Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networks
Quadratic unconstrained binary optimization (QUBO) is at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others (Bangert 2012 Optimization for Industrial Problems (Springer Science & Busin...
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IOP Publishing
2025-01-01
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| Series: | Machine Learning: Science and Technology |
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| Online Access: | https://doi.org/10.1088/2632-2153/addb97 |
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| author | Chia-Tso Lai Carsten Blank Peter Schmelcher Rick Mukherjee |
| author_facet | Chia-Tso Lai Carsten Blank Peter Schmelcher Rick Mukherjee |
| author_sort | Chia-Tso Lai |
| collection | DOAJ |
| description | Quadratic unconstrained binary optimization (QUBO) is at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others (Bangert 2012 Optimization for Industrial Problems (Springer Science & Business Media)). These problems typically involve optimizing a large number of binary variables, which makes finding exact solutions exponentially more difficult. Consequently, most QUBO problems are classified as NP-hard (Garey and Johnson 1979 Computers and Intractability vol 174 (Freeman); Lucas 2014 Front. Phys. 2 5). To address this challenge, we developed a powerful feedforward neural network (FNN) optimizer for arbitrary QUBO problems. In this work, we demonstrate that the FNN optimizer can provide high-quality approximate solutions for large problems, including dense 80-variable weighted MaxCut and random QUBOs, achieving an average accuracy of over 99% in less than 1.1 s on an 8-core CPU. Additionally, the FNN optimizer outperformed the Gurobi optimizer (Gurobi Optimization, LLC 2023 Gurobi Optimizer Reference Manual) by 72% on 200-variable random QUBO problems within a 100 s computation time limit, exhibiting strong potential for real-time optimization tasks. Building on this model, we explored the novel approach of integrating FNNs with a quantum annealer-based activation function to create a quantum–classical encoder–decoder optimizer, aiming to further enhance the performance of FNNs in QUBO optimization. |
| format | Article |
| id | doaj-art-6cdd85b0c56d4ea7b3fb084d055724fd |
| institution | DOAJ |
| issn | 2632-2153 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-6cdd85b0c56d4ea7b3fb084d055724fd2025-08-20T03:19:24ZengIOP PublishingMachine Learning: Science and Technology2632-21532025-01-016202504910.1088/2632-2153/addb97Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networksChia-Tso Lai0https://orcid.org/0009-0003-3373-1336Carsten Blank1https://orcid.org/0000-0003-3450-0823Peter Schmelcher2https://orcid.org/0000-0002-2637-0937Rick Mukherjee3https://orcid.org/0000-0001-9267-4421Fakultät für Physik und Erdsystemwissenschaften, Universität Leipzig , Linnéstraße 5, 04103 Leipzig, Germany; Zentrum für Optische Quantentechnologien, Universität Hamburg , Luruper Chaussee 149, 22761 Hamburg, GermanyData Cybernetics , 86899 Landsberg, GermanyZentrum für Optische Quantentechnologien, Universität Hamburg , Luruper Chaussee 149, 22761 Hamburg, GermanyZentrum für Optische Quantentechnologien, Universität Hamburg , Luruper Chaussee 149, 22761 Hamburg, GermanyQuadratic unconstrained binary optimization (QUBO) is at the heart of many industries and academic fields such as logistics, supply chain, finance, pharmaceutical science, chemistry, IT, and energy sectors, among others (Bangert 2012 Optimization for Industrial Problems (Springer Science & Business Media)). These problems typically involve optimizing a large number of binary variables, which makes finding exact solutions exponentially more difficult. Consequently, most QUBO problems are classified as NP-hard (Garey and Johnson 1979 Computers and Intractability vol 174 (Freeman); Lucas 2014 Front. Phys. 2 5). To address this challenge, we developed a powerful feedforward neural network (FNN) optimizer for arbitrary QUBO problems. In this work, we demonstrate that the FNN optimizer can provide high-quality approximate solutions for large problems, including dense 80-variable weighted MaxCut and random QUBOs, achieving an average accuracy of over 99% in less than 1.1 s on an 8-core CPU. Additionally, the FNN optimizer outperformed the Gurobi optimizer (Gurobi Optimization, LLC 2023 Gurobi Optimizer Reference Manual) by 72% on 200-variable random QUBO problems within a 100 s computation time limit, exhibiting strong potential for real-time optimization tasks. Building on this model, we explored the novel approach of integrating FNNs with a quantum annealer-based activation function to create a quantum–classical encoder–decoder optimizer, aiming to further enhance the performance of FNNs in QUBO optimization.https://doi.org/10.1088/2632-2153/addb97QUBOquantum annealerRydberg physicsneural networksoptimizationquantum-inspired algorithm |
| spellingShingle | Chia-Tso Lai Carsten Blank Peter Schmelcher Rick Mukherjee Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networks Machine Learning: Science and Technology QUBO quantum annealer Rydberg physics neural networks optimization quantum-inspired algorithm |
| title | Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networks |
| title_full | Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networks |
| title_fullStr | Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networks |
| title_full_unstemmed | Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networks |
| title_short | Towards arbitrary QUBO optimization: analysis of classical and quantum-activated feedforward neural networks |
| title_sort | towards arbitrary qubo optimization analysis of classical and quantum activated feedforward neural networks |
| topic | QUBO quantum annealer Rydberg physics neural networks optimization quantum-inspired algorithm |
| url | https://doi.org/10.1088/2632-2153/addb97 |
| work_keys_str_mv | AT chiatsolai towardsarbitraryqubooptimizationanalysisofclassicalandquantumactivatedfeedforwardneuralnetworks AT carstenblank towardsarbitraryqubooptimizationanalysisofclassicalandquantumactivatedfeedforwardneuralnetworks AT peterschmelcher towardsarbitraryqubooptimizationanalysisofclassicalandquantumactivatedfeedforwardneuralnetworks AT rickmukherjee towardsarbitraryqubooptimizationanalysisofclassicalandquantumactivatedfeedforwardneuralnetworks |