Unified sparse optimization via quantum architectures and hybrid techniques

Abstract In an era of rapid technological advancements and unprecedented data inundation, sparsity has emerged as a key property with profound implications in various fields. One important application of sparsity is sparse signal recovery, which involves reconstructing signals from limited observations and is of great importance in medical imaging, communication systems, and data compression. However, traditional sparse signal recovery methods often require computationally intensive algorithms, especially for large-scale problems. In this paper, we investigate the application of the coherent Ising machine (CIM), a hybrid quantum computing paradigm, as a novel approach to efficiently solve several sparsity-related optimization problems, presenting significant contributions in terms of model development and experimental validation. Our proposed models surpass existing approaches by reducing the computational resource requirements and enhancing problem-solving capabilities. Additionally, we also provide theoretical analysis on the performance guarantees of the proposed models, offering insights into their reliability and robustness. To further enhance the scalability and efficiency of the proposed model, we incorporate Benders Decomposition to decompose large-scale problems into smaller subproblems that can be solved more effectively. In addition, the efficiency and accuracy of the CIM-based sparse optimization approach are demonstrated through the experiments on the CIM platform, which highlights its potential to solve complex combinatorial optimization problems in practical scenarios.