Single-Step Quantum Search Using Problem Structure

Details Single-Step Quantum Search Using Problem Structure Single-Step Quantum Search Using Problem Structure

1998-12-17

arxiv.org/abs/quant-ph/9812049v2

Int.J.Mod.Phys. C11 (2000) 739-773

Physics

Quantum Physics

39 pages, 12 figures. Revision describes further improvement with multiple steps (section 7). See also http://www.parc.xerox

Scientific paper

10.1142/S0129183100000663

The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT allows determining the asymptotic average behavior of these algorithms, showing they improve on quantum algorithms, such as amplitude amplification, that ignore detailed problem structure but remain exponential for hard problem instances. Compared to good classical methods, the algorithm performs better, on average, for weakly and highly constrained problems but worse for hard cases. The analytic techniques introduced here also apply to other quantum algorithms, supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of NP search problems.

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