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Physics Letters A

Quantum inspired kernel matrices: Exploring symmetry in machine learning

Sebastian Raubitzek, Sebastian Schrittwieser, Alexander Schatten, Kevin Mallinger

Published Sep 12, 2024• 8 citations
Publisher
DOI
10.1016/j.physleta.2024.129895

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This paper explores a novel approach to kernel design for machine learning, drawing inspiration from the principles of quantum entanglement. Traditional kernel functions in Support Vector Machines (SVMs) frequently necessitate extensive manual tuning and often fail to achieve optimal performance. We introduce a kernel design algorithm that mimics the correlated behavior observed in entangled quantum systems. The algorithm constructs kernel functions based on the correlated features of data points, effectively simulating entanglement effects to potentially enhance classification accuracy. This work presents a fundamental shift in kernel design, moving away from hand-crafted kernels towards a more adaptive and potentially more powerful approach guided by quantum-inspired concepts. The core contribution lies in the methodology for generating kernels that dynamically capture complex relationships within data, leading to improved classification outcomes. We demonstrate the potential of this approach through a theoretical framework and outline a design strategy that can be readily applied to various machine learning tasks.
Support Vector Machines (SVMs) are a cornerstone of supervised learning, widely used for data classification. A central component of their success lies in kernel functions, which enable efficient computation of inner products in high-dimensional feature spaces. Recent years have seen growing interest in leveraging quantum circuits -- both qubit-based and quantum optical -- for computing kernel matrices, with ongoing research exploring potential quantum advantages. In this work, we investigate two classical techniques for enhancing SVM performance through kernel learning -- the Fisher criterion and quasi-conformal transformations -- and translate them into the framework of quantum optical circuits. Conversely, using the example of the displaced squeezed vacuum state, we demonstrate how established concepts from quantum optics can inspire novel perspectives and enhancements in SVM methodology. This cross-disciplinary approach highlights the potential of quantum optics to both inform and benefit from advances in machine learning.