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 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
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The Quantum Setting with Randomized Queries for Continuous Problems
Quantum Information Processing
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We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show specific query and error lower bounds and the algorithms that achieve them. We also study the worst expected error and the average expected error of quantum algorithms and show the respective query lower bounds. Our results extend the optimality of the algorithm of Brassard et al.