Nonadaptive quantum query complexity
We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that computes a total boolean function depending on n variables must make Omega(n) queries to the input in total. Second, we show that, if there exists a quantum algorithm that uses k nonadaptive oracle queries to learn which one of a set of m boolean functions it has been given, there exists a nonadaptive classical algorithm using O(k logm) queries to solve the same problem. Thus, in the nonadaptive setting, quantum algorithms for these tasks can achieve at most a very limited speed-up over classical query algorithms. (C) 2010 Elsevier B.V. All rights reserved.
quantum query complexity quantum computing decision tree complexity theory of computation