## 5 Conclusions  
Recently, due to the development of quantum computers, much attention has been paid to the development and implementation of reversible gates. This is because effective implementation of reversible gates can accelerate the development of universal quantum \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Circuit**} & \multicolumn{2}{c}{**Carry**} & \multicolumn{2}{c}{**Borrow**} & \multicolumn{2}{c}{**Sum/Diff**} & \multicolumn{2}{c}{**Total**} \\ \cline{2-10}  & **AOP** & **Ratio** & **AOP** & **Ratio** & **AOP** & **Ratio** & **AOP** & **Ratio** \\ \hline [33] & 9.540 & 0.967 & - & - & 9.550 & 0.969 & 9.545 & 0.966 \\ [34] & 9.540 & 0.967 & - & - & 9.550 & 0.969 & 9.545 & 0.966 \\ [35] & 9.540 & 0.967 & 9.550 & 0.963 & 9.540 & 0.968 & 9.543 & 0.966 \\ [36] & 9.540 & 0.967 & 9.530 & 0.961 & 9.530 & 0.967 & 9.533 & 0.965 \\ [37] & 9.540 & 0.967 & 9.530 & 0.961 & 9.475 & 0.961 & 9.515 & 0.963 \\ Ours & 9.870 & 1.000 & 9.920 & 1.000 & 9.860 & 1.000 & 9.883 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average output polarization of RFA(S) circuits. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Circuit**} & \multicolumn{2}{c}{**Cell Count**} & \multicolumn{2}{c}{**Area**} & \multicolumn{2}{c}{**Delay**} & \multicolumn{2}{c}{**Cost\({}_{\mathrm{AD}}\)**} & \multirow{2}{*}{**Operation**} \\ \cline{2-2} \cline{6-9}  & **no.** & **Ratio** & \(\mathbf{\mu m^{2}}\) & **Ratio** & **Clock** & **Ratio** & **AD\({}^{2}\)** & **Ratio** & \\ \hline [32] & 399 & 5.18 & 0.50 & 4.2 & 2 & 2.67 & 2.00 & 29.6 & RFAS \\ [33] & 236 & 3.06 & 0.32 & 2.7 & 3.25 & 4.33 & 3.38 & 50.1 & RFA \\ [34] & 178 & 2.31 & 0.23 & 1.9 & 3.25 & 4.33 & 2.43 & 36.0 & RFA \\ [35] & 228 & 2.96 & 0.28 & 2.3 & 1.75 & 2.33 & 0.86 & 12.7 & RFAS \\ [36] & 121 & 1.57 & 0.14 & 1.2 & 1.25 & 1.67 & 0.22 & 3.2 & RFAS \\ [37] & 123 & 1.60 & 0.12 & 1.0 & 1.25 & 1.67 & 0.19 & 2.8 & RFAS \\ Ours & 77 & 1.00 & 0.12 & 1.0 & 0.75 & 1.00 & 0.07 & 1.0 & RFAS \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison of RFA(S) circuits. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Circuit**} & \multicolumn{2}{c}{**Avg\_Ebath**} & \multicolumn{2}{c}{**Error\_Avg**} & \multicolumn{2}{c}{**Sum\_Ebath**} & \multicolumn{2}{c}{**Error\_Sum**} & \multicolumn{2}{c}{**Cost\({}_{\mathrm{ED}}\)**} \\ \cline{2-2} \cline{6-9}  & \(\mathbf{10^{-3}}\)**eV** & **Ratio** & \(\mathbf{-10^{-4}}\)**eV** & **Ratio** & \(\mathbf{10^{-2}}\)**eV** & **Ratio** & \(\mathbf{-10^{-3}}\)**eV** & **Ratio** & \(\mathbf{E^{2}D^{2}}\)** & **Ratio** \\ \hline [33] & 5.39 & 2.74 & 4.21 & 2.52 & 5.93 & 2.73 & 4.63 & 2.52 & 371.43 & 140.23 \\ [34] & 4.90 & 2.49 & 3.95 & 2.37 & 5.38 & 2.48 & 4.35 & 2.36 & 305.73 & 115.42 \\ [35] & 4.66 & 2.37 & 3.45 & 2.07 & 5.13 & 2.36 & 3.79 & 2.06 & 80.60 & 30.43 \\ [36] & 3.52 & 1.79 & 3.01 & 1.80 & 3.87 & 1.78 & 3.31 & 1.80 & 23.40 & 8.83 \\ [37] & 3.04 & 1.54 & 2.49 & 1.49 & 3.35 & 1.54 & 2.74 & 1.49 & 17.54 & 6.62 \\ Ours & 1.97 & 1.00 & 1.67 & 1.00 & 2.17 & 1.00 & 1.84 & 1.00 & 2.65 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Energy dissipations and \(\mathit{Cost}_{ED}\) comparison of RFA(S) circuits. computers and dramatically improve the performance of computing systems by minimizing energy and information loss. The proposed study constructed a FAS, one of the operation circuits that has the greatest impact on the performance of computing systems, as a circuit capable of reversible operation using QCA-based reversible gates. Although there have been QCA implementations for circuit design using various existing reversible gates, the RFAS using multilayer RQG proposed in this study was verified to be the best in all performance aspects such as area, delay, energy dissipation, and AOP required for circuit design. In addition, it demonstrated outstanding excellence in two standard design cost indicators compared to existing excellent circuits.