Learning kernels with quantum optical circuits

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.