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• W2563622299 abstract "In this paper, we study the properties of lackadaisical quantum walks on a line. This model is first proposed in~cite{wong2015grover} as a quantum analogue of lazy random walks where each vertex is attached $tau$ self-loops. We derive an analytic expression for the localization probability of the walker at the origin after infinite steps, and obtain the peak velocities of the walker. We also calculate rigorously the wave function of the walker starting from the origin and obtain a long time approximation for the entire probability density function. As an application of the density function, we prove that lackadaisical quantum walks spread ballistically for arbitrary $tau$, and give an analytic solution for the variance of the walker's probability distribution." @default.
• W2563622299 created "2017-01-06" @default.
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• W2563622299 date "2016-12-11" @default.
• W2563622299 modified "2023-10-16" @default.
• W2563622299 title "The Lackadaisical Quantum Walker is NOT Lazy at all" @default.
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• W2563622299 hasPublicationYear "2016" @default.
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