Quantum algorithms for subset finding
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Recently, Ambainis gave an $O(N^{2/3})$-query discrete-time quantum walk algorithm for the element distinctness problem, and more generally, an $O(N^{L/(L+1)})$-query algorithm for finding $L$ equal numbers. We review this algorithm and give a simplified and tightened analysis of its query complexity using techniques previously applied to the analysis of continuous-time quantum walk. We also briefly discuss applications of the algorithm and pose two open problems regarding continuous-time quantum walk and lower bounds.
2016 ◽
Vol 380
(11-12)
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pp. 1125-1134
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2013 ◽
Vol 10
(7)
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pp. 1558-1570
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