  This work introduces a relative diffusion transformation (RDT) - a simple
unitary transformation which acts in a subspace, localized by an oracle. Such a
transformation can not be fulfilled on quantum Turing machines with this oracle
in polynomial time in general case. It is proved, that every function
computable in time T and space S on classical 1-dimensional cellular automaton,
can be computed with certainty in time O(S \sqrt T) on quantum computer with
RDTs over the parts of intermediate products of classical computation. This
requires multiprocessor, which consists of \sqrt T quantum devices each of O(S)
size, working in parallel-serial mode and interacting by classical lows.
