\documentclass[border=2px]{standalone}

\usepackage[braket, qm]{qcircuit}
\usepackage{graphicx}

\begin{document}
\scalebox{1.0}{
\Qcircuit @C=1.0em @R=0.2em @!R { \\
	 	\nghost{{veryLongQuantumRegisterName}_{0} :  } & \lstick{{veryLongQuantumRegisterName}_{0} :  } & \gate{\mathrm{H}} & \gate{\mathrm{H}} & \gate{\mathrm{H}} & \qw & \qw\\
	 	\nghost{{veryLongQuantumRegisterName}_{1} :  } & \lstick{{veryLongQuantumRegisterName}_{1} :  } & \gate{\mathrm{H}} & \gate{\mathrm{H}} & \gate{\mathrm{H}} & \qw & \qw\\
	 	\nghost{{veryLongQuantumRegisterName}_{2} :  } & \lstick{{veryLongQuantumRegisterName}_{2} :  } & \gate{\mathrm{H}} & \gate{\mathrm{H}} & \gate{\mathrm{H}} & \qw & \qw\\
	 	\nghost{{veryLongQuantumRegisterName}_{3} :  } & \lstick{{veryLongQuantumRegisterName}_{3} :  } & \gate{\mathrm{H}} & \gate{\mathrm{H}} & \gate{\mathrm{H}} & \qw & \qw\\
	 	\nghost{{q0} :  } & \lstick{{q0} :  } & \qw & \qw & \qw & \qw & \qw\\
\\ }}
\end{document}