solQHealer: Quantum Procedures for Rendering Infeasible Solutions Feasible: A Proof of Concept with the Maximum Independent Set Problem and 3-SAT

Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of active debate. Although current analog quantum machines do not guarantee optimality, operating instead as heuristic solvers, the technology is evolving rapidly. Beyond performanc...

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Veröffentlicht in:Journal of heuristics Jg. 31; H. 3; S. 30
Hauptverfasser: Deleplanque, Samuel, Pérez Armas, Luis Fernando, Creemers, Stefan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer Nature B.V 01.09.2025
Springer Verlag
Schlagworte:
Algorithms
Combinatorial analysis
Computer Science
Data Structures and Algorithms
Economics and Finance
Feasibility studies
Fines & penalties
Humanities and Social Sciences
Markov analysis
Optimization
Physics
Problem solving
Quantum Physics
Qubits (quantum computing)
Real time
Stochastic models
Variables
3-SAT
Maximum Independent Set
Reverse Quantum Annealing
Quantum optimization
Reverse Quantum Annealing Quantum optimization Maximum Independent Set 3-SAT
ISSN:1381-1231, 1572-9397
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Abstract Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of active debate. Although current analog quantum machines do not guarantee optimality, operating instead as heuristic solvers, the technology is evolving rapidly. Beyond performance alone, this emerging technologies offers fundamentally new approaches to problem-solving that are not readily accessible to classical exact methods particularly in dynamic environments or online optimization settings. This paper focuses on one such approaches: Reverse Quantum Annealing (RQA). Unlike classical exact methods, RQA allows the optimization process to begin from an initial infeasible solution by embedding it directly into the qubits’ initial state. We leverage this capability by formulating problem constraints as penalty terms within Quadratic Unconstrained Binary Optimization (QUBO) models, thereby preserving infeasible solutions within the quantum search space. We propose iterative strategies that apply RQA in three distinct modes to rapidly repair infeasible solutions. These methods are evaluated on two well-known NP-hard problems: the Maximum Independent Set (MIS) and the 3-SAT problem. Our results demonstrate the effectiveness of RQA in steering infeasible configurations toward feasibility, offering promising potential for real-time applications where problem data may change suddenly and solutions must be repaired swiftly.
AbstractList Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of active debate. Although current analog quantum machines do not guarantee optimality, operating instead as heuristic solvers, the technology is evolving rapidly. Beyond performance alone, this emerging technologies offers fundamentally new approaches to problem-solving that are not readily accessible to classical exact methods particularly in dynamic environments or online optimization settings. This paper focuses on one such approaches: Reverse Quantum Annealing (RQA). Unlike classical exact methods, RQA allows the optimization process to begin from an initial infeasible solution by embedding it directly into the qubits’ initial state. We leverage this capability by formulating problem constraints as penalty terms within Quadratic Unconstrained Binary Optimization (QUBO) models, thereby preserving infeasible solutions within the quantum search space. We propose iterative strategies that apply RQA in three distinct modes to rapidly repair infeasible solutions. These methods are evaluated on two well-known NP-hard problems: the Maximum Independent Set (MIS) and the 3-SAT problem. Our results demonstrate the effectiveness of RQA in steering infeasible configurations toward feasibility, offering promising potential for real-time applications where problem data may change suddenly and solutions must be repaired swiftly.
Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of active debate. Although current analog quantum machines do not guarantee optimality, operating instead as heuristic solvers, the technology is evolving rapidly. Beyond performance alone, this emerging technologies offers fundamentally new approaches to problem-solving that are not readily accessible to classical exact methods particularly in dynamic environments or online optimization settings. This paper focuses on one such approaches: Reverse Quantum Annealing (RQA). Unlike classical exact methods, RQA allows the optimization process to begin from an initial infeasible solution by embedding it directly into the qubits' initial state. We leverage this capability by formulating problem constraints as penalty terms within Quadratic Unconstrained Binary Optimization (QUBO) models, thereby preserving infeasible solutions within the quantum search space. We propose iterative strategies that apply RQA in three distinct modes to rapidly repair infeasible solutions. These methods are evaluated on two well-known NP-hard problems: the Maximum Independent Set (MIS) and the 3-SAT problem. Our results demonstrate the effectiveness of RQA in steering infeasible configurations toward feasibility, offering B Samuel Deleplanque
ArticleNumber 30
Author Deleplanque, Samuel
Pérez Armas, Luis Fernando
Creemers, Stefan
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  surname: Pérez Armas
  fullname: Pérez Armas, Luis Fernando
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  surname: Creemers
  fullname: Creemers, Stefan
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Issue 3
Keywords 3-SAT
Maximum Independent Set
Reverse Quantum Annealing
Quantum optimization
Reverse Quantum Annealing Quantum optimization Maximum Independent Set 3-SAT
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  publication-title: Quantum
  doi: 10.22331/q-2020-09-21-327
– volume: 107
  issue: 3
  year: 2023
  ident: 9564_CR40
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.107.032426
– volume: 2
  start-page: 1
  year: 2021
  ident: 9564_CR45
  publication-title: SN Comput. Sci.
  doi: 10.1007/s42979-021-00483-1
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Snippet Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of active debate. Although current...
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SubjectTerms Algorithms
Combinatorial analysis
Computer Science
Data Structures and Algorithms
Economics and Finance
Feasibility studies
Fines & penalties
Humanities and Social Sciences
Markov analysis
Optimization
Physics
Problem solving
Quantum Physics
Qubits (quantum computing)
Real time
Stochastic models
Variables
Title solQHealer: Quantum Procedures for Rendering Infeasible Solutions Feasible: A Proof of Concept with the Maximum Independent Set Problem and 3-SAT
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https://hal.univ-lille.fr/hal-05204085
Volume 31
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