Interactive Proofs for Quantum Computation

Abstract

It is by now well established that quantum machines can solve certain computational problems much faster than the best algorithms known in the standard Turing machine model. The complexity question of which problems can be feasibly computed by quantum machines has also been extensively investigated in recent years, both in the context of one machine models (quantum polynomial classes) and various flavors of multi-machine models (single and multiple prover quantum interactive proofs). In this talk we examine the more general (but less theoretically investigated) question of which quantum states can be feasibly computed. Specifically, we will focus on the question of what quantum states can be generated by quantum interactive proofs. We will show that several classical interactive proof theorems have analogs in such models. For example, we show that any quantum state computable in quantum polynomial space has a 2-prover quantum interactive proof. Open questions will be discussed.