Zobrazit v EDS

Analysis of variational quantum algorithms for differential equations in the presence of quantum noise : application to the stationary Gross-Pitaevskii equation ; Analyse d'algorithmes quantiques variationnels pour la résolution d'équations différentielles en présence de bruit quantique : application à l'équation de Gross-Pitaevskii stationnaire

Uloženo v:
Podrobná bibliografie
Název: Analysis of variational quantum algorithms for differential equations in the presence of quantum noise : application to the stationary Gross-Pitaevskii equation ; Analyse d'algorithmes quantiques variationnels pour la résolution d'équations différentielles en présence de bruit quantique : application à l'équation de Gross-Pitaevskii stationnaire
Autoři: Serret, Michel Fabrice
Přispěvatelé: Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université, Laurent Boudin, Yvon Maday, Thomas Ayral
Zdroj: https://theses.hal.science/tel-04833499 ; Numerical Analysis [math.NA]. Sorbonne Université, 2024. English. ⟨NNT : 2024SORUS298⟩.
Informace o vydavateli: CCSD
Rok vydání: 2024
Témata: Quantum computing, Numerical analysis, Differential equations, Numerical resolution, Quantum, Informatique quantique, Analyse numérique, Équations différentielles, Résolution numérique, Quantique, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Popis: Variational quantum algorithms (VQAs) have been proposed for solvingpartial differential equations on quantum computers. This thesis focuses on analyzingVQAs for the stationary Gross-Pitaevskii Equation (GPE) both under ideal (noiseless) conditionsand in the presence of quantum noise, providing error bounds, convergence properties, and estimatesfor the number of samples required.A central concept, make use of a relationship between the representation of functions and functional operators on dyadic rationals, through the Walsh basis, and the encoding offunctions and operators for N-qubit quantum systems through the Pauli operators and their eigenstates.In chapter 1, we link Pauli operators of N-qubit quantum systems with the Walsh basis on N-bit dyadic rationals, presenting new error bounds for the convergence of the N-bit Walsh series for functions in H^1(0,1) and presenting some results on the representation of Fourier basis functions in the Walsh basis.In chapter 2 we analyse VQAs for the GPE without noise, detailing the mathematicalsetting, discretization, and a-priori analysis. We introduce new energyestimators, either based on the Walsh decomposition of operators or obtained through inductive methods, and compare them to directsampling, in the diagonal basis of the operators, and the Hadamard-test method. Our results show that in the absence of noise the most promising methods for energyestimation is direct sampling in the diagonal basis, yielding the lowest variance and sample requirements.In chapter 3, we further examine the impact of quantum noise on energy estimation.Depolarizing noise introduces bias and shifts the variance of estimators. We show that the Pauli estimators proves least affected bynoise, due to their lower circuit size requirement,outperforming others both without mitigation, due to a lower bias, and with mitigation, as its sample efficiency is less affected.In the last chapter, devoted to work in progress, we present some preliminary results on decomposing differential operators in the ...
Druh dokumentu: doctoral or postdoctoral thesis
Jazyk: English
Relation: NNT: 2024SORUS298
Dostupnost: https://theses.hal.science/tel-04833499
https://theses.hal.science/tel-04833499v1/document
https://theses.hal.science/tel-04833499v1/file/143095_SERRET_2024_archivage.pdf
Rights: info:eu-repo/semantics/OpenAccess
Přístupové číslo: edsbas.CE8C930B
Databáze: BASE
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://theses.hal.science/tel-04833499#
    Name: EDS - BASE (s4221598)
    Category: fullText
    Text: View record from BASE
  – Url: https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=EBSCO&SrcAuth=EBSCO&DestApp=WOS&ServiceName=TransferToWoS&DestLinkType=GeneralSearchSummary&Func=Links&author=Serret%20MF
    Name: ISI
    Category: fullText
    Text: Nájsť tento článok vo Web of Science
    Icon: https://imagesrvr.epnet.com/ls/20docs.gif
    MouseOverText: Nájsť tento článok vo Web of Science
Header DbId: edsbas
DbLabel: BASE
An: edsbas.CE8C930B
RelevancyScore: 891
AccessLevel: 3
PubType: Dissertation/ Thesis
PubTypeId: dissertation
PreciseRelevancyScore: 890.605651855469
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Analysis of variational quantum algorithms for differential equations in the presence of quantum noise : application to the stationary Gross-Pitaevskii equation ; Analyse d'algorithmes quantiques variationnels pour la résolution d'équations différentielles en présence de bruit quantique : application à l'équation de Gross-Pitaevskii stationnaire
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Serret%2C+Michel+Fabrice%22">Serret, Michel Fabrice</searchLink>
– Name: Author
  Label: Contributors
  Group: Au
  Data: Laboratoire Jacques-Louis Lions (LJLL (UMR_7598))<br />Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)<br />Sorbonne Université<br />Laurent Boudin<br />Yvon Maday<br />Thomas Ayral
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <i>https://theses.hal.science/tel-04833499 ; Numerical Analysis [math.NA]. Sorbonne Université, 2024. English. ⟨NNT : 2024SORUS298⟩</i>.
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: CCSD
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2024
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Quantum+computing%22">Quantum computing</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+resolution%22">Numerical resolution</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum%22">Quantum</searchLink><br /><searchLink fieldCode="DE" term="%22Informatique+quantique%22">Informatique quantique</searchLink><br /><searchLink fieldCode="DE" term="%22Analyse+numérique%22">Analyse numérique</searchLink><br /><searchLink fieldCode="DE" term="%22Équations+différentielles%22">Équations différentielles</searchLink><br /><searchLink fieldCode="DE" term="%22Résolution+numérique%22">Résolution numérique</searchLink><br /><searchLink fieldCode="DE" term="%22Quantique%22">Quantique</searchLink><br /><searchLink fieldCode="DE" term="%22[MATH%2EMATH-NA]Mathematics+[math]%2FNumerical+Analysis+[math%2ENA]%22">[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: Variational quantum algorithms (VQAs) have been proposed for solvingpartial differential equations on quantum computers. This thesis focuses on analyzingVQAs for the stationary Gross-Pitaevskii Equation (GPE) both under ideal (noiseless) conditionsand in the presence of quantum noise, providing error bounds, convergence properties, and estimatesfor the number of samples required.A central concept, make use of a relationship between the representation of functions and functional operators on dyadic rationals, through the Walsh basis, and the encoding offunctions and operators for N-qubit quantum systems through the Pauli operators and their eigenstates.In chapter 1, we link Pauli operators of N-qubit quantum systems with the Walsh basis on N-bit dyadic rationals, presenting new error bounds for the convergence of the N-bit Walsh series for functions in H^1(0,1) and presenting some results on the representation of Fourier basis functions in the Walsh basis.In chapter 2 we analyse VQAs for the GPE without noise, detailing the mathematicalsetting, discretization, and a-priori analysis. We introduce new energyestimators, either based on the Walsh decomposition of operators or obtained through inductive methods, and compare them to directsampling, in the diagonal basis of the operators, and the Hadamard-test method. Our results show that in the absence of noise the most promising methods for energyestimation is direct sampling in the diagonal basis, yielding the lowest variance and sample requirements.In chapter 3, we further examine the impact of quantum noise on energy estimation.Depolarizing noise introduces bias and shifts the variance of estimators. We show that the Pauli estimators proves least affected bynoise, due to their lower circuit size requirement,outperforming others both without mitigation, due to a lower bias, and with mitigation, as its sample efficiency is less affected.In the last chapter, devoted to work in progress, we present some preliminary results on decomposing differential operators in the ...
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: doctoral or postdoctoral thesis
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: NoteTitleSource
  Label: Relation
  Group: SrcInfo
  Data: NNT: 2024SORUS298
– Name: URL
  Label: Availability
  Group: URL
  Data: https://theses.hal.science/tel-04833499<br />https://theses.hal.science/tel-04833499v1/document<br />https://theses.hal.science/tel-04833499v1/file/143095_SERRET_2024_archivage.pdf
– Name: Copyright
  Label: Rights
  Group: Cpyrght
  Data: info:eu-repo/semantics/OpenAccess
– Name: AN
  Label: Accession Number
  Group: ID
  Data: edsbas.CE8C930B
PLink https://erproxy.cvtisr.sk/sfx/access?url=https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.CE8C930B
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Quantum computing
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Differential equations
        Type: general
      – SubjectFull: Numerical resolution
        Type: general
      – SubjectFull: Quantum
        Type: general
      – SubjectFull: Informatique quantique
        Type: general
      – SubjectFull: Analyse numérique
        Type: general
      – SubjectFull: Équations différentielles
        Type: general
      – SubjectFull: Résolution numérique
        Type: general
      – SubjectFull: Quantique
        Type: general
      – SubjectFull: [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
        Type: general
    Titles:
      – TitleFull: Analysis of variational quantum algorithms for differential equations in the presence of quantum noise : application to the stationary Gross-Pitaevskii equation ; Analyse d'algorithmes quantiques variationnels pour la résolution d'équations différentielles en présence de bruit quantique : application à l'équation de Gross-Pitaevskii stationnaire
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Serret, Michel Fabrice
      – PersonEntity:
          Name:
            NameFull: Laboratoire Jacques-Louis Lions (LJLL (UMR_7598))
      – PersonEntity:
          Name:
            NameFull: Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
      – PersonEntity:
          Name:
            NameFull: Sorbonne Université
      – PersonEntity:
          Name:
            NameFull: Laurent Boudin
      – PersonEntity:
          Name:
            NameFull: Yvon Maday
      – PersonEntity:
          Name:
            NameFull: Thomas Ayral
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2024
          Identifiers:
            – Type: issn-locals
              Value: edsbas
            – Type: issn-locals
              Value: edsbas.oa
          Titles:
            – TitleFull: https://theses.hal.science/tel-04833499 ; Numerical Analysis [math.NA]. Sorbonne Université, 2024. English. ⟨NNT : 2024SORUS298⟩
              Type: main
ResultId 1