Other information

% This is the source code of the picture, and can be put in a .tex-file, and compiled by e.g. pdflatex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass{amsart}

\usepackage[matrix,frame,arrow]{xypic}
\usepackage[braket]{qcircuit}

\vfuzz2pt % Don't report over-full v-boxes if over-edge is small

%%% ----------------------------------------------------------------------
\begin{document}
\[
\Qcircuit @C=0.5em @R=.5em {
    \lstick{\ket{0}}   & \qw   & \gate{H}  & \ctrl{3}  & \qw       & \qw       & \multigate{2}{F}  & \qw & \\
    \lstick{\ket{0}}   & \qw   & \gate{H}  & \qw       & \ctrl{3}  & \qw       & \ghost{F}         & \qw & \rstick{\Bigg\}A = F\frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^{n}-1}|k\rangle = F|B\rangle} \\
    \lstick{\ket{0}}   & \qw   & \gate{H}  & \qw       & \qw       & \ctrl{3}  & \ghost{F}         & \qw & \\ 
    \lstick{\ket{0}}   & \qw   & \qw       & \targ     & \qw       & \qw       & \qw               & \qw & \\
    \lstick{\ket{0}}   & \qw   & \qw       & \qw       & \targ     & \qw       & \qw               & \qw & \rstick{\Bigg\}B = \frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^{n}-1}|k\rangle = F^{\dagger}|A\rangle} \\
    \lstick{\ket{0}}   & \qw   & \qw       & \qw       & \qw       & \targ     & \qw               & \qw &
}\]

The equivalences are the same

\[
\Qcircuit @C=0.5em @R=.5em {
    \lstick{\ket{0}}   & \qw   & \gate{H}  & \ctrl{3}  & \qw       & \qw       & \qw                & \qw       & \\
    \lstick{\ket{0}}   & \qw   & \gate{H}  & \qw       & \ctrl{3}  & \qw       & \qw                & \qw       & \rstick{\Bigg\}A = \frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^{n}-1}|k\rangle = F^{\dagger\dagger}|B\rangle = F|B\rangle} \\
    \lstick{\ket{0}}   & \qw   & \gate{H}  & \qw       & \qw       & \ctrl{3}  & \qw                & \qw       & \\
    \lstick{\ket{0}}   & \qw   & \qw       & \targ     & \qw       & \qw       & \multigate{2}{F^\dag}  & \qw   & \\
    \lstick{\ket{0}}   & \qw   & \qw       & \qw       & \targ     & \qw       & \ghost{F^\dag}         & \qw   & \rstick{\Bigg\}B = F^{\dagger}\frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^{n}-1}|k\rangle = F^{\dagger}|A\rangle} \\
    \lstick{\ket{0}}   & \qw   & \qw       & \qw       & \qw       & \targ     & \ghost{F^\dag}         & \qw   &
}\]

\end{document}
%

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