Level 2, Tinkerer

X gate

On the state certain to read 0, X moves the whole amplitude from 0 to 1. On the |+⟩ state the two amplitudes are already equal, sign included, so the swap leaves both bars where they stand.

The X gate swaps the amplitude for 0 with the amplitude for 1. On a state certain to read 0 or 1 that swap is an ordinary bit flip, the quantum version of a NOT.

On the |+⟩ state, X leaves the state as it stands. On the |−⟩ state, X multiplies the whole state by a minus, and no measurement can see a minus that sits on every amplitude at once, so the button looks idle precisely when a newcomer expects drama.

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