The issue seems related with https://sourceforge.net/p/standalone/tickets/1/
The following latex produced a cropped PDF:
\documentclass{standalone}
\usepackage[braket, qm]{qcircuit}
\begin{document}
\Qcircuit @C=1.0em @R=0.2em @!R {
\lstick{ {q}_{0} : } & \gate{\mathrm{H}} & \ctrl{1} & \qw & \qw\\
\lstick{ {q}_{1} : } & \qw & \targ & \qw & \qw\\
}
\end{document}

Notice that the $q_0$ and $q_1$ are fully cropped out. It seems a like a problem with bounding box setting. The data is there (see with \documentclass[border=20px]{standalone})
