Quantum algorithms for subset finding

Authors:
Andrew M. Childs;Jason M. Eisenberg
Affiliations:
Institute for Quantum Information, California Institute of Technology, Pasadena, CA and Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA;Center for Theoretical Physics and Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA
Venue:
Quantum Information & Computation
Year:
2005

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Abstract

Recently, Ambainis gave an O(N2/3)-query discrete-time quantum walk algorithm forthe element distinctness problem, and more generally, an O(NL/(L+1))-query algorithmfor finding L equal numbers. We review this algorithm and give a simplified and tightenedanalysis of its query complexity using techniques previously applied to the analysis ofcontinuous-time quantum walk. We also briefly discuss applications of the algorithm andpose two open problenm regarding continuous-time quantum walk and lower bounds.