# Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester

 Title Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester Publication Type Journal Article Year of Publication 2016 Authors Lin, CYen-Yu, Lin, H-H Journal Theory of Computing Volume 12 Issue 18 Pages 1-35 Date Published 2016/11/28 Abstract 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. URL http://theoryofcomputing.org/articles/v012a018/ DOI 10.4086/toc.2016.v012a018 Original Publication Proceeding CCC '15 Proceedings of the 30th Conference on Computational Complexity, Pages 537-566