Systematic and Efficient Construction of Quadratic Unconstrained Binary Optimization Forms for High-order and Dense Interactions

• URL: http://arxiv.org/abs/2506.08448v1
• Date: Tue, 10 Jun 2025 04:50:09 GMT
• Title: Systematic and Efficient Construction of Quadratic Unconstrained Binary Optimization Forms for High-order and Dense Interactions
• Authors: Hyakka Nakada, Shu Tanaka,
• Abstract summary: Quantum Annealing (QA) can efficiently solve optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations.<n>We propose quadratization methods for complex problems involving Machine Learning (ML)<n>In this study, we model target functions by the sum of rectified linear unit bases, which have the ability of universal approximation.<n>We design a new black-box optimization scheme, in which ML surrogate regressors are inputted to QA after the quadratization process.
• Score: 1.342834401139078
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum Annealing (QA) can efficiently solve combinatorial optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations. For broader applicability of QA, quadratization methods are used to transform higher-order problems into QUBOs. However, quadratization methods for complex problems involving Machine Learning (ML) remain largely unknown. In these problems, strong nonlinearity and dense interactions prevent conventional methods from being applied. Therefore, we model target functions by the sum of rectified linear unit bases, which not only have the ability of universal approximation, but also have an equivalent quadratic-polynomial representation. In this study, the proof of concept is verified both numerically and analytically. In addition, by combining QA with the proposed quadratization, we design a new black-box optimization scheme, in which ML surrogate regressors are inputted to QA after the quadratization process.

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