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A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004).
Random walks on graphs: A survey
László Lovász · 1996
Earlier work this paper cites.
3.0.CO;2-P" title="" class="ltx_ref ltx_href">Tight bounds on quantum searching
Michel Boyer, Gilles Brassard, Peter Høyer, and Alain Tapp · 1998
Earlier work this paper cites.
Computational Methods for Inverse Problems
Curtis R. Vogel · 2002
Earlier work this paper cites.
Quantum speed-up of Markov chain based algorithms
Márió Szegedy · 2004
Earlier work this paper cites.
Faster quantum-walk algorithm for the two-dimensional spatial search
Avatar Tulsi · 2008
Earlier work this paper cites.
Search via quantum walk
Frédéric Magniez, Ashwin Nayak, Jérémie Roland, and Miklos Santha · 2011
Cited alongside, same era.
On the hitting times of quantum versus random walks
Frédéric Magniez, Ashwin Nayak, Peter C. Richter, and Miklos Santha · 2012
Cited alongside, same era.
Quantum walks can find a marked element on any graph
Hari Krovi, Frédéric Magniez, Maris Ozols, and Jérémie Roland · 2016
Cited alongside, same era.
Controlled quantum amplification
Cǎtǎlin Dohotaru and Peter Høyer · 2017
Cited alongside, same era.
Efficient quantum walk on the grid with multiple marked elements
Peter Høyer and Mojtaba Komeili · 2017
Cited alongside, same era.
Hamiltonian simulation by uniform spectral amplification
Guang Hao Low and Isaac L. Chuang · 2017
Later among the works it cites.
Markov chains and mixing times
David A. Levin, Yuval Peres, and Elizabeth L. Wilmer · 2017
Later among the works it cites.
Quantum fast-forwarding Markov chains
Simon Apers and Alain Sarlette · 2018
Later among the works it cites.
Shantanav Chakraborty, András Gilyén, and Stacey Jeffery · 2018
Later among the works it cites.
András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe · 2019
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