Quantum Computing.
the non invertible function ƒ(x) and define the unitary transformation U_ƒ |x⟩|y⟩ = |x⟩|y ⊕ ƒ(x)⟩ Then U_ƒ |x⟩|0⟩ = |x⟩|ƒ(x)⟩. In any case typically ƒ(x) is going to have a classical circuit implementation. In this case one would simply use controlled gates such as Toffoli’s gate to translate the