On the expressivity of embedding quantum kernels.

Seminar author:Elies Gil-Fuster

Event date and time:04/02/2024 04:00:pm

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One of the most natural connections between quantum and classical machine learning is kernel methods. Kernel methods rely on kernels, which are inner products of feature vectors living in large feature spaces. Quantum kernels are typically evaluated by explicitly constructing quantum feature states and then taking their inner product, here called embedding quantum kernels. Since classical kernels are usually evaluated without using the feature vectors explicitly, we wonder how expressive embedding quantum kernels are. In this talk, I will elucidate on the fundamental question: can all quantum kernels be expressed as the inner product of quantum feature states? In order to present this question in all its glory I will introduce kernels methods and quantum kernels from scratch, so this seminar should be appealing and understandable to everyone: QML people and not.

arXiv: https://arxiv.org/abs/2309.14419