## 5 Simulation Results and Discussion
### Network Lifetime  
This section compares the network lifetime between the proposed methodology and existing protocols. The lifetime of a network is defined as the number of rounds when the total number of nodes completely exhausts their energy, and it is the most important metric for measuring the protocol. Table 5 shows the simulation results of the first node death round (FND), half node death round (HND), and all node death round (LND) for different protocols. In addition, the simulation results of the number of surviving nodes in the network are shown in Figure 8.  
As shown in Table 5, our proposed protocol overcomes the shortcomings of other protocols while extending the network lifetime; it also performs well in HND and LND. The BOA-ACO protocol utilizes the ACO algorithm to determine the optimal path from CHs to the BS, which has the risk of falling into local optima. OAFS-IMFO introduced two different meta-heuristic algorithms in the CH selection and routing path planning, which increases the risk of falling into the local optimal solution. The two sets of fuzzy rules of FC-RBAT significantly prolong system computation time, leading to higher energy consumption and reduced network lifetime. Our protocol uses the fuzzy system in CHs selection to plan cluster distribution accurately and choose a quantum annealing algorithm in the routing stage. Compared with the FRNSEER protocol, it can quickly obtain the optimal solution in all the transmission paths from CHs to the BS. As shown in Figure 8, our protocol provides better performance in terms of network lifetime. The alive nodes of the proposed protocol are sustained until 2838, 2489, 3040, and 1482  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Parameters** & **Scenario 1** & **Scenario 2** & **Scenario 3** & **Scenario 4** \\ \hline Area & 100 m \(\times\) 100 m & 100 m \(\times\) 100 m & 200 m \(\times\) 200 m & 200 m \(\times\) 200 m \\ Number of nodes & 70 & 70 & 100 & 100 \\ BS Location & x = 50, y = 50 & x = 50, y = 100 & x = 100, y = 100 & x = 0, y = 0 \\ Proportions of CHs & 15\% & 15\% & 10\% & 10\% \\ \hline \end{tabular}
\end{table}
Table 4: Descriptions of scenarios.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Items** & **Protocol** & **OAFS-IMFO** & **FC-RBAT** & **FRNSEER** & **BOA-ACO** & **FQA** \\ \hline \multirow{3}{*}{Scenario 1} & FND & 539 & 785 & 739 & 803 & 997 \\ \cline{2-6}  & HND & 1033 & 1244 & 1766 & 1288 & 1724 \\ \cline{2-6}  & LND & 1566 & 1939 & 2186 & 2469 & 2838 \\ \hline \multirow{3}{*}{Scenario 2} & FND & 340 & 807 & 876 & 760 & 324 \\ \cline{2-6}  & HND & 1034 & 1209 & 1734 & 1294 & 1003 \\ \cline{2-6}  & LND & 1343 & 1673 & 2145 & 2174 & 2489 \\ \hline \multirow{3}{*}{Scenario 3} & FND & 280 & 629 & 518 & 104 & 362 \\ \cline{2-6}  & HND & 551 & 941 & 854 & 1028 & 1418 \\ \cline{2-6}  & LND & 1658 & 1775 & 2357 & 2635 & 3040 \\ \hline \multirow{3}{*}{Scenario 4} & FND & 176 & 157 & 610 & 588 & 446 \\ \cline{2-6}  & HND & 524 & 893 & 987 & 950 & 1030 \\ \cline{2-6}  & LND & 1143 & 1249 & 1271 & 1307 & 1482 \\ \hline \end{tabular}
\end{table}
Table 5: FND, HND, LND in different scenarios.  
The performance of the proposed protocol is 81.23%, 85.33%, 83.35%, and 29.66% higher than OAFS-IMFO; 46.36%, 48.77%, 71.27%, and 18.65% higher than FC-RBAT, 29.83%, 16.04%, 28.98%, and 16.60% higher than FRNSEER; and 14.95%, 14.49%, 15.37%, and 13.39% higher than BOA-ACO, respectively, in the different scenarios.