Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Quantum summation with an application to integration
Journal of Complexity
On a problem in quantum summation
Journal of Complexity
Quantum integration in Sobolev classes
Journal of Complexity
Quantum approximation I. Embeddings of finite-dimensional Lp spaces
Journal of Complexity
Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers
Foundations of Computational Mathematics
Quantum approximation I. Embeddings of finite-dimensional Lp spaces
Journal of Complexity
Randomized and quantum algorithms yield a speed-up for initial-value problems
Journal of Complexity
Classical and Quantum Complexity of the Sturm--Liouville Eigenvalue Problem
Quantum Information Processing
On the Complexity of Searching for a Maximum of a Function on a Quantum Computer
Quantum Information Processing
Improved bounds on the randomized and quantum complexity of initial-value problems
Journal of Complexity
The Quantum Setting with Randomized Queries for Continuous Problems
Quantum Information Processing
A lower bound for the Sturm-Liouville eigenvalue problem on a quantum computer
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
The quantum query complexity of elliptic PDE
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
The Sturm-Liouville Eigenvalue Problem and NP-Complete Problems in the Quantum Setting with Queries
Quantum Information Processing
Quantum lower bounds by entropy numbers
Journal of Complexity
Improved bounds on the randomized and quantum complexity of initial-value problems
Journal of Complexity
Numerical analysis on a quantum computer
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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A basic problem of approximation theory, the approximation of functions from the Sobolev space Wpr([0,1]d) in the norm of Lq([0,1]d), is considered from the point of view of quantum computation. We determine the quantum query complexity of this problem (up to logarithmic factors). It turns out that in certain regions of the domain of parameters p,q,r,d quantum computation can reach a speedup of roughly squaring the rate of convergence of classical deterministic or randomized approximation methods. There are other regions where the best possible rates coincide for all three settings.