Algorithm 1: QGA Procedure

Begin $$\begin{gathered} \hspace{1em}t=0 \\ \hspace{1em}\mathrm{Initialize} Q\left(t\right) \\ \hspace{1em}\mathrm{Make} P\left(t\right) \mathrm{by} \mathrm{observing} Q\left(t\right) \mathrm{states} \\ \hspace{1em}\mathrm{Evaluate} P\left(t\right) \\ \hspace{1em}\mathrm{Save} \mathrm{the} \mathrm{best} \mathrm{solution} \mathrm{among} P\left(t\right) \\ \hspace{1em}\mathrm{While} (\mathrm{not} \mathrm{termination-condition}) \mathrm{do} \\ \hspace{1em}\mathrm{Begin} \\ \hspace{1em} t=t+1 \\ \hspace{1em} \mathrm{Make} P\left(t\right) \mathrm{by} \mathrm{observing} Q(t-1) \mathrm{states} \\ \hspace{1em} \mathrm{Evaluate} P\left(t\right) \\ \hspace{1em} \mathrm{Update} Q\left(t\right) \mathrm{using} \mathrm{quantum} \mathrm{gates} U\left(t\right) \\ \hspace{1em} \mathrm{Store} \mathrm{the} \mathrm{best} \mathrm{solution} \mathrm{among} P\left(t\right) \end{gathered}$$  End End