# Is there any known nontrivial result on QIP systems having a space-bounded verifier?

Is there any known nontrivial result on quantum interactive proof (QIP) systems having a space-bounded verifier?

The only paper I know is An application of quantum finite automata to interactive proof systems by Nishimura and Yamakami, in which a restricted 2QFA (two-way quantum finite automaton) model is used as a verifier and the following result is given: $\mathsf{QIP(2qfa,polytime)} \subseteq \mathsf{NP}$.

The motivation: I am preparing a paper containing some new results on space-bounded QIP systems and I want to be sure not missing any related known result!

• Do you know what happens when you restrict an IP system to have a space-bounded verifier? That might be a good place to start. Apr 2, 2012 at 17:59
• @Robin: Yes, I am aware many of the classical results. In fact, I am preparing a paper containing some new results on space-bounded QIP systems and I want to be sure not missing any related known result! Apr 2, 2012 at 19:21