Exact quantum algorithms have advantage for almost all Boolean functions (pp0435-0452)
          Andris Ambainis, Jozef Gruska, and Shenggen Zheng
          doi: https://doi.org/10.26421/QIC15.5-6-5
Abstracts: 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.
Key words: Quantum computing, Quantum query complexity, Boolean function, Symmetric Boolean function, Monotone Boolean function, Read-once Boolean function