Quantum Kernel Methods

Quantum kernel methods embed data into a quantum Hilbert space and classify with the resulting kernel -- a quantum feature map plugged into a classical support-vector machine.

A quantum feature map

Kernel methods classify by comparing data through a similarity measure -- the kernel. Quantum kernel methods encode each input x into a quantum state |phi(x)> with a parameterized circuit, then define the kernel as the state overlap k(x, x') = ||^2. That overlap is estimated on quantum hardware, for instance with a swap test, and the resulting Gram matrix is handed to a classical SVM.

The hope and the reality

The feature map can reach a space that is hard to compute classically, which is the source of the optimism. But there is no general advantage: many quantum kernels are either classically simulable or so expressive that similarities concentrate, hurting generalization. Whether a quantum kernel helps is an empirical, dataset-by-dataset question.

A Kronos data point

KQERN builds a real quantum-kernel classifier on genuine MAST disruption features and reaches an AUC of 0.919 versus 0.929 for a classical RBF kernel -- a tie, and an honest null result. The pipeline is real and runs on a simulator now (and on hardware with one environment variable), but it is not a speedup. A quantum-kernel advantage for fusion is a post-~2036 prospect.