The minimum mathematics and physical language needed before qubits.

State vectors, superposition, Bloch sphere intuition, and tensor products.

Quantum gates, CNOT, circuit notation, and reversible computation.

Born rule, bases, entanglement, no-cloning, and what quantum information means.

Deutsch-Jozsa, Grover, phase estimation, and the structure behind Shor.

Real devices, decoherence, error models, and why quantum computers are hard.

Small simulations, notebooks, and explainers that make the ideas concrete.