Feedback-based quantum strategies for constrained combinatorial optimization problems
Feedback-based quantum algorithms have recently emerged as potential methods for approximating the ground states of Hamiltonians. One such algorithm, the feedback-based algorithm for quantum optimization (FALQON), is specifically designed to solve quadratic unconstrained binary optimization problems...
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| Published in: | Future generation computer systems Vol. 174; p. 107979 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.01.2026
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| ISSN: | 0167-739X |
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| Abstract | Feedback-based quantum algorithms have recently emerged as potential methods for approximating the ground states of Hamiltonians. One such algorithm, the feedback-based algorithm for quantum optimization (FALQON), is specifically designed to solve quadratic unconstrained binary optimization problems. Its extension, the feedback-based algorithm for quantum optimization with constraints (FALQON-C), was introduced to handle constrained optimization problems with equality and inequality constraints. In this work, we extend the feedback-based quantum algorithms framework to address a broader class of constraints known as invalid configuration (IC) constraints, which explicitly prohibit specific configurations of decision variables. We first present a transformation technique that converts the constrained optimization problem with invalid configuration constraints into an equivalent unconstrained problem by incorporating a penalizing term into the cost function. Then, leaning upon control theory, we propose an alternative method tailored for feedback-based quantum algorithms that directly tackles IC constraints without requiring slack variables. Our approach introduces a new operator that encodes the optimal feasible solution of the constrained optimization problem as its ground state. Then, a controlled quantum system based on the Lyapunov control technique is designed to ensure convergence to the ground state of this operator. Two approaches are introduced in the design of this operator to address IC constraints: the folded spectrum approach and the deflation approach. These methods eliminate the need for slack variables, significantly reducing the quantum circuit depth and the number of qubits required. We show the effectiveness of our proposed algorithms through numerical simulations.
•Feedback-based quantum algorithms are extended to handle invalid configuration constraints.•We introduce a conversion from constrained to unconstrained optimization problems.•As an alternative strategy, Lyapunov-based update laws are proposed for circuit parameters.•Folded spectrum and deflation techniques are used to design the new update laws.•Our approach reduces quantum resources by lowering circuit depth and qubit count. |
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| AbstractList | Feedback-based quantum algorithms have recently emerged as potential methods for approximating the ground states of Hamiltonians. One such algorithm, the feedback-based algorithm for quantum optimization (FALQON), is specifically designed to solve quadratic unconstrained binary optimization problems. Its extension, the feedback-based algorithm for quantum optimization with constraints (FALQON-C), was introduced to handle constrained optimization problems with equality and inequality constraints. In this work, we extend the feedback-based quantum algorithms framework to address a broader class of constraints known as invalid configuration (IC) constraints, which explicitly prohibit specific configurations of decision variables. We first present a transformation technique that converts the constrained optimization problem with invalid configuration constraints into an equivalent unconstrained problem by incorporating a penalizing term into the cost function. Then, leaning upon control theory, we propose an alternative method tailored for feedback-based quantum algorithms that directly tackles IC constraints without requiring slack variables. Our approach introduces a new operator that encodes the optimal feasible solution of the constrained optimization problem as its ground state. Then, a controlled quantum system based on the Lyapunov control technique is designed to ensure convergence to the ground state of this operator. Two approaches are introduced in the design of this operator to address IC constraints: the folded spectrum approach and the deflation approach. These methods eliminate the need for slack variables, significantly reducing the quantum circuit depth and the number of qubits required. We show the effectiveness of our proposed algorithms through numerical simulations.
•Feedback-based quantum algorithms are extended to handle invalid configuration constraints.•We introduce a conversion from constrained to unconstrained optimization problems.•As an alternative strategy, Lyapunov-based update laws are proposed for circuit parameters.•Folded spectrum and deflation techniques are used to design the new update laws.•Our approach reduces quantum resources by lowering circuit depth and qubit count. |
| ArticleNumber | 107979 |
| Author | Abdul Rahman, Salahuddin Karabacak, Özkan Wisniewski, Rafal |
| Author_xml | – sequence: 1 givenname: Salahuddin orcidid: 0009-0002-9686-8586 surname: Abdul Rahman fullname: Abdul Rahman, Salahuddin email: saabra@es.aau.dk organization: Aalborg University, Aalborg, Denmark – sequence: 2 givenname: Özkan surname: Karabacak fullname: Karabacak, Özkan organization: Kadir Has University, Istanbul, Turkey – sequence: 3 givenname: Rafal surname: Wisniewski fullname: Wisniewski, Rafal organization: Aalborg University, Aalborg, Denmark |
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| Keywords | Feedback-based quantum algorithms Folded spectrum method Quadratic constrained binary optimization problems Variational quantum algorithms Noisy-intermediate scale quantum algorithms Hotelling’s deflation method |
| Language | English |
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| SubjectTerms | Feedback-based quantum algorithms Folded spectrum method Hotelling’s deflation method Noisy-intermediate scale quantum algorithms Quadratic constrained binary optimization problems Variational quantum algorithms |
| Title | Feedback-based quantum strategies for constrained combinatorial optimization problems |
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