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Extracting Dynamical Equations from Experimental Data is NP Hard

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Cubitt, Toby S. and Eisert, Jens and Wolf, Michael M. (2012) Extracting Dynamical Equations from Experimental Data is NP Hard. Physical Review Letters, 108 (12). ISSN 0031-9007

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Official URL: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.120503



Abstract

The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this Letter, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP hard), both for classical and quantum mechanical systems. As a by-product of this work, we give complexity-theoretic answers to both the quantum and classical embedding problems, two long-standing open problems in mathematics (the classical problem, in particular, dating back over 70 years).


Item Type:Article
Subjects:Sciences > Physics > Mathematical physics
Sciences > Physics > Quantum theory
ID Code:27969
Deposited On:13 Feb 2015 12:54
Last Modified:13 Feb 2015 12:54

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