Quantum Generator Kernels

Abstract: Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, necessitates effective strategies to compress and embed large-scale real-world data like images into the constrained capacities of existing quantum devices or simulators. To this end, we propose Quantum Generator Kernels (QGKs), a generator-based approach to quantum kernels, comprising a set of Variational Generator Groups (VGGs) that merge universal generators into a parameterizable operator, ensuring scalable coverage of the available quantum space. Thereby, we address shortcomings of current leading strategies employing hybrid architectures, which might prevent exploiting quantum computing's full potential due to fixed intermediate embedding processes. To optimize the kernel alignment to the target domain, we train a weight vector to parameterize the projection of the VGGs in the current data context. Our empirical results demonstrate superior projection and classification capabilities of the QGK compared to state-of-the-art quantum and classical kernel approaches and show its potential to serve as a versatile framework for various QML applications.