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Quantum Walks

Author: Daniel Reitzner, Daniel Nagaj, Vladimir Buzek
Url: http://arxiv.org/abs/1207.7283
Format: Ps, Pdf
Year: 2012
Category: Advanced Quantum Mechanics
Pages: 124
Clicks: 1291

This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of processes (with rather different underlying dynamics) for producing random distributions. We discuss algorithmic applications for graph-searching and compare the two approaches. Next, we look at quantization of Markov chains and show how it can lead to speedups for sampling schemes. Finally, we turn to continuous time quantum walks and their applications, which provide interesting (even exponential) speedups over classical approaches.

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