Adaptive Learning for Quantum Linear Regression

• URL: http://arxiv.org/abs/2408.02833v1
• Date: Mon, 5 Aug 2024 21:09:01 GMT
• Title: Adaptive Learning for Quantum Linear Regression
• Authors: Costantino Carugno, Maurizio Ferrari Dacrema, Paolo Cremonesi,
• Abstract summary: In a recent work, linear regression was formulated as a quadratic binary optimization problem. This approach promises a computational time advantage for large datasets. However, the quality of the solution is limited by the necessary use of a precision vector. In this work, we focus on the practical challenge of improving the precision vector encoding.
• Score: 10.445957451908695
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The recent availability of quantum annealers as cloud-based services has enabled new ways to handle machine learning problems, and several relevant algorithms have been adapted to run on these devices. In a recent work, linear regression was formulated as a quadratic binary optimization problem that can be solved via quantum annealing. Although this approach promises a computational time advantage for large datasets, the quality of the solution is limited by the necessary use of a precision vector, used to approximate the real-numbered regression coefficients in the quantum formulation. In this work, we focus on the practical challenge of improving the precision vector encoding: instead of setting an array of generic values equal for all coefficients, we allow each one to be expressed by its specific precision, which is tuned with a simple adaptive algorithm. This approach is evaluated on synthetic datasets of increasing size, and linear regression is solved using the D-Wave Advantage quantum annealer, as well as classical solvers. To the best of our knowledge, this is the largest dataset ever evaluated for linear regression on a quantum annealer. The results show that our formulation is able to deliver improved solution quality in all instances, and could better exploit the potential of current quantum devices.

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