i-QLS: Quantum-supported Algorithm for Least Squares Optimization in Non-Linear Regression
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916997633146880 |
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| author | Venkatesh, Supreeth Mysore Macaluso, Antonio Arenas, Diego Klusch, Matthias Dengel, Andreas |
| author_facet | Venkatesh, Supreeth Mysore Macaluso, Antonio Arenas, Diego Klusch, Matthias Dengel, Andreas |
| contents | We propose an iterative quantum-assisted least squares (i-QLS) optimization method that leverages quantum annealing to overcome the scalability and precision limitations of prior quantum least squares approaches. Unlike traditional QUBO-based formulations, which suffer from a qubit overhead due to fixed discretization, our approach refines the solution space iteratively, enabling exponential convergence while maintaining a constant qubit requirement per iteration. This iterative refinement transforms the problem into an anytime algorithm, allowing for flexible computational trade-offs. Furthermore, we extend our framework beyond linear regression to non-linear function approximation via spline-based modeling, demonstrating its adaptability to complex regression tasks. We empirically validate i-QLS on the D-Wave quantum annealer, showing that our method efficiently scales to high-dimensional problems, achieving competitive accuracy with classical solvers while outperforming prior quantum approaches. Experiments confirm that i-QLS enables near-term quantum hardware to perform regression tasks with improved precision and scalability, paving the way for practical quantum-assisted machine learning applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | i-QLS: Quantum-supported Algorithm for Least Squares Optimization in Non-Linear Regression Venkatesh, Supreeth Mysore Macaluso, Antonio Arenas, Diego Klusch, Matthias Dengel, Andreas Quantum Physics Discrete Mathematics 05-08 F.4.1; F.2.2 We propose an iterative quantum-assisted least squares (i-QLS) optimization method that leverages quantum annealing to overcome the scalability and precision limitations of prior quantum least squares approaches. Unlike traditional QUBO-based formulations, which suffer from a qubit overhead due to fixed discretization, our approach refines the solution space iteratively, enabling exponential convergence while maintaining a constant qubit requirement per iteration. This iterative refinement transforms the problem into an anytime algorithm, allowing for flexible computational trade-offs. Furthermore, we extend our framework beyond linear regression to non-linear function approximation via spline-based modeling, demonstrating its adaptability to complex regression tasks. We empirically validate i-QLS on the D-Wave quantum annealer, showing that our method efficiently scales to high-dimensional problems, achieving competitive accuracy with classical solvers while outperforming prior quantum approaches. Experiments confirm that i-QLS enables near-term quantum hardware to perform regression tasks with improved precision and scalability, paving the way for practical quantum-assisted machine learning applications. |
| title | i-QLS: Quantum-supported Algorithm for Least Squares Optimization in Non-Linear Regression |
| topic | Quantum Physics Discrete Mathematics 05-08 F.4.1; F.2.2 |
| url | https://arxiv.org/abs/2505.02788 |