The quantum walk is a powerful tool to develop quantum algorithms, such as Ambainis’s quantum algorithm for solving the element distinctnessproblem . In this work, we address the problem of calculating analytical expressions of the time complexity of finding a markedvertex using quantum walk-based search algorithms with multiple marked vertices . We extend previous analytical methods based on Szegedy’s quantum walk, which can be applied only to bipartite graphs . Two examples based on the coined quantum walk on two-dimensional lattices and hypercubes show thedetails of our method .

Author(s) : G. A. Bezerra, P. H. G. Lug√£o, R. Portugal

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Keywords : quantum - walk - based - algorithms - multiple -

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