## Physical Systems for the Solution of Hard Computational Problems (2003)

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@MISC{Mattsson03physicalsystems,

author = {Peter Mattsson},

title = {Physical Systems for the Solution of Hard Computational Problems},

year = {2003}

}

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### Abstract

We start from Landauer's realization that "information is physical", i.e. that computation cannot be disentangled from the physical system used to perform it, and ask what the capabilities of physical systems really are. In particular, is it possible to design a physical system which is able to solve hard (i.e. NP-complete) problems more e#ciently than conventional computers? Chaotic physical systems (such as the weather) are hard to predict or simulate, but we find that they are also hard to control. The requirement of control turns out to pin down the non-conventional options to either neural networks or quantum computers. Alternatively, we can give up the possibility of control in favour of a system which is basically chaotic, but is able to settle at a solution if it reaches one. However, systems of this type appear inevitably to perform a type of stochastic local search.