SVM: Classical and Quantum Kernel Classifiers

A four-part series: from margin geometry to a side-by-side comparison of classical and quantum kernels.
Author

Samer El Kababji

This SVM series builds from first principles to a head-to-head comparison of classical and quantum kernel classifiers. Each notebook follows the same pattern: mathematics first, then code.

1. Support Vector Machines

Derive the maximum-margin hyperplane, read the primal and dual forms of the SVM, and control the soft-margin trade-off with \(C\).

Prerequisites: vectors, inner products, and basic Python.

2. Kernels in Support Vector Machines

Understand feature maps, the kernel trick, and the kernel SVM decision function through polynomial and RBF examples.

Prerequisites: 1. Support Vector Machines.

3. SVM: Classical and Quantum Kernel Classifiers

Compare a classical RBF kernel and a quantum feature-map kernel side by side on the same dataset using the same support-vector learning rule.

Prerequisites: 2. Kernels in SVMs.

Refreshers

1.1 SVM Margin Geometry in Two Features

Draw the decision and margin lines and prove that the full geometric margin is \(2/\lVert\mathbf{w}\rVert\).

Companion to: 1. Support Vector Machines, Section 2.