## 4 Quantum Exchange Lock Parallel Scheduler
### Quantum Circuit Hierarchical Strategy Based on Qelps
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Names** & **Qubits** & **Initial Circuit** & **2 QAN** & **QELPS** & **FJOSA** \\ \hline decod24-v2\_43 & 4 & 52 & 0 & 0 & 0 \\
4 mod5-v1\_22 & 5 & 25 & 1 & 0 & 0 \\ mod5 mils\_65 & 5 & 37 & 4 & 8 & 4 \\ alu-v0\_27 & 5 & 38 & 0 & 4 & 0 \\
4 gt13\_92 & 5 & 68 & 9 & 8 & 7 \\ ising\_model\_10 & 10 & 478 & 13 & 0 & 0 \\ qft\_10 & 10 & 198 & 26 & 16 & 20 \\ sqm\_258 & 10 & 10,225 & 4949 & 3374 & 3054 \\ sym9\_148 & 10 & 9410 & 4064 & 851 & 673 \\
9 symm1\_195 & 11 & 34,883 & 13,953 & 9859 & 8373 \\ z4\_268 & 11 & 3075 & 1770 & 766 & 547 \\ wim\_266 & 11 & 425 & 232 & 125 & 91 \\ sym9\_193 & 11 & 34,879 & 13,948 & 9751 & 8416 \\ rd84\_253 & 12 & 13,660 & 5680 & 4673 & 3762 \\ cycle10\_2\_110 & 12 & 6048 & 2675 & 674 & 477 \\ sqrt8\_260 & 12 & 1312 & 848 & 756 & 500 \\ ising\_model\_13 & 13 & 635 & 85 & 47 & 19 \\ radd\_250 & 13 & 3215 & 1470 & 879 & 620 \\ qft\_13 & 13 & 401 & 206 & 95 & 75 \\ adr4\_197 & 13 & 3437 & 1689 & 752 & 625 \\ clip\_206 & 14 & 14,774 & 6013 & 3230 & 2764 \\ pm1\_249 & 14 & 1774 & 1242 & 429 & 399 \\ sym6\_316 & 14 & 268 & 99 & 69 & 30 \\ rd84\_142 & 15 & 341 & 226 & 82 & 59 \\ misex1\_241 & 15 & 4815 & 2814 & 1206 & 1043 \\ square\_root\_7 & 15 & 7628 & 3645 & 1001 & 852 \\ urf6 & 15 & 171,842 & 74,317 & 4453 & 4109 \\ col14\_215 & 15 & 17,934 & 8381 & 580 & 418 \\ ising\_model\_16 & 16 & 784 & 314 & 160 & 125 \\ qft\_16 & 16 & 510 & 332 & 135 & 92 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the additional gate counts of 2 QAN, QELPS, and FJOSA. significant. This suggests that the weight assigned to SWAP gate overhead should be larger, while the weight of algorithm complexity should be relatively smaller due to its exponential relationship. By appropriately increasing algorithm complexity, the number of SWAP gate insertions can be effectively reduced. Compared to the QELPS algorithm, the FJOSA algorithm reduces SWAP gate insertions by an average of 16.15% and CNOT gate insertions by an average of 16.2% in quantum \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Names** & **Qubits** & **2 QAN** & **QELPS** & **FJOSA** \\ \hline decod24-v2\_43 & 4 & 0.12 & 0.06 & 0.12 \\
4 mod5-v1\_22 & 5 & 0.15 & 0.1 & 0.14 \\ mod5 mils\_65 & 5 & 0.17 & 0.05 & 0.13 \\ alu-v0\_27 & 5 & 0.14 & 0.05 & 0.17 \\
4 gt13\_92 & 5 & 0.17 & 0.04 & 0.2 \\ ising\_model\_10 & 10 & 1.24 & 0.05 & 0.1 \\ qft\_10 & 10 & 1.23 & 0.05 & 0.06 \\ sqn\_258 & 10 & 94.59 & 25.81 & 18.23 \\ sym9\_148 & 10 & 65.09 & 32.11 & 17.32 \\
9 symml\_195 & 11 & 305.49 & 232.72 & 210.15 \\ z4\_268 & 11 & 40.24 & 7.9 & 5.54 \\ wim\_266 & 11 & 74.51 & 33.93 & 20.22 \\ sym9\_193 & 11 & 314.21 & 213.42 & 184.61 \\ rd84\_253 & 12 & 140.57 & 63.91 & 45.96 \\ cycle10\_2\_110 & 12 & 59.09 & 15.35 & 13.48 \\ sqrt8\_260 & 12 & 96.68 & 26.82 & 12.67 \\ ising\_model\_13 & 13 & 7.31 & 0.2 & 0.12 \\ radd\_250 & 13 & 15.79 & 0.24 & 0.2 \\ qft\_13 & 13 & 14.24 & 0.54 & 0.16 \\ adr4\_197 & 13 & 45.72 & 11.77 & 9.98 \\ clip\_206 & 14 & 80.06 & 19.66 & 15.52 \\ pm1\_249 & 14 & 105.4 & 30.26 & 15.24 \\ sym6\_316 & 14 & 118.15 & 31.21 & 18.88 \\ rd84\_142 & 15 & 2.84 & 0.07 & 0.16 \\ misex1\_241 & 15 & 50.6 & 14.52 & 10.45 \\ square\_root\_7 & 15 & 84.13 & 20.37 & 10.32 \\ urf6 & 15 & 95.74 & 21.17 & 9.7 \\ co14\_215 & 15 & 186.2 & 94.35 & 53.19 \\ ising\_model\_16 & 16 & 3.7 & 0.12 & 0.2 \\ qft\_16 & 16 & 9.28 & 0.15 & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of execution time of 2 QAN, QELPS and FJOSA. Figure 7: Comparison of optimization results between QELPS and FJOSA: (**a**) Comparison of SWAP gate counts; (**b**) Comparison of CNOT gate counts. circuits ranging from 22 to 12 qubits. In circuits with 10 to four qubits, SWAP gate insertions decrease by an average of 10.4%, while CNOT gate insertions are reduced by an average of 7.7%. These results demonstrate that the FJOSA algorithm is particularly well-suited for large-scale quantum circuits.