Quantum Computer Can Not Speed Up Iterated Applications of a Black Box

Authors:
Yuri Ozhigov
Affiliations:
-
Venue:
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Year:
1998

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Abstract

Let a classical algorithm be determined by sequential applications of a black box performing one step of this algorithm. If we consider this black box as an oracle which gives a value f(a) for a query a, we can compute T sequential applications of f on a classical computer relative to this oracle in time T. It is proved that if T = O(2n/7), where n is the length of input, then the result of T sequential applications of f can not be computed on quantum computer with oracle for f for all possible f faster than in time Ω(T). This means that there is no general method of quantum speeding up of classical algorithms provided in such a general method a classical algorithm is regarded as iterated applications of a given black box.