About the quantum mechanical speeding up of classical algorithms

Details About the quantum mechanical speeding up of classical algorithms About the quantum mechanical speeding up of classical algorithms

1997-06-02

arxiv.org/abs/quant-ph/9706003v4

Physics

Quantum Physics

9 pages, LATEX, 2 figures in one GIF-file (the essential revision of the previous version, some errors are corrected)

Scientific paper

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.

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