Structural Signatures through Continuous-Time Quantum Walks with Decoherence

Abstract

Quantum walks are the analogue of classical random walks, and have been recently used to study and develop quantum algorithms: unlike the classical case, where the evolution of the walk is governed by a stochastic matrix, in the quantum case the evolution of the walk is governed by a complex unitary matrix. This implies that Quantum walks are non-ergodic and do not posses a limiting distribution. Quantum walks can be divided in two classes, the ones which have a discrete-time parameter and the ones with a continuous-time parameter. We focused our attention on the Continuous-time quantum random walks. In quantum mechanics, Decoherence describes the transition of quantum density matrices to classical probability distributions, in other words it describes the emergence of classical properties due to the interaction of the quantum system with the surrounding environment. In this work we studied the effects of Decoherence on continuous-time quantum walks in order to build a novel structural signature that is used to characterize nodes of a graph.