13.4 Quantum kernels for SVMs

In section 1.4, we saw the concept of a support vector machine, or SVM, for binary classification. We mentioned kernel functions and the kernel trick to move points to a higher dimension where we can separate them with a hyperplane. An SVM is an example of a kernel machine. Let’s clarify their definitions and see where quantum may help. algorithm$support vector machine algorithm$SVM algorithm$classification kernel$trick kernel$function quantum$kernel kernel support vector machine kernel$machine

13.4.1 Hyperplanes and feature maps

A hyperplane is an n – 1 dimension linear object within an n-dimensional vector space. We assume the vector space is over R in this section. For example, a line is a hyperplane in R², and a plane is a hyperplane in R³. Though harder to visualize, the 3-dimensional object defined with coordinates (x₁, x₂, x₃, x₄) in R⁴ by the equation hyperplane

is a hyperplane...