Quantum walk-based search algorithms with multiple marked vertices
- URL: http://arxiv.org/abs/2103.12878v4
- Date: Tue, 20 Dec 2022 15:50:14 GMT
- Title: Quantum walk-based search algorithms with multiple marked vertices
- Authors: G. A. Bezerra, P. H. G. Lug\~ao, and R. Portugal
- Abstract summary: The quantum walk is a powerful tool to develop quantum algorithms.
We extend previous analytical methods based on Szegedy's quantum walk.
Two examples based on the coined quantum walk on two-dimensional lattices and hypercubes show the details of our method.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The quantum walk is a powerful tool to develop quantum algorithms, which
usually are based on searching for a vertex in a graph with multiple marked
vertices, Ambainis's quantum algorithm for solving the element distinctness
problem being the most shining example. In this work, we address the problem of
calculating analytical expressions of the time complexity of finding a marked
vertex using quantum walk-based search algorithms with multiple marked vertices
on arbitrary graphs, extending 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 the
details of our method.
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