To build sophisticated Quantum Machine Learning (QML) models, a solid grasp of the underlying principles is necessary. This chapter reinforces the essential concepts from quantum computation and classical machine learning that form the bedrock for advanced QML algorithms.

We will review advanced linear algebra specific to quantum states, focusing on tensor products ($V \otimes W$) and Hilbert spaces for multi-qubit descriptions. We will revisit quantum circuit construction and the significance of universal gate sets in the QML context. Key quantum phenomena like entanglement and their role as resources will be analyzed, alongside the formalism of density matrices ($\rho = \sum_i p_i |\psi_i\rangle\langle\psi_i|$) for handling mixed states and noise. We'll also refresh classical optimization methods frequently used in training machine learning models and touch upon computational complexity considerations relevant to comparing classical and quantum approaches. Introduction to concepts from information geometry will provide a geometric perspective on both classical and quantum models.