Is there a quantum computing model that allows you to add different states?

[IttyBittyBit]

I want to know if a quantum computing model exists where you can prepare two different states on n qubits and interfere (i.e. add) them together. For example, for two qubits, consider the states (|00> + |01>)/√2 and -(|00> + |10>)/√2 (both pretty easy to prepare in most quantum computing models). Adding these two states would give (|01> - |10>)√2. Is there a model where any two states that can be prepared can also be added together?

 

[IttyBittyBit]

Just as a follow-up to my own question, I'm guessing no, since addition is a non-unitary operation... but then again it seems to me that in optical quantum computation it would be straightforward to have the qubits interfere with other qubits from the same laser source. An answer to this would be appreciated.