Explain why a qubit is a complex amplitude state, not a hidden classical bit.
The move: distinguish amplitudes from ordinary probabilities before you discuss speedup. In a one-qubit state, |0> and |1> are not two hidden bins waiting to be opened. They are basis states with amplitudes attached. When you measure, the squared size of each amplitude becomes the chance of seeing that basis outcome. Before measurement, gates rotate and phase-shift those amplitudes. The mechanism is interference. A later gate can cause paths leading to a bad outcome to cancel and paths leading to a useful outcome to reinforce. That is why quantum algorithm design is closer to choreography than brute force. For a…
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