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» Quantum lower bound for the collision problem
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TOC
2010
155views Management» more  TOC 2010»
13 years 14 days ago
A New Quantum Lower Bound Method, with an Application to a Strong Direct Product Theorem for Quantum Search
Abstract: We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of the adversary method, by analyzing the eigenspace structur...
Andris Ambainis
IPL
2006
114views more  IPL 2006»
13 years 5 months ago
Quantum lower bounds for the Goldreich-Levin problem
At the heart of the Goldreich-Levin Theorem is the problem of determining an n-bit string a by making queries to two oracles, referred to as IP (inner product) and EQ (equivalence...
Mark Adcock, Richard Cleve, Kazuo Iwama, Raymond H...
FOCS
2006
IEEE
13 years 12 months ago
On the Quantum Query Complexity of Local Search in Two and Three Dimensions
The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been...
Xiaoming Sun, Andrew Chi-Chih Yao
STOC
2006
ACM
166views Algorithms» more  STOC 2006»
14 years 6 months ago
New upper and lower bounds for randomized and quantum local search
Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexi...
Shengyu Zhang