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...

Full description

Saved in:
Bibliographic Details
Main Authors: Chia-Tso Lai, Carsten Blank, Peter Schmelcher, Rick Mukherjee
Format: Article
Language:English
Published: IOP Publishing 2025-01-01
Series:Machine Learning: Science and Technology
Subjects:
Online Access:https://doi.org/10.1088/2632-2153/addb97
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849696587496816640
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