Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation

ilustraciones, diagramas

Autores:: Vargas Calderón, Vladimir

Tipo de recurso:: Doctoral thesis

Fecha de publicación:: 2022

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: eng

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repository_id_str
dc.title.eng.fl_str_mv	Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation
dc.title.translated.spa.fl_str_mv	Simbiosis entre la física cuántica y el machine learning: Aplicaciones en ciencia de datos, física de muchos cuerpos y computación cuántica
title	Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation
spellingShingle	Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation 530 - Física FISICA CUANTICA APRENDIZAJE AUTOMATICO (INTELIGENCIA ARTIFICIAL) Quantum physical Quantum physics Machine learning Data science Quantum computing Física cuántica Ciencia de datos Computación cuántica
title_short	Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation
title_full	Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation
title_fullStr	Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation
title_full_unstemmed	Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation
title_sort	Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation
dc.creator.fl_str_mv	Vargas Calderón, Vladimir
dc.contributor.advisor.none.fl_str_mv	Vinck Posada, Herbert González Osorio, Fabio Augusto
dc.contributor.author.none.fl_str_mv	Vargas Calderón, Vladimir
dc.contributor.researchgroup.spa.fl_str_mv	Grupo de Óptica E Información Cuántica Superconductividad y Nanotecnología
dc.contributor.orcid.spa.fl_str_mv	Vladimir Vargas-Calderón [0000000154763300]
dc.contributor.researchgate.spa.fl_str_mv	Vladimir Vargas-Calderón [Vladimir-Vargas-Calderon]
dc.contributor.googlescholar.spa.fl_str_mv	Vladimir Vargas-Calderón [SfLRhYcAAAAJ]
dc.subject.ddc.spa.fl_str_mv	530 - Física
topic	530 - Física FISICA CUANTICA APRENDIZAJE AUTOMATICO (INTELIGENCIA ARTIFICIAL) Quantum physical Quantum physics Machine learning Data science Quantum computing Física cuántica Ciencia de datos Computación cuántica
dc.subject.lemb.spa.fl_str_mv	FISICA CUANTICA APRENDIZAJE AUTOMATICO (INTELIGENCIA ARTIFICIAL)
dc.subject.lemb.eng.fl_str_mv	Quantum physical
dc.subject.proposal.eng.fl_str_mv	Quantum physics Machine learning Data science Quantum computing
dc.subject.proposal.spa.fl_str_mv	Física cuántica Ciencia de datos Computación cuántica
description	ilustraciones, diagramas
publishDate	2022
dc.date.issued.none.fl_str_mv	2022-12-01
dc.date.accessioned.none.fl_str_mv	2023-07-26T19:20:31Z
dc.date.available.none.fl_str_mv	2023-07-26T19:20:31Z
dc.type.spa.fl_str_mv	Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv	http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv	Text
dc.type.redcol.spa.fl_str_mv	http://purl.org/redcol/resource_type/TD
format	http://purl.org/coar/resource_type/c_db06
status_str	acceptedVersion
dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/84294
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/84294 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	eng
language	eng
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
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dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
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spelling	Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Vinck Posada, Herbertcb451c328e333b7d420c1effb3732257González Osorio, Fabio Augusto35912f60905ba6e179208c70e6024e80Vargas Calderón, Vladimir2975d7228cef335804ee66caa57fe8b6Grupo de Óptica E Información CuánticaSuperconductividad y NanotecnologíaVladimir Vargas-Calderón [0000000154763300]Vladimir Vargas-Calderón [Vladimir-Vargas-Calderon]Vladimir Vargas-Calderón [SfLRhYcAAAAJ]2023-07-26T19:20:31Z2023-07-26T19:20:31Z2022-12-01https://repositorio.unal.edu.co/handle/unal/84294Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasThis thesis explores the intersections between quantum computing, quantum physics and machine learning. In the three fields, estimating probability distributions plays a central role. In the case of quantum computing and quantum physics, a central object of study is the quantum state of a system, which encodes a probability dis- tribution (the converse is not true, however, as a quantum state is an object that is more general than a classical probability distribution). In the case of machine learning, most of supervised and unsupervised learning tasks can be seen as esti- mating probability distributions from a training data set, which then can be used to predict by sampling or evaluating such probability distribution. Due to the famous curse of dimensionality, both present in machine learning but also in the natural intractability of Hilbert spaces, it has been established that quantum theory and machine learning have a lot to give and learn from each other. The journey depicted in this thesis stems from quantum optics and its application to modelling quantum devices for quantum computation or simulation, such as quantum dots and their interaction with optical and acoustic cavities. Indeed, quan- tum computation has long been sought by the physics community and stands–in the collective imagination–as a “holy grail” to solve several problems in the indus- try and science. Of particular interest of mine is the study of quantum many-body problems themselves, which, in combination with quantum computing, establishes an interesting circular set of resources: quantum computation to study quantum systems that can be used for quantum computation. Unfortunately, the promise of the “holy grail” of quantum computation has not materialised to date (even though there are known applications which are expo- nentially faster than any classical algorithm, e.g. the famous Deutsch-Jozsa algo- rithm), which is why the best known approaches to studying quantum physics or quantum chemistry are still classical algorithms. In particular, there are machine learning models, known as neural quantum states, that can be used to study quan- tum many-body problems. Neural quantum states are an application of machine learning techniques for studying quantum physics. In this thesis, we show fruitful approaches to studying ground states, steady-states and closed dynamics of quan- tum systems through neural quantum states. This knowledge transfer does not only occur in one direction: quantum physics can also contribute to machine learning with quantum-inspired machine learning methods. In this thesis, we also present a framework that establishes an analogy between quantum state preparation and training, and also between quantum pro- jective measurements and prediction. Our approach condenses classical data into the quantum state of a system. We manage to show that arbitrary probability dis- tributions can be encoded in such a quantum state to arbitrary precision, given enough degrees of freedom of the quantum state. Moreover, we can condense ar- bitrarily large data sets into quantum states, which allow us to have gradient-free (actually, optimisation-free) training. This framework of ours was also put into action by implementing it on a real quantum computer for toy data sets. Finally, I also present applications of neural quantum states and quantum-inspired generative modelling to industry problems such as the famous travelling salesman problem, for which we propose a qudit-based Hamiltonian whose ground state en- codes its solution; and other problems such as the portfolio optimisation problem using tensor network generative models.Esta tesis explora las intersecciones entre la computación cuántica, la física cuántica y el aprendizaje automático. En los tres campos, la estimación de distribuciones de probabilidad desempeña un papel central. En el caso de la computación cuántica y la física cuántica, un objeto de estudio central es el estado cuántico de un sistema, que codifica una distribución de probabilidad (sin embargo, lo contrario no es cierto, ya que un estado cuántico es un objeto más general que una distribución de probabilidad clásica). En el caso del aprendizaje automático, la mayoría de las tareas de aprendizaje supervisado y no supervisado pueden considerarse como la estimación de distribuciones de probabilidad a partir de un conjunto de datos de entrenamiento, que luego pueden utilizarse para predecir mediante el muestreo o la evaluación de dicha distribución de probabilidad. Debido a la famosa maldición de la dimensionalidad, presente tanto en el aprendizaje automático como en la intratabilidad natural de los espacios de Hilbert, se ha establecido que la teoría cuántica y el aprendizaje automático tienen mucho que dar y aprender la una de la otra. El viaje descrito en esta tesis parte de la óptica cuántica y su aplicación al modelado de dispositivos cuánticos para la computación o la simulación cuánticas, como los puntos cuánticos y su interacción con cavidades ópticas y acústicas. De hecho, la comunidad de físicos lleva mucho tiempo buscando la computación cuántica y se erige–en el imaginario colectivo–como un “santo grial” para resolver varios problemas de la industria y la ciencia. De particular interés para mı es el estudio de los problemas cuánticos de muchos cuerpos, que, en combinación con la computación cuántica, establece un interesante conjunto circular de recursos: computación cuántica para estudiar sistemas cuánticos que pueden utilizarse para la computación cuántica. Por desgracia, la promesa del “santo grial” de la computación cuántica no se ha materializado hasta la fecha (aunque se conocen aplicaciones exponencialmente más rápidas que cualquier algoritmo clásico, por ejemplo, el famoso algoritmo Deutsch-Jozsa), por lo que los enfoques más conocidos para estudiar la física o la química cuánticas siguen siendo los algoritmos clásicos. En particular, existen modelos de aprendizaje automático, conocidos como estados cuánticos neuronales, que pueden utilizarse para estudiar problemas cuánticos de muchos cuerpos. Los estados cuánticos neuronales son una aplicación de las técnicas de aprendizaje automático para estudiar la física cuántica. En esta tesis, mostramos enfoques fructíferos para estudiar estados básicos, estados estacionarios y dinámicas cerradas de sistemas cuánticos mediante estados cuánticos neuronales. Esta transferencia de conocimientos no solo se produce en una dirección: la física cuántica también puede contribuir al aprendizaje automático con métodos de aprendizaje automático inspirados en la cuántica. En esta tesis también presentamos un marco que establece una analogía entre la preparación del estado cuántico y el entrenamiento, y también entre las mediciones proyectivas cuánticas y la predicción. Nuestro enfoque condensa los datos clásicos en el estado cuántico de un sistema. Conseguimos demostrar que se pueden codificar distribuciones de probabilidad arbitrarias en dicho estado cuántico con una precisión arbitraria, dados suficientes grados de libertad del estado cuántico. Además, podemos condensar conjuntos de datos arbitrariamente grandes en estados cuánticos, lo que nos permite tener un entrenamiento sin gradiente (en realidad, sin optimización). Este marco nuestro también se puso en práctica implementándolo en un ordenador cuántico real para conjuntos de datos de juguete. Por último, también presento aplicaciones de los estados cuánticos neuronales y el modelado generativo de inspiración cuántica a problemas industriales como el famoso problema del viajante de comercio, para el que proponemos un Hamiltoniano basado en el qudit cuyo estado fundamental codifica su solución; y otros problemas como el de optimización de carteras mediante modelos generativos de redes tensoriales. (Texto tomado de la fuente)DoctoradoDoctor en Ciencias - Físicaix, 119 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - FísicaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá530 - FísicaFISICA CUANTICAAPRENDIZAJE AUTOMATICO (INTELIGENCIA ARTIFICIAL)Quantum physicalQuantum physicsMachine learningData scienceQuantum computingFísica cuánticaCiencia de datosComputación cuánticaSymbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computationSimbiosis entre la física cuántica y el machine learning: Aplicaciones en ciencia de datos, física de muchos cuerpos y computación cuánticaTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDAbbas, A., Sutter, D., Zoufal, C., Lucchi, A., Figalli, A., and Woerner, S. (2021). 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Phys. Rev. A, 41:475–476.InvestigadoresLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84294/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53ORIGINAL1019108908.pdf1019108908.pdfTesis de Doctorado en Físicaapplication/pdf29947786https://repositorio.unal.edu.co/bitstream/unal/84294/4/1019108908.pdf7f58a72f5f74928db44b382e97935f16MD54THUMBNAIL1019108908.pdf.jpg1019108908.pdf.jpgGenerated Thumbnailimage/jpeg5833https://repositorio.unal.edu.co/bitstream/unal/84294/5/1019108908.pdf.jpg1543cf9fa677c1959377edfa10d25740MD55unal/84294oai:repositorio.unal.edu.co:unal/842942023-08-11 23:04:09.654Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.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Symbiosis between quantum physics and machine learning: Applications in data science, many-body physics and quantum computation

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