynamics of discrete-time quantum walks on a multilayer network. We derive a recurrence formula for the coefficients of the wave function of a quantum walker on an undirected graph with a finite number of nodes. By extending this formula to include extra layers, we develop a simulation model to describe the time evolution of the quantum walker on a multilayer network. The time-averaged probability and the return probability of the quantum walker are studied with Fourier, and Grover walks on multilayer networks. Furthermore, we analyze the impact of decoherence on quantum transport, shedding light on how environmental interactions may impact the behavior of quantum walkers on multilayer network structures.
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