Szegedy’s Quantum Walk
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In this chapter, we describe Szegedy’s model, which is a collection of discrete-time coinless quantum walks on symmetric bipartite digraphs. A symmetric bipartite digraph can be obtained from an underlying digraph by a duplication process. The underlying digraph defines a classical Markov chain , and Szegedy’s model is usually said to be the quantized version of this Markov chain.