# Why do Transformations on Qubits for Quantum Computation have to be Unitary?

In the quantum circuit model we prepare some inital state $|\psi\rangle$ and throw our algorithm in form of some unitary transformation(s) $U$ on it to get our result $|\Psi\rangle$:

$|\Psi\rangle$=$U$ $|\psi\rangle$.

Why does $U$ need to be unitary in this quantum computation model? I think traditional (classical) computer stuff is not time-reversible so why do we want/demand it here?

The time-reversal thing is all I have in mind when I think about unitarity or why it could be nice but it does not seem necessary. In the end we just want the output/result $|\Psi\rangle$ so I don't see any reason why we should restrict our transformations in that way.