Gustavo Bezerra
Quantum Walk-based Search Algorithms With Multiple Marked Vertices
This paper was a colaboration between me, Pedro Lugão, and Renato Portugal. We generalised a technique for finding the hitting time of a quantum walk search from one to multiple marked elements. The technique has a few requirements to work. The paper was published in Physical Review A journal in June 1st, 2021. It is also available on arXiv.
The abstract is as follows. “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.”
Tags: Paper - Quantum Computing - Quantum Algorithm - Quantum Walk - Quantum Search - Graphs - Journal - Physical Review A