## 4 Quantum Exchange Lock Parallel Scheduler
### Quantum Circuit Hierarchical Strategy Based on Qelps
Experimental results indicate that the conflict problem of SWAP gates is effectively resolved by the QELPS algorithm through preliminary stratification. This approach results in a significant reduction in the number of inserted SWAP and CNOT gates, thereby improving the efficiency of quantum gate usage. Based on this, a secondary stratification strategy combined with quantum locks is employed, further reducing runtime overhead and enhancing scheduling efficiency. Finally, the FJOSA algorithm is applied within this stratified framework to further decrease the overhead of SWAP and CNOT gates, ultimately achieving a comprehensive optimization of quantum circuit depth and execution efficiency. ## 7 Conclusions

In response to the core challenges of quantum circuit scheduling in the NISQ era, we propose the QELPS-FJOSA framework. This framework integrates dynamic hierarchical optimization with global coordination strategies. In the QELPS component, SWAP conflict characteristics are employed to control the quantum gate layout in real time. The inter-layer coupling effect is decoupled via a quantum locking mechanism, thereby significantly optimizing circuit depth and reducing SWAP operation redundancy. The FJOSA component is based on cross-layer heuristic search driven by a cost function, which overcomes the limitations of traditional local optimization and achieves a globally optimal approximation of multi-level resource allocation. The framework demonstrates strong generalization capabilities in heterogeneous architectures such as superconducting, photonic, and ion trap systems. Challenges related to the collaborative optimization of topological constraints, noise accumulation, and timing competition are effectively alleviated, while theoretical and methodological support is provided to improve the practical performance of quantum hardware. Future research will explore the integration of fault-tolerant mechanisms and verify the scalability of the framework in distributed quantum systems, thereby promoting the practical application of quantum computing in the NISQ era. Conceptualization, Z.D. and X.L. ; Methodology, X.L. and H.L. ; Software, Z.D. ; Validation, Z.D., X.L. and H.L. ; Formal analysis, X.L. ; Investigation, Z.D., X.L. and H.L. ; Resources, Z.D., X.L. and H.L. ; Data curation, H.L. ; Writing--original draft preparation, X.L. ; Writing--review and editing, Z.D. ; Visualization, H.L. ; Supervision, Z.D. ; Project administration, Z.D. ; Funding acquisition, H.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the Natural Science Foundation of Heilongjiang Province LH2024F042. Not applicable. All values used in the study have been presented in the manuscript, but the complete recorded data are unavailable due to privacy restrictions. We extend our sincere gratitude to [PERSON] and [PERSON] for their invaluable technical and administrative support throughout the study, which significantly facilitated its successful completion. The authors declare no conflicts of interest. ## References

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