Discrete-time Walk on One-Dimensional Lattice under Stochastic Resetting: Advantage of Quantum over Classical Scenario.

Przemysław Chełminiak,Jan Wójcik, Antoni Wójcik

Physical review E（2025）

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Abstract

We investigate the effect of stochastic restart/resetting on discrete-time quantum walks concerning its impact on the meantime to absorption in the walk on the one-dimensional lattice terminated by a pair of totally absorbing sites. The two distinguished sites also play the role of an apparatus that detects the moment of time when a quantum walk reaches these boundaries. Our results reveal a notable difference between the quantum walk and its classical counterpart. Specifically, we focus on instances of classical random walks in which stochastic resetting fails to reduce the meantime to absorption. Conversely, we show that stochastic resetting can be utilized to effectively diminish the meantime to absorption in the quantum version of this walk. We relate the observed difference between quantum and classical cases to the fact that restarting the quantum state not only changes position distribution but inevitably changes complementary quasimomentum distribution.

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