Systematic and Efficient Construction of Quadratic Unconstrained Binary Optimization Forms for High-order and Dense Interactions
This addresses a bottleneck in applying Quantum Annealing to complex machine learning problems with strong nonlinearities, though it appears incremental as it builds on existing quadratization methods.
The paper tackles the problem of transforming higher-order optimization problems with dense interactions into Quadratic Unconstrained Binary Optimization (QUBO) forms for use in Quantum Annealing, by modeling functions with rectified linear unit bases that have equivalent quadratic representations, and demonstrates proof of concept numerically and analytically.
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.