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
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
Complexity and information
Quantum complexity of integration
Journal of Complexity
Quantum computation and quantum information
Quantum computation and quantum information
Quantum summation with an application to integration
Journal of Complexity
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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
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The computation of combinatorial and numerical problems on quantum computers is often much faster than on a classical computer in numbers of queries. A query is a procedure by which the quantum computer gains information about the specific problem. Different query definitions were given and our aim is to review them and to show that these definitions are not equivalent. To achieve this result we will study the simulation and approximation of one query type by another. While approximation is "easy" in one direction, we will show that it is "hard" in the other direction by a lower bound for the numbers of queries needed in the simulation. The main tool in this lower bound proof is a relationship between quantum algorithms and trigonometric polynomials that we will establish.