Before qubits, the useful foundations are:

• complex numbers
• vectors and inner products
• matrices as transformations
• probability and normalization
• classical bits and reversible logic
• the idea that physical systems can carry information

The goal is to make the notation feel like a language for describing possible states and allowed transformations.

Lessons To Add

• Why Quantum Computing?
• Quiz: Why Quantum Computing?
• Complex amplitudes
• Vectors and state spaces
• Matrices as operations
• Probability from amplitudes
• Classical information and reversible gates