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» Average-Case Quantum Query Complexity
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110
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STOC
2004
ACM
153views Algorithms» more  STOC 2004»
15 years 12 months ago
Quantum and classical query complexities of local search are polynomially related
Let f be an integer valued function on a finite set V . We call an undirected graph G(V, E) a neighborhood structure for f. The problem of finding a local minimum for f can be phr...
Miklos Santha, Mario Szegedy
JC
2007
94views more  JC 2007»
14 years 11 months ago
On the complexity of the multivariate Sturm-Liouville eigenvalue problem
We study the complexity of approximating the smallest eigenvalue of −∆ + q with Dirichlet boundary conditions on the d-dimensional unit cube. Here ∆ is the Laplacian, and th...
A. Papageorgiou
110
Voted
JCSS
2008
120views more  JCSS 2008»
14 years 11 months ago
Quantum certificate complexity
Given a Boolean function f, we study two natural generalizations of the certificate complexity C (f): the randomized certificate complexity RC (f) and the quantum certificate comp...
Scott Aaronson
102
Voted
COLT
2010
Springer
14 years 9 months ago
Quantum Predictive Learning and Communication Complexity with Single Input
We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to a...
Dmitry Gavinsky
83
Voted
ICALP
2005
Springer
15 years 5 months ago
Quantum Complexity of Testing Group Commutativity
We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pa...
Frédéric Magniez, Ashwin Nayak