\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{quantikz2}
\begin{document}
     \begin{tikzpicture}[column sep=0.7cm]
        \node(q){\begin{quantikz}
            \lstick{$\ket{0}$} & \gate[4, disable auto height][2cm]{U(\vec{\theta})}\slice{$\vert\psi(\vec{\theta})\rangle$} & \gate[4, disable auto height][2cm]{\begin{gathered}\text{Measure } \langle H \rangle \\ \langle {\psi(\vec\theta)}\vert H\vert{\psi(\vec\theta)}\rangle \end{gathered}} \\
            \lstick{$\ket{0}$} & & \\
            \setwiretype{n}\push{\vdots} & & \arrow[r] & \push{\begin{gathered}
                \text{Update choice of } \vec\theta \\ \text{ to try reducing }\langle H \rangle
            \end{gathered}}\\
            \lstick{$\ket{0}$} & & 
        \end{quantikz}};
        \coordinate (bottom_text) at ($(q.east)+(-1.5,-1)$);
        \coordinate (bottom_oracle) at ($(q.south)+(-2.7,0.34)$);
        \draw[->] (bottom_text) -- (q.south -| bottom_text) -- (q.south -| bottom_oracle) -- (bottom_oracle);
    \end{tikzpicture}
\end{document}