Average-Case Quantum Query Complexity
- Cite this paper as:
- Ambainis A., de Wolf R. (2000) Average-Case Quantum Query Complexity. In: Reichel H., Tison S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial . We show that for average-case complexity under the uniform distribution, quantum algorithms can be exponentially faster than classical algorithms. Under non-uniform distributions the gap can even be super-exponential. We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical complexity.
Unable to display preview. Download preview PDF.