I recently learned of a technique known as "block-encoding" which embeds any $M \times N$ matrix into a unitary matrix, given that the spectral norm is at most $1$. This type of result is pretty astounding--- but with this being able to work, I have had a thought.
Is there a method to embed a nonlinear operator into a quantum circuit? This does not necessarily have to be constrained by the math around quantum circuits, but it can be a physical process perhaps?
I don't see how this is non-reversible, as this type of nonlinear operator can be embedded into a reversible operator, similar to the block encoding technique.