Quantum Feature Map

Let $\mathcal{X}$ be a set of input data, we have a quantum feature map such that

$$\mathcal{X} \rightarrow \phi \rightarrow \mathcal{F}$$

In general, $\mathcal{F}$ is just a vector space.

• A quantum feature map $\phi: \mathcal{X} \rightarrow \mathcal{F}$ where $\mathcal{F}$ is a Hilbert space and the feature vectos are quantum states.
• The map transforms $x \rightarrow |\phi(x)\rangle$ by way of a unitary transformation $U_{\phi}(x)$. Where $U_{\phi}(x)$ is a variational circuit whose parameters depend on the input data.

Reference

1. PENNYLANE - Quantum Feature Map: https://pennylane.ai/qml/glossary/quantum_feature_map