Exact quantum algorithms have advantage for almost all Boolean functions
Andris Ambainis, Jozef Gruska, Shenggen Zheng · Quantum Information and Computation · 2015
It has been proved that almost all n-bit Boolean functions have exact classical query complexity n. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost all n-bit Boolean functions can be computed by an exact quantum algorithm with less than n queries. More exactly, we prove that ANDn is the only n-bit Boolean function, up to isomorphism, that requires n queries.