Average-case quantum query complexity

Andris Ambainis, Ronald de Wolf
2001 Journal of Physics A: Mathematical and General  
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 [3] . 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
more » ... case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical complexity.
doi:10.1088/0305-4470/34/35/302 fatcat:wndxdkajcjdmhlkr4qb36fsgay