Quantum Computing.
is only one x such that ƒ(x) = y. That means that the number of bits n of x and ƒ(x) are the same and ƒ(x) is simply a permutation of the numbers that can be represented with n bits. In this case there is a unitary transformation U_ƒ such that U_ƒ|x⟩ = |ƒ(x)⟩ and that is U_ƒ = |ƒ(0)⟩⟨0| + |ƒ(1)⟩⟨1|