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.

用核方法重新描述监督式的量子模型，用支持向量机进行训练可以得到比变分电路训练更好或同等的结果。