Quantum Complexities and Interactive Proof Systems

In complexity studies, Interactive Proof Systems are a very helpful means to establish relationships between major complexity classes. The rise of new complexity classes, which follow the properties of quantum computation, suggests a new set of variants of these systems. This paper focuses on the currently established theories in quantum complexity studies, and studies how quantum complexity classes relate to some variants of Interactive Proof Systems. Outline. In this paper, we will first overview the history and fundamentals of quantum complexity studies and interactive proof systems. Then, we will go on a journey from classical complexity classes to quantum ones, to introducing interactive proof systems and their relationships with quantum complexity classes. Lastly, we will study the relationships between the complexity classes studied so far.