Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Introduction to Recent Quantum Algorithms
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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We construct a quantum black-box algorithm that computes the majority of N bits exactly using N + 1 - w(N) queries, where w(N) denotes the number of ones in the binary expansion of N. We establish a matching lower bound in a generalized classical decision tree model in which the equivalent of our quantum algorithm is optimal. We also provide an exact quantum algorithm that almost surely makes no more than 2^{-1/2} N + O((N log N)^{2/3}) queries.