Search via quantum walk

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Search via quantum walk (2007)

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by Frédéric Magniez , Ashwin Nayak , Jérémie Roland , Miklos Santha

Venue:	LOGIC PROGRAMMING, PROC. OF THE 1994 INT. SYMP
Citations:	56 - 8 self

BibTeX

@INPROCEEDINGS{Magniez07searchvia,
    author = {Frédéric Magniez and Ashwin Nayak and Jérémie Roland and Miklos Santha},
    title = {Search via quantum walk},
    booktitle = {LOGIC PROGRAMMING, PROC. OF THE 1994 INT. SYMP},
    year = {2007},
    pages = {575--584},
    publisher = {MIT Press}
}

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Abstract

We propose a new method for designing quantum search algorithms for finding a “marked ” element in the state space of a classical Markov chain. The algorithm is based on a quantum walk à la Szegedy [24] that is defined in terms of the Markov chain. The main new idea is to apply quantum phase estimation to the quantum walk in order to implement an approximate reflection operator. This operator is then used in an amplitude amplification scheme. As a result we considerably expand the scope of the previous approaches of Ambainis [6] and Szegedy [24]. Our algorithm combines the benefits of these approaches in terms of being able to find marked elements, incurring the smaller cost of the two, and being applicable to a larger class of Markov chain. In addition, it is conceptually simple, avoids several technical difficulties in the previous analyses, and leads to improvements in various aspects of several algorithms based on quantum walk.

Keyphrases

quantum walk marked element markov chain amplitude amplification scheme state space main new idea quantum search algorithm new method approximate reflection operator quantum walk la szegedy several algorithm various aspect previous approach classical markov chain previous analysis avoids several technical difficulty quantum phase estimation

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