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You have the right idea, but not the right operation. XOR is reversible.

To give a better example: COPY is not reversible. Imagine that you have two qubits [A, B] as an input and you want to output [A, A]. That is not possible with quantum computers.

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XOR has 2 inputs and 1 output so cannot be reversible. CNOT is the closest reversible gate

To elaborate: CNOT outputs the pair (A xor B, B). By also outputting B, it becomes reversible.

Isn't everything reversible if enough information is stored? Instead of COPY [A, B] -> [A, A]; you could have [A, B, 0] -> [A, A, B] which saves the value of B.

IIRC this is how you implement stuff, you always keep the inputs, so everything stays reversible.

Yes, but "keeping the inputs" is non-trivial in quantum-land because of the no-cloning theorem. You can't just make a copy of your inputs and stash them. You have to be more clever than that.

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