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Average-case quantum query complexity
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
doi:10.1088/0305-4470/34/35/302
fatcat:wndxdkajcjdmhlkr4qb36fsgay