Information-based complexity
A framework for fast quantum mechanical algorithms
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantum complexity of integration
Journal of Complexity
An Introduction to Quantum Computing Algorithms
An Introduction to Quantum Computing Algorithms
Quantum computation and quantum information
Quantum computation and quantum information
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 summation with an application to integration
Journal of Complexity
On a problem in quantum summation
Journal of Complexity
From Monte Carlo to quantum computation
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Quantum approximation I. Embeddings of finite-dimensional Lp spaces
Journal of Complexity
Quantum approximation II. Sobolev embeddings
Journal of Complexity
Quantum complexity of parametric integration
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
The randomized information complexity of elliptic PDE
Journal of Complexity
The Quantum Setting with Randomized Queries for Continuous Problems
Quantum Information Processing
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
On the complexity of the multivariate Sturm--Liouville eigenvalue problem
Journal of Complexity
Optimal integration error on anisotropic classes for restricted Monte Carlo and quantum algorithms
Journal of Approximation Theory
The randomized information complexity of elliptic PDE
Journal of Complexity
Quantum integration error for some sobolev classes
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Numerical analysis on a quantum computer
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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We study high-dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes Wpr([0,1]d) and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Novak on integration of functions from Hölder classes.