On the Complexity of Quantum Languages

The standard inputs given to a quantum machine are classical binary strings. In this view, any quantum complexity class is a collection of subsets of $\{0,1\}^{*}$. However, a quantum machine can also accept quantum states as its input. T. Yamakami has introduced a general framework for quantum operators and inputs \cite{Yam02}. In this paper we present several quantum languages within this model and by generalizing the complexity classes QMA and QCMA we analyze the complexity of the introduced languages. We also discuss how to derive a classical language from a given quantum language and as a result we introduce new QCMA and QMA languages.