In computational complexity theory, the class QIP (which stands for Quantum Interactive Proof) is the quantum computing analogue of the classical complexity class IP, which is the set of problems solvable by an interactive proof system with a polynomial-time verifier and one computationally unbounded prover.
Informally, IP is the set of languages for which a computationally unbounded prover can convince a polynomial-time verifier to accept when the input is in the language (with high probability) and cannot convince the verifier to accept when the input is not in the language (again, with high probability).
By restricting the number of messages used in the protocol to at most k, we get the complexity class QIP(k).
Kitaev and Watrous also showed that QIP is contained in EXP, the class of problems solvable by a deterministic Turing machine in exponential time.
[2] QIP(2) was then shown to be contained in PSPACE, the set of problems solvable by a deterministic Turing machine in polynomial space.