Tradeoffs in the Quantum Search Algorithm

Details Tradeoffs in the Quantum Search Algorithm Tradeoffs in the Quantum Search Algorithm

2002-01-31

arxiv.org/abs/quant-ph/0201152v1

Physics

Quantum Physics

11 pages

Scientific paper

10.1103/PhysRevA.66.052314

Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires cannot be reduced. However, as this paper shows, the number of non-query operations, and thus the total number of operations, can be reduced. The number of non-query unitary operations can be reduced by a factor of log N/alpha*log(log N) while increasing the number of queries by a factor of only (1+(log N)^{-alpha}). Various choices of alpha yield different variants of the algorithm. For example, by choosing alpha to be O(log N/log(log N)), the number of non-query unitary operations can be reduced by 40% while increasing the number of queries by just two.

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