Fault tolerant quantum algorithms

The framework of this thesis is fault-tolerant quantum algorithms, which can roughly be divided into the following non-disjoint families: a) Grover’s algorithm and quantum walks, b) Shor’s algorithm and hidden subgroup problems, c) quantum simulation algorithms, d) quantum linear algebra, and e) var...

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Detalles Bibliográficos
Autor: Moreno Casares, Pablo Antonio
Tipo de recurso: tesis doctoral
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/4210
Acceso en línea:https://hdl.handle.net/20.500.14352/4210
Access Level:acceso abierto
Palabra clave:510.5(043.2)
Algorithms
Algoritmos
Física matemática
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spelling Fault tolerant quantum algorithmsAlgoritmos cuánticos tolerantes a fallosMoreno Casares, Pablo Antonio510.5(043.2)AlgorithmsAlgoritmosFísica matemáticaThe framework of this thesis is fault-tolerant quantum algorithms, which can roughly be divided into the following non-disjoint families: a) Grover’s algorithm and quantum walks, b) Shor’s algorithm and hidden subgroup problems, c) quantum simulation algorithms, d) quantum linear algebra, and e) variational quantum algorithms. All of them are covered, to some extent, in this thesis. Grover’s algorithm and quantum walks are described in Chapter 2. We start by highlighting the central role that rotations play in quantum algorithms, explaining Grover’s, why it is optimal, and how it may be extended. Key subroutines explained in this area are amplitude amplification and quantum walks, which will constitute useful parts of other algorithms. In this chapter, we present our Ref. [62], where we explore the heuristic use of quantum Metropolis and quantum walk algorithms for solving anNP-hard problem. This method has been suggested as an avenue to digitally simulate quantum annealing and preparing ground states of many-body Hamiltonians. In the third chapter, in contrast, we turn to the exponential advantages promisedby the Fourier transform in the context of the hidden subgroup problem. However, since this application is restricted to cryptography, we later explore its use in quantum linear algebra problems. Here we explain the development of the original quantum linear solver algorithm, its improvements, and finally the dequantization techniques that would often restrict the quantum advantage to polynomial...Universidad Complutense de MadridUniversidad Complutense de Madrid20232023-05-1820232023-05-18doctoral thesishttp://purl.org/coar/resource_type/c_db06info:eu-repo/semantics/doctoralThesisapplication/pdfhttps://hdl.handle.net/20.500.14352/4210reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/42102026-06-02T12:44:21Z
dc.title.none.fl_str_mv Fault tolerant quantum algorithms
Algoritmos cuánticos tolerantes a fallos
title Fault tolerant quantum algorithms
spellingShingle Fault tolerant quantum algorithms
Moreno Casares, Pablo Antonio
510.5(043.2)
Algorithms
Algoritmos
Física matemática
title_short Fault tolerant quantum algorithms
title_full Fault tolerant quantum algorithms
title_fullStr Fault tolerant quantum algorithms
title_full_unstemmed Fault tolerant quantum algorithms
title_sort Fault tolerant quantum algorithms
dc.creator.none.fl_str_mv Moreno Casares, Pablo Antonio
author Moreno Casares, Pablo Antonio
author_facet Moreno Casares, Pablo Antonio
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 510.5(043.2)
Algorithms
Algoritmos
Física matemática
topic 510.5(043.2)
Algorithms
Algoritmos
Física matemática
description The framework of this thesis is fault-tolerant quantum algorithms, which can roughly be divided into the following non-disjoint families: a) Grover’s algorithm and quantum walks, b) Shor’s algorithm and hidden subgroup problems, c) quantum simulation algorithms, d) quantum linear algebra, and e) variational quantum algorithms. All of them are covered, to some extent, in this thesis. Grover’s algorithm and quantum walks are described in Chapter 2. We start by highlighting the central role that rotations play in quantum algorithms, explaining Grover’s, why it is optimal, and how it may be extended. Key subroutines explained in this area are amplitude amplification and quantum walks, which will constitute useful parts of other algorithms. In this chapter, we present our Ref. [62], where we explore the heuristic use of quantum Metropolis and quantum walk algorithms for solving anNP-hard problem. This method has been suggested as an avenue to digitally simulate quantum annealing and preparing ground states of many-body Hamiltonians. In the third chapter, in contrast, we turn to the exponential advantages promisedby the Fourier transform in the context of the hidden subgroup problem. However, since this application is restricted to cryptography, we later explore its use in quantum linear algebra problems. Here we explain the development of the original quantum linear solver algorithm, its improvements, and finally the dequantization techniques that would often restrict the quantum advantage to polynomial...
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-05-18
2023
2023-05-18
dc.type.none.fl_str_mv doctoral thesis
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dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/4210
url https://hdl.handle.net/20.500.14352/4210
dc.language.none.fl_str_mv Inglés
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language_invalid_str_mv Inglés
language eng
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eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Universidad Complutense de Madrid
publisher.none.fl_str_mv Universidad Complutense de Madrid
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
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