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ALGORITHMICA
2002

The Quantum Black-Box Complexity of Majority

8 years 10 months ago
The Quantum Black-Box Complexity of Majority
We describe a quantum black-box network computing the majority of N bits with zerosided error using only 2 3 N + O( N log( -1 log N)) queries: the algorithm returns the correct answer with probability at least 1 - , and "I don't know" otherwise. Our algorithm is given as a randomized "XOR decision tree" for which the number of queries on any input is strongly concentrated around a value of at most 2 3 N. We provide a nearly matching lower bound of 2 3 N - O( 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.
Thomas P. Hayes, Samuel Kutin, Dieter van Melkebee
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2002
Where ALGORITHMICA
Authors Thomas P. Hayes, Samuel Kutin, Dieter van Melkebeek
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