  Let $f$ denote length preserving function on words. A classical algorithm can
be considered as $T$ iterated applications of black box representing $f$,
beginning with input word $x$ of length $n$.
  It is proved that if $T=O(2^{n/(7+e)}), e >0$, and $f$ is chosen randomly
then with probability 1 every quantum computer requires not less than $T$
evaluations of $f$ to obtain the result of classical computation. It means that
the set of classical algorithms admitting quantum speeding up has probability
measure zero.
  The second result is that for arbitrary classical time complexity $T$ and $f$
chosen randomly with probability 1 every quantum simulation of classical
computation requires at least $\Omega (\sqrt {T})$ evaluations of $f$.

Quantum Physics