Efficient quantum walk on the grid with multiple marked elements
arXiv:1612.08958 · doi:10.4230/LIPIcs.STACS.2017.42
Abstract
We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known quantum walk that finds a marked element in a number of steps less than the square-root of the extended hitting time. We also give a new tighter upper bound on the extended hitting time of a marked subset, expressed in terms of the hitting times of its members.
18 pages, to appear in STACS 2017, the 34th International Symposium on Theoretical Aspects of Computer Science
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