Quantum Computing and Phase Transitions in Combinatorial Search

Details Quantum Computing and Phase Transitions in Combinatorial Search Quantum Computing and Phase Transitions in Combinatorial Search

1995-08-16

arxiv.org/abs/quant-ph/9508012v1

J. of Artificial Intelligence Research 4,91-128 (1996)

Physics

Quantum Physics

29 pages, uuencoded tar compressed postscript in a self-unpacking shell script created using the uufiles script. For related i

Scientific paper

We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem structure as used by classical backtrack methods to avoid unproductive search choices. This quantum algorithm is much more likely to find solutions than the simple direct use of quantum parallelism. Furthermore, empirical evaluation on small problems shows this quantum algorithm displays the same phase transition behavior, and at the same location, as seen in many previously studied classical search methods. Specifically, difficult problem instances are concentrated near the abrupt change from underconstrained to overconstrained problems.

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