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Quantum variational optimization methods and their applications ; Méthodes d'optimisation variationnelles quantiques et leurs applications

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Název: Quantum variational optimization methods and their applications ; Méthodes d'optimisation variationnelles quantiques et leurs applications
Autoři: Chatterjee, Yagnik
Přispěvatelé: Methods, Algorithms for Operations REsearch (LIRMM, Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Université de Montpellier, Eric Bourreau
Zdroj: https://theses.hal.science/tel-04766221 ; Micro and nanotechnologies/Microelectronics. Université de Montpellier, 2024. English. ⟨NNT : 2024UMONS022⟩.
Informace o vydavateli: CCSD
Rok vydání: 2024
Sbírka: Université de Montpellier: HAL
Témata: Combinatorial Optimization, Quantum variational algorithms, Quantum computing, Calcul Quantique, Algorithmes variationnels quantiques, Optimisation combinatoire, [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics
Popis: Quantum computing is a rapidly developing field that has seen a huge amount of interest in the last couple of decades due to its promise of revolutionizing several domains of business and science. It presents a new way of doing computations by making use of fundamental properties of quantum mechanics such as superposition and entanglement. Optimization, on the other hand, is a field that is omnipresent in the industry and where small improvements can have a significant impact. This thesis aims to tackle optimization problems using quantum algorithms.NP-hard optimization problems are not believed to be exactly solvable through general polynomial time algorithms. Variational quantum algorithms (VQAs) to address such combinatorial problems have been of great interest recently. Such algorithms are heuristic and aim to obtain an approximate solution. The hardware, however, is still in its infancy and the current Noisy Intermediate Scale Quantum (NISQ) computers are not able to optimize industrially relevant problems. Moreover, the storage of qubits and introduction of entanglement require extreme physical conditions.An issue with contemporary quantum optimization algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) is that they scale linearly with problem size. To tackle this issue, we present the LogQ encoding, using which we can design quantum variational algorithms that scale logarithmically with problem size - opening an avenue for treating optimization problems of unprecedented scale on gate-based quantum computers. We show how this algorithm can be applied to several combinatorial optimization problems such as Maximum Cut, Minimum Partition, Maximum Clique and Maximum Weighted Independent Set (MWIS). Subsequently, these algorithms are tested on a quantum simulator with graph sizes of over a hundred nodes and on a real quantum computer up to graph sizes of 256. To our knowledge, these constitute the largest realistic combinatorial optimization problems ever run on a NISQ device, overcoming ...
Druh dokumentu: doctoral or postdoctoral thesis
Jazyk: English
Relation: NNT: 2024UMONS022
Dostupnost: https://theses.hal.science/tel-04766221
https://theses.hal.science/tel-04766221v1/document
https://theses.hal.science/tel-04766221v1/file/CHATTERJEE_2024_archivage.pdf
Rights: info:eu-repo/semantics/OpenAccess
Přístupové číslo: edsbas.5A7FE48E
Databáze: BASE
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  Data: Quantum computing is a rapidly developing field that has seen a huge amount of interest in the last couple of decades due to its promise of revolutionizing several domains of business and science. It presents a new way of doing computations by making use of fundamental properties of quantum mechanics such as superposition and entanglement. Optimization, on the other hand, is a field that is omnipresent in the industry and where small improvements can have a significant impact. This thesis aims to tackle optimization problems using quantum algorithms.NP-hard optimization problems are not believed to be exactly solvable through general polynomial time algorithms. Variational quantum algorithms (VQAs) to address such combinatorial problems have been of great interest recently. Such algorithms are heuristic and aim to obtain an approximate solution. The hardware, however, is still in its infancy and the current Noisy Intermediate Scale Quantum (NISQ) computers are not able to optimize industrially relevant problems. Moreover, the storage of qubits and introduction of entanglement require extreme physical conditions.An issue with contemporary quantum optimization algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) is that they scale linearly with problem size. To tackle this issue, we present the LogQ encoding, using which we can design quantum variational algorithms that scale logarithmically with problem size - opening an avenue for treating optimization problems of unprecedented scale on gate-based quantum computers. We show how this algorithm can be applied to several combinatorial optimization problems such as Maximum Cut, Minimum Partition, Maximum Clique and Maximum Weighted Independent Set (MWIS). Subsequently, these algorithms are tested on a quantum simulator with graph sizes of over a hundred nodes and on a real quantum computer up to graph sizes of 256. To our knowledge, these constitute the largest realistic combinatorial optimization problems ever run on a NISQ device, overcoming ...
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      – Text: English
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      – SubjectFull: Combinatorial Optimization
        Type: general
      – SubjectFull: Quantum variational algorithms
        Type: general
      – SubjectFull: Quantum computing
        Type: general
      – SubjectFull: Calcul Quantique
        Type: general
      – SubjectFull: Algorithmes variationnels quantiques
        Type: general
      – SubjectFull: Optimisation combinatoire
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      – SubjectFull: [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics
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