Time-Efficient quantum walks for 3-distinctness

Authors:
Aleksandrs Belovs;Andrew M. Childs;Stacey Jeffery;Robin Kothari;Frédéric Magniez
Affiliations:
Faculty of Computing, University of Latvia, Latvia;Department of Combinatorics & Optimization, University of Waterloo, Canada,Institute for Quantum Computing, University of Waterloo, Canada;David R. Cheriton School of Computer Science, University of Waterloo, Canada,Institute for Quantum Computing, University of Waterloo, Canada;David R. Cheriton School of Computer Science, University of Waterloo, Canada,Institute for Quantum Computing, University of Waterloo, Canada;CNRS, LIAFA, Univ Paris Diderot, Sorbonne Paris-Cité, France
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Year:
2013

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Abstract

We present two quantum walk algorithms for 3-Distinctness. Both algorithms have time complexity $\tilde{O}(n^{5/7})$, improving the previous $\tilde{O}(n^{3/4})$ and matching the best known upper bound for query complexity (obtained via learning graphs) up to log factors. The first algorithm is based on a connection between quantum walks and electric networks. The second algorithm uses an extension of the quantum walk search framework that facilitates quantum walks with nested updates.