Hadamard gate
The gate that takes a qubit from a definite value into even superposition — the opening move of nearly every quantum algorithm.
Applied to a qubit that is zero, it produces a state that measures zero or one with fifty per cent probability each. Applied twice, you are back where you started, which is precisely the point: it is its own inverse, and the superposition is not randomness but something you can compute backwards from.
Put a Hadamard on each of n qubits and the register lands in superposition over all 2ⁿ possible bit strings at once. That sounds like magic and is not — you cannot read them out. The craft in quantum algorithms lies in making the unwanted alternatives cancel each other through interference before you measure.