How to write two subscripts on top of each other in math mode?

Use \substack:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[ Q_{\substack{a\in A\\b\in B}} \]%

 \end{document} 

Use the \genfrac command from the amsmath package.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
Q_{\genfrac{}{}{0pt}{}{a\in A}{b\in B}} 
\end{equation*}
\end{document}