Supervised quantum machine learning models are kernel methods

TL;DR

This paper demonstrates that supervised quantum machine learning models can be understood as kernel methods, highlighting the importance of data encoding in quantum advantage and providing a framework for improved model training.

Contribution

It systematically rephrases supervised quantum models as kernel methods, enabling the use of support vector machines and kernel-based training for quantum data analysis.

Findings

Quantum models analyzed as kernel methods can outperform variational training.

Kernel perspective links data encoding to quantum advantage.

Support vector machines can replace many near-term quantum models.

Abstract

With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum circuit. While such "quantum models" are sometimes called "quantum neural networks", it has been repeatedly noted that their mathematical structure is actually much more closely related to kernel methods: they analyse data in high-dimensional Hilbert spaces to which we only have access through inner products revealed by measurements. This technical manuscript summarises and extends the idea of systematically rephrasing supervised quantum models as a kernel method. With this, a lot of near-term and fault-tolerant quantum models can be replaced by a general support vector machine whose kernel computes distances between data-encoding quantum states. Kernel-based training is then guaranteed to find better or equally good quantum models than variational circuit training. Overall, the kernel perspective of quantum machine learning tells us that the way that data is encoded into quantum states is the main ingredient that can potentially set quantum models apart from classical machine learning models.