



@article {1517,
	title = {Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman  bomb tester},
	journal = {Theory of Computing},
	volume = {12},
	year = {2016},
	month = {2016/11/28},
	pages = {1-35},
	abstract = {<p>Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity $Q(f)$, and show that $B(f)=\Theta(Q(f)^2)$. This result gives a new method to upper bound the quantum query complexity: we give a method of finding bomb query algorithms from classical algorithms, which then provide nonconstructive upper bounds on $Q(f)=\Theta(\sqrt{B(f)})$. We subsequently were able to give explicit quantum algorithms matching our upper bound method. We apply this method on the single-source shortest paths problem on unweighted graphs, obtaining an algorithm with $O(n^{1.5})$ quantum query complexity, improving the best known algorithm of $O(n^{1.5}\sqrt{\log n})$ [arXiv:quant-ph/0606127]. Applying this method to the maximum bipartite matching problem gives an $O(n^{1.75})$ algorithm, improving the best known trivial $O(n^2)$ upper bound.</p>},
	doi = {10.4086/toc.2016.v012a018},
	url = {http://theoryofcomputing.org/articles/v012a018/},
	author = {Cedric Yen-Yu Lin and Han-Hsuan Lin}
}
