Information-based complexity
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
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
Quantum summation with an application to integration
Journal of Complexity
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
On a problem in quantum summation
Journal of Complexity
Quantum integration in Sobolev classes
Journal of Complexity
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Quantum approximation I. Embeddings of finite-dimensional Lp spaces
Journal of Complexity
The quantum query complexity of elliptic PDE
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
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Quantum computing was so far mainly concerned with discrete problems. Recently, Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, what advantages quantum computing can bring over classical deterministic or randomized methods for this type of a problem.In this paper we give a short introduction to the basic ideas of quantum computing and survey recent results on high dimensional integration. We discuss connections to the Monte Carlo methology and compare the optimal error rates of quantum algorithms to those of classical deterministic and randomized algorithms.