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- W2951924060 abstract "We describe a quantum black-box network computing the majority of N bits with zero-sided error eps using only 2N/3 + O(sqrt{N (log log N + log 1/eps)}) queries: the algorithm returns the correct answer with probability at least 1 - eps, and I don't know otherwise. Our algorithm is given as a randomized decision for which the number of queries on any input is strongly concentrated around a value of at most 2N/3. We provide a nearly matching lower bound of 2N/3 - O(sqrt(N)) on the expected number of queries on a worst-case input in the randomized XOR decision tree model with zero-sided error o(1). Any classical randomized decision tree computing the majority on N bits with zero-sided error 1/2 has cost N." @default.
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- W2951924060 date "2001-09-20" @default.
- W2951924060 modified "2023-09-27" @default.
- W2951924060 title "On the Quantum Black-Box Complexity of Majority" @default.
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