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With near-term quantum devices available and the race for fault-tolerantquantum computers in full swing, researchers became interested in the questionof what happens if we replace a supervised machine learning model with aquantum circuit. While such "quantum models" are sometimes called "quantumneural networks", it has been repeatedly noted that their mathematicalstructure is actually much more closely related to kernel methods: they analysedata in high-dimensional Hilbert spaces to which we only have access throughinner products revealed by measurements. This technical manuscript summarisesand extends the idea of systematically rephrasing supervised quantum models asa kernel method. With this, a lot of near-term and fault-tolerant quantummodels can be replaced by a general support vector machine whose kernelcomputes distances between data-encoding quantum states. Kernel-based trainingis then guaranteed to find better or equally good quantum models thanvariational circuit training. Overall, the kernel perspective of quantummachine learning tells us that the way that data is encoded into quantum statesis the main ingredient that can potentially set quantum models apart fromclassical machine learning models.

Supervised quantum machine learning models are kernel methods