Extracting Dynamical Equations from Experimental Data is NP Hard

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...

Descripción completa

Detalles Bibliográficos
Autores: Cubitt, Toby S., Eisert, Jens, Wolf, Michael M.
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/44447
Acceso en línea:https://hdl.handle.net/20.500.14352/44447
Access Level:acceso abierto
Palabra clave:51-73
530.145
Física matemática
Teoría de los quanta
2210.23 Teoría Cuántica
id ES_32157f59ef74432f7254e4e5eceb76f7
oai_identifier_str oai:docta.ucm.es:20.500.14352/44447
network_acronym_str ES
network_name_str España
repository_id_str
spelling Extracting Dynamical Equations from Experimental Data is NP HardCubitt, Toby S.Eisert, JensWolf, Michael M.51-73530.145Física matemáticaTeoría de los quanta2210.23 Teoría CuánticaThe 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).American Physical SocietyUniversidad Complutense de Madrid20122012-03-2220122012-03-22journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/44447reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/444472026-06-02T12:44:21Z
dc.title.none.fl_str_mv Extracting Dynamical Equations from Experimental Data is NP Hard
title Extracting Dynamical Equations from Experimental Data is NP Hard
spellingShingle Extracting Dynamical Equations from Experimental Data is NP Hard
Cubitt, Toby S.
51-73
530.145
Física matemática
Teoría de los quanta
2210.23 Teoría Cuántica
title_short Extracting Dynamical Equations from Experimental Data is NP Hard
title_full Extracting Dynamical Equations from Experimental Data is NP Hard
title_fullStr Extracting Dynamical Equations from Experimental Data is NP Hard
title_full_unstemmed Extracting Dynamical Equations from Experimental Data is NP Hard
title_sort Extracting Dynamical Equations from Experimental Data is NP Hard
dc.creator.none.fl_str_mv Cubitt, Toby S.
Eisert, Jens
Wolf, Michael M.
author Cubitt, Toby S.
author_facet Cubitt, Toby S.
Eisert, Jens
Wolf, Michael M.
author_role author
author2 Eisert, Jens
Wolf, Michael M.
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-73
530.145
Física matemática
Teoría de los quanta
2210.23 Teoría Cuántica
topic 51-73
530.145
Física matemática
Teoría de los quanta
2210.23 Teoría Cuántica
description 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).
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-03-22
2012
2012-03-22
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/44447
url https://hdl.handle.net/20.500.14352/44447
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869405653019131904
score 15.301629

Similares en LA Referencia