{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T02:03:47Z","timestamp":1780711427904,"version":"3.54.1"},"reference-count":20,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,7]],"date-time":"2023-03-07T00:00:00Z","timestamp":1678147200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of Chin","doi-asserted-by":"publisher","award":["62072259"],"award-info":[{"award-number":["62072259"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of Chin","doi-asserted-by":"publisher","award":["SJCX22_1617"],"award-info":[{"award-number":["SJCX22_1617"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postgraduate Research and Practice Innovation Program of Jiangsu Province","award":["62072259"],"award-info":[{"award-number":["62072259"]}]},{"name":"Postgraduate Research and Practice Innovation Program of Jiangsu Province","award":["SJCX22_1617"],"award-info":[{"award-number":["SJCX22_1617"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In order to implement a quantum circuit on an NISQ device, it must be transformed into a functionally equivalent circuit that satisfies the device\u2019s connectivity constraints. However, NISQ devices are inherently noisy, and minimizing the number of SWAP gates added to the circuit is crucial for reducing computation errors. To achieve this, we propose a subgraph isomorphism algorithm based on the timing weight priority of quantum gates, which provides a better initial mapping for a specific two-dimensional quantum architecture. Additionally, we introduce a heuristic swap sequence selection optimization algorithm that uses a distance optimization measurement function to select the ideal sequence and reduce the number of SWAP gates, thereby optimizing the circuit transformation. Our experiments demonstrate that our proposed algorithm is effective for most benchmark quantum circuits, with a maximum optimization rate of up to 43.51% and an average optimization rate of 13.51%, outperforming existing related methods.<\/jats:p>","DOI":"10.3390\/e25030465","type":"journal-article","created":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T02:30:23Z","timestamp":1678242623000},"page":"465","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Method Based on Timing Weight Priority and Distance Optimization for Quantum Circuit Transformation"],"prefix":"10.3390","volume":"25","author":[{"given":"Yang","family":"Qian","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Nantong University, Nantong 226000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhijin","family":"Guan","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Nantong University, Nantong 226000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7325-2506","authenticated-orcid":false,"given":"Shenggen","family":"Zheng","sequence":"additional","affiliation":[{"name":"Peng Cheng Laboratory, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5110-3881","authenticated-orcid":false,"given":"Shiguang","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Nantong University, Nantong 226000, China"},{"name":"School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1484","DOI":"10.1137\/S0097539795293172","article-title":"Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer","volume":"26","author":"Shor","year":"1997","journal-title":"SIAM J. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"150502","DOI":"10.1103\/PhysRevLett.103.150502","article-title":"Quantum Algorithm for Linear Systems of Equations","volume":"103","author":"Harrow","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","article-title":"Quantum Computing in the NISQ era and beyond","volume":"2","author":"Preskill","year":"2018","journal-title":"Quantum"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Murali, P., Baker, J.M., Javadi-Abhari, A., Chong, F.T., and Martonosi, M. (2019, January 13\u201317). Noise-adaptive compiler mappings for noisy intermediate-scale quantum computers. Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, Providence, RI, USA.","DOI":"10.1145\/3297858.3304075"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s11128-022-03698-0","article-title":"The complexity of quantum circuit mapping with fixed parameters","volume":"21","author":"Zhu","year":"2022","journal-title":"Quantum Inf. Process."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Li, G., Ding, Y., and Xie, Y. (2019, January 13\u201317). Tackling the qubit mapping problem for NISQ-era quantum devices. Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, Providence, RI, USA.","DOI":"10.1145\/3297858.3304023"},{"key":"ref_7","unstructured":"Phillips, I., and Rahaman, H. (2017, January 6\u20137). Exact Global Reordering for Nearest Neighbor Quantum Circuits Using A. Proceedings of the Reversible Computation, Kolkata, India."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhou, X., Feng, Y., and Li, S. (2020, January 2\u20135). A Monte Carlo Tree Search Framework for Quantum Circuit Transformation. Proceedings of the 39th International Conference on Computer-Aided Design, Virtual.","DOI":"10.1145\/3400302.3415621"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s00354-022-00163-5","article-title":"Mapping Quantum Circuits in IBM Q Devices Using Progressive Qubit Assignment for Global Ordering","volume":"40","author":"Chhangte","year":"2022","journal-title":"New Gener. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3101614","DOI":"10.1109\/TQE.2020.3026544","article-title":"A Hardware-Aware Heuristic for the Qubit Mapping Problem in the NISQ Era","volume":"1","author":"Niu","year":"2020","journal-title":"IEEE Trans. Quantum Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2587","DOI":"10.1109\/TCAD.2021.3112143","article-title":"An Iterated Local Search Methodology for the Qubit Mapping Problem","volume":"41","author":"Zhu","year":"2021","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_12","first-page":"3:1\u20133:24","article-title":"Circuit Transformations for Quantum Architectures","volume":"Volume 135","author":"Mancinska","year":"2019","journal-title":"Proceedings of the 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4683","DOI":"10.1109\/TCAD.2020.2969647","article-title":"Quantum circuit transformation based on simulated annealing and heuristic search","volume":"39","author":"Zhou","year":"2020","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1777","DOI":"10.1109\/TC.2020.3023247","article-title":"Qubit mapping based on subgraph isomorphism and filtered depth-limited search","volume":"70","author":"Li","year":"2020","journal-title":"IEEE Trans. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4721","DOI":"10.1109\/TCAD.2020.2970594","article-title":"A dynamic look-ahead heuristic for the qubit mapping problem of NISQ computers","volume":"39","author":"Zhu","year":"2020","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_16","unstructured":"Bhattacharjee, D., and Chattopadhyay, A. (2017). Depth-Optimal Quantum Circuit Placement for Arbitrary Topologies. arXiv."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Booth, K., do, M., Beck, J., Rieffel, E., Venturelli, D., and Frank, J. (2018, January 24\u201329). Comparing and Integrating Constraint Programming and Temporal Planning for Quantum Circuit Compilation. Proceedings of the International Conference on Automated Planning and Scheduling, Delft, The Netherlands.","DOI":"10.1609\/icaps.v28i1.13920"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Wille, R., Burgholzer, L., and Zulehner, A. (2019, January 2\u20136). Mapping quantum circuits to IBM QX architectures using the minimal number of SWAP and H operations. Proceedings of the 2019 56th ACM\/IEEE Design Automation Conference (DAC), Las Vegas, NV, USA.","DOI":"10.1145\/3316781.3317859"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1109\/TCAD.2018.2846658","article-title":"An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures","volume":"38","author":"Zulehner","year":"2019","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_20","unstructured":"Nielsen, M.A., and Chuang, I.L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition, Cambridge University Press."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/3\/465\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:50:01Z","timestamp":1760122201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/3\/465"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,7]]},"references-count":20,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["e25030465"],"URL":"https:\/\/doi.org\/10.3390\/e25030465","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,7]]}}}