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Quantum algorithms for energy management optimization problems ; Algorithmes quantiques pour les problèmes d'optimisation du management de l'énergie

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Title: Quantum algorithms for energy management optimization problems ; Algorithmes quantiques pour les problèmes d'optimisation du management de l'énergie
Authors: Veshchezerova, Margarita
Contributors: Designing the Future of Computational Models (MOCQUA), Centre Inria de l'Université de Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Formal Methods (LORIA - FM), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), EDF Labs, Convention CIFRE - EDF, Université de Lorraine, Emmanuel Jeandel, Simon Perdrix
Source: https://hal.univ-lorraine.fr/tel-04105922 ; Computer Science [cs]. Université de Lorraine, 2022. English. ⟨NNT : 2022LORR0346⟩.
Publisher Information: CCSD
Publication Year: 2022
Collection: Université de Lorraine: HAL
Subject Terms: Smart charging, ZX-Calculus, Energy management, Quantum computing, Combinatorial optimization, Recharge intelligente, Management de l'énergie, Algorithmes quantiques, Optimisation combinatoire, [INFO]Computer Science [cs], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-RO]Computer Science [cs]/Operations Research [math.OC], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Description: The domain of energy management involves many combinatorial optimization problems known to be computationally hard. The emergence of quantum computers suggests new approaches for these problems. For near-future machines particularly promising are variational quantum heuristics such as QAOA that can leverage the computational power of the imperfect quantum hardware. We explore the potential of variational quantum algorithms for optimization problems issued from the field of "smart charging"}of electrical vehicles. We consider two problems inspired by real-world usecases. In the first problem, modeled as Max-K-Cut, we search to schedule a set of prioritized charges on several stations while minimizing the weighted completion time. In the second problem, modeled as Maximum Independent Set, we aim to maximize the number of satisfied charge demands on a single station while respecting the conflicts between demands. For both problems, we develop an experimental protocol specifying the encoding step and the parameter optimization routine. Our numerical experiments confirm the interest of quantum heuristics for these problems as well as the quality of our experimental protocol. In order to extend the applicability of quantum heuristics beyond QUBO we introduce a new hybrid approach that integrates quantum routines in the classical Branch & Price algorithm for large integer linear programs. We test this approach on a smart charging problem that is modeled as graph coloring problem. Our computational results affirm the potential of the hybrid approach while revealing the considerable dependence of the performance gain on the particular instance of the problem. Important components of variational algorithms can be represented as ZX-diagrams. We demonstrate how the rewriting rules of ZX-calculus can be used to derive the analytical formula for the mean energy of a general Ising model in a QAOA of depth 1 state. Furthermore, we contribute to the theoretical exploration of variational algorithms by extending the ...
Document Type: doctoral or postdoctoral thesis
Language: English
Relation: NNT: 2022LORR0346
Availability: https://hal.univ-lorraine.fr/tel-04105922
https://hal.univ-lorraine.fr/tel-04105922v1/document
https://hal.univ-lorraine.fr/tel-04105922v1/file/DDOC_T_2022_0346_VESHCHEZEROVA.pdf
Rights: info:eu-repo/semantics/OpenAccess
Accession Number: edsbas.9A77F4A5
Database: BASE
Description
Abstract:The domain of energy management involves many combinatorial optimization problems known to be computationally hard. The emergence of quantum computers suggests new approaches for these problems. For near-future machines particularly promising are variational quantum heuristics such as QAOA that can leverage the computational power of the imperfect quantum hardware. We explore the potential of variational quantum algorithms for optimization problems issued from the field of "smart charging"}of electrical vehicles. We consider two problems inspired by real-world usecases. In the first problem, modeled as Max-K-Cut, we search to schedule a set of prioritized charges on several stations while minimizing the weighted completion time. In the second problem, modeled as Maximum Independent Set, we aim to maximize the number of satisfied charge demands on a single station while respecting the conflicts between demands. For both problems, we develop an experimental protocol specifying the encoding step and the parameter optimization routine. Our numerical experiments confirm the interest of quantum heuristics for these problems as well as the quality of our experimental protocol. In order to extend the applicability of quantum heuristics beyond QUBO we introduce a new hybrid approach that integrates quantum routines in the classical Branch & Price algorithm for large integer linear programs. We test this approach on a smart charging problem that is modeled as graph coloring problem. Our computational results affirm the potential of the hybrid approach while revealing the considerable dependence of the performance gain on the particular instance of the problem. Important components of variational algorithms can be represented as ZX-diagrams. We demonstrate how the rewriting rules of ZX-calculus can be used to derive the analytical formula for the mean energy of a general Ising model in a QAOA of depth 1 state. Furthermore, we contribute to the theoretical exploration of variational algorithms by extending the ...