{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T23:25:51Z","timestamp":1784762751833,"version":"3.55.0"},"publisher-location":"Cham","reference-count":43,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032135889","type":"print"},{"value":"9783032135896","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-13589-6_18","type":"book-chapter","created":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T05:22:02Z","timestamp":1767331322000},"page":"239-253","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Exhaustive Search for\u00a0Quantum Circuit Optimization Using ZX Calculus"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-2535-2577","authenticated-orcid":false,"given":"Tobias","family":"Fischbach","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9202-4541","authenticated-orcid":false,"given":"Pierre","family":"Talbot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9338-2834","authenticated-orcid":false,"given":"Pascal","family":"Bouvry","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,3]]},"reference":[{"issue":"5","key":"18_CR1","doi-asserted-by":"publisher","first-page":"052328","DOI":"10.1103\/PhysRevA.70.052328","volume":"70","author":"S Aaronson","year":"2004","unstructured":"Aaronson, S., Gottesman, D.: Improved simulation of stabilizer circuits. Phys. Rev. A 70(5), 052328 (2004). https:\/\/doi.org\/10.1103\/PhysRevA.70.052328","journal-title":"Phys. Rev. A"},{"issue":"10","key":"18_CR2","doi-asserted-by":"publisher","first-page":"1476","DOI":"10.1109\/TCAD.2014.2341953","volume":"33","author":"M Amy","year":"2014","unstructured":"Amy, M., Maslov, D., Mosca, M.: Polynomial-time T-depth optimization of Clifford+T circuits via matroid partitioning. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 33(10), 1476\u20131489 (2014). https:\/\/doi.org\/10.1109\/TCAD.2014.2341953","journal-title":"IEEE Trans. Comput. Aided Des. Integr. Circuits Syst."},{"issue":"9","key":"18_CR3","doi-asserted-by":"publisher","first-page":"093021","DOI":"10.1088\/1367-2630\/16\/9\/093021","volume":"16","author":"M Backens","year":"2014","unstructured":"Backens, M.: The ZX-calculus is complete for stabilizer quantum mechanics. New J. Phys. 16(9), 093021 (2014). https:\/\/doi.org\/10.1088\/1367-2630\/16\/9\/093021","journal-title":"New J. Phys."},{"key":"18_CR4","doi-asserted-by":"publisher","first-page":"17","DOI":"10.4204\/EPTCS.195.2","volume":"195","author":"M Backens","year":"2015","unstructured":"Backens, M.: Making the stabilizer ZX-calculus complete for scalars. Electron. Proc. Theor. Comput. Sci. 195, 17\u201332 (2015). https:\/\/doi.org\/10.4204\/EPTCS.195.2","journal-title":"Electron. Proc. Theor. Comput. Sci."},{"key":"18_CR5","doi-asserted-by":"publisher","unstructured":"Backens, M., Miller-Bakewell, H., de Felice, G., Lobski, L., van de Wetering, J.: There and back again: a circuit extraction tale. https:\/\/arxiv.org\/abs\/2003.01664v3 (2020). https:\/\/doi.org\/10.22331\/q-2021-03-25-421","DOI":"10.22331\/q-2021-03-25-421"},{"key":"18_CR6","doi-asserted-by":"publisher","unstructured":"de\u00a0Beaudrap, N., Kissinger, A., van\u00a0de Wetering, J.: Circuit extraction for ZX-diagrams can be #P-Hard. In: Boja\u0144czyk, M., Merelli, E., Woodruff, D.P. (eds.) 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), vol.\u00a0229, pp. 119:1\u2013119:19. Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl (2022). https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2022.119, https:\/\/drops.dagstuhl.de\/entities\/document\/10.4230\/LIPIcs.ICALP.2022.119","DOI":"10.4230\/LIPIcs.ICALP.2022.119"},{"key":"18_CR7","doi-asserted-by":"publisher","unstructured":"Berent, L., Burgholzer, L., Wille, R.: Towards a SAT encoding for quantum circuits: a journey from classical circuits to clifford circuits and beyond. In: DROPS-IDN\/v2\/Document\/10.4230\/LIPIcs.SAT.2022.18. Schloss-Dagstuhl - Leibniz Zentrum f\u00fcr Informatik (2022). https:\/\/doi.org\/10.4230\/LIPIcs.SAT.2022.18","DOI":"10.4230\/LIPIcs.SAT.2022.18"},{"key":"18_CR8","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.mejo.2018.08.011","volume":"81","author":"L Biswal","year":"2018","unstructured":"Biswal, L., Das, R., Bandyopadhyay, C., Chattopadhyay, A., Rahaman, H.: A template-based technique for efficient Clifford+T-based quantum circuit implementation. Microelectron. J. 81, 58\u201368 (2018). https:\/\/doi.org\/10.1016\/j.mejo.2018.08.011","journal-title":"Microelectron. J."},{"issue":"7671","key":"18_CR9","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1038\/nature23460","volume":"549","author":"ET Campbell","year":"2017","unstructured":"Campbell, E.T., Terhal, B.M., Vuillot, C.: Roads towards fault-tolerant universal quantum computation. Nature 549(7671), 172\u2013179 (2017). https:\/\/doi.org\/10.1038\/nature23460","journal-title":"Nature"},{"key":"18_CR10","doi-asserted-by":"publisher","unstructured":"Chi-Chih Yao, A.: Quantum circuit complexity. In: Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science, pp. 352\u2013361 (1993). https:\/\/doi.org\/10.1109\/SFCS.1993.366852","DOI":"10.1109\/SFCS.1993.366852"},{"key":"18_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1007\/978-3-540-70583-3_25","volume-title":"Automata, Languages and Programming","author":"B Coecke","year":"2008","unstructured":"Coecke, B., Duncan, R.: Interacting quantum observables. In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 298\u2013310. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-70583-3_25"},{"key":"18_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1007\/978-3-540-70583-3_25","volume-title":"Automata, Languages and Programming","author":"B Coecke","year":"2008","unstructured":"Coecke, B., Duncan, R.: Interacting quantum observables. In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 298\u2013310. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-70583-3_25"},{"key":"18_CR13","doi-asserted-by":"publisher","unstructured":"Coecke, B., Kissinger, A.: Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, Cambridge (2017). https:\/\/doi.org\/10.1017\/9781316219317","DOI":"10.1017\/9781316219317"},{"key":"18_CR14","doi-asserted-by":"publisher","unstructured":"Ding, Y., Holmes, A., Javadi-Abhari, A., Franklin, D., Martonosi, M., Chong, F.T.: Magic-state functional units: mapping and scheduling multi-level distillation circuits for fault-tolerant quantum architectures (2018). https:\/\/arxiv.org\/abs\/1809.01302v1, https:\/\/doi.org\/10.1109\/MICRO.2018.00072","DOI":"10.1109\/MICRO.2018.00072"},{"key":"18_CR15","doi-asserted-by":"publisher","unstructured":"Duncan, R., Kissinger, A., Perdrix, S., van\u00a0de Wetering, J.: Graph-theoretic simplification of quantum circuits with the ZX-calculus. Quantum 4, 279 (2020). https:\/\/doi.org\/10.22331\/q-2020-06-04-279","DOI":"10.22331\/q-2020-06-04-279"},{"key":"18_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/978-3-642-03073-4_18","volume-title":"Mathematical Theory and Computational Practice","author":"R Duncan","year":"2009","unstructured":"Duncan, R., Perdrix, S.: Graph states and the necessity of Euler decomposition. In: Ambos-Spies, K., L\u00f6we, B., Merkle, W. (eds.) CiE 2009. LNCS, vol. 5635, pp. 167\u2013177. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-03073-4_18"},{"issue":"1","key":"18_CR17","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1140\/epjqt\/s40507-024-00225-1","volume":"11","author":"N Elsayed Amer","year":"2024","unstructured":"Elsayed Amer, N., Gomaa, W., Kimura, K., Ueda, K., El-Mahdy, A.: On the optimality of quantum circuit initial mapping using reinforcement learning. EPJ Quantum Technol. 11(1), 19 (2024). https:\/\/doi.org\/10.1140\/epjqt\/s40507-024-00225-1","journal-title":"EPJ Quantum Technol."},{"key":"18_CR18","doi-asserted-by":"publisher","first-page":"85","DOI":"10.4204\/EPTCS.287.5","volume":"287","author":"A Fagan","year":"2019","unstructured":"Fagan, A., Duncan, R.: Optimising clifford circuits with quantomatic. Electron. Proc. Theor. Comput. Sci. 287, 85\u2013105 (2019). https:\/\/doi.org\/10.4204\/EPTCS.287.5","journal-title":"Electron. Proc. Theor. Comput. Sci."},{"key":"18_CR19","doi-asserted-by":"publisher","unstructured":"Fowler, A.G., Mariantoni, M., Martinis, J.M., Cleland, A.N.: Surface codes: towards practical large-scale quantum computation (2012). https:\/\/arxiv.org\/abs\/1208.0928v2, https:\/\/doi.org\/10.1103\/PhysRevA.86.032324","DOI":"10.1103\/PhysRevA.86.032324"},{"key":"18_CR20","unstructured":"F\u00f6sel, T., Niu, M.Y., Marquardt, F., Li, L.: Quantum circuit optimization with deep reinforcement learning (2021). https:\/\/arxiv.org\/abs\/2103.07585"},{"key":"18_CR21","doi-asserted-by":"publisher","unstructured":"Gogioso, S., Yeung, R.: Annealing optimisation of mixed ZX phase circuits (2023). https:\/\/doi.org\/10.48550\/arXiv.2206.11839","DOI":"10.48550\/arXiv.2206.11839"},{"key":"18_CR22","unstructured":"Harvey, W.D., Ginsberg, M.L.: Limited discrepancy search. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI), pp. 607\u2013615 (1995)"},{"issue":"2","key":"18_CR23","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1049\/iet-qtc.2020.0026","volume":"1","author":"V Hassija","year":"2020","unstructured":"Hassija, V., Chamola, V., Goyal, A., Kanhere, S.S., Guizani, N.: Forthcoming applications of quantum computing: peeking into the future. IET Quantum Commun. 1(2), 35\u201341 (2020). https:\/\/doi.org\/10.1049\/iet-qtc.2020.0026","journal-title":"IET Quantum Commun."},{"key":"18_CR24","doi-asserted-by":"publisher","unstructured":"Holker, C.: Causal flow preserving optimisation of quantum circuits in the ZX-calculus (2024). https:\/\/doi.org\/10.48550\/arXiv.2312.02793","DOI":"10.48550\/arXiv.2312.02793"},{"key":"18_CR25","doi-asserted-by":"publisher","unstructured":"Iten, R., Moyard, R., Metger, T., Sutter, D., Woerner, S.: Exact and practical pattern matching for quantum circuit optimization. ACM Trans. Quantum Comput. 3(1), 4:1\u20134:41 (2022). https:\/\/doi.org\/10.1145\/3498325","DOI":"10.1145\/3498325"},{"key":"18_CR26","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.vlsi.2019.10.004","volume":"70","author":"T Itoko","year":"2020","unstructured":"Itoko, T., Raymond, R., Imamichi, T., Matsuo, A.: Optimization of quantum circuit mapping using gate transformation and commutation. Integration 70, 43\u201350 (2020). https:\/\/doi.org\/10.1016\/j.vlsi.2019.10.004","journal-title":"Integration"},{"key":"18_CR27","doi-asserted-by":"publisher","unstructured":"Jeandel, E., Perdrix, S., Vilmart, R.: A complete axiomatisation of the ZX-calculus for Clifford+T quantum mechanics. In: Proceedings of the 33rd Annual ACM\/IEEE Symposium on Logic in Computer Science, pp. 559\u2013568. LICS 2018. Association for Computing Machinery, New York (2018). https:\/\/doi.org\/10.1145\/3209108.3209131","DOI":"10.1145\/3209108.3209131"},{"key":"18_CR28","doi-asserted-by":"publisher","unstructured":"Jeandel, E., Perdrix, S., Vilmart, R.: Diagrammatic reasoning beyond Clifford+T quantum mechanics. In: Proceedings of the 33rd Annual ACM\/IEEE Symposium on Logic in Computer Science, LICS 2018, pp. 569\u2013578. Association for Computing Machinery, New York (2018). https:\/\/doi.org\/10.1145\/3209108.3209139","DOI":"10.1145\/3209108.3209139"},{"key":"18_CR29","doi-asserted-by":"publisher","unstructured":"Joshi, A., et al.: Quantum circuit optimization of arithmetic circuits using ZX calculus (2023). https:\/\/doi.org\/10.48550\/arXiv.2306.02264","DOI":"10.48550\/arXiv.2306.02264"},{"key":"18_CR30","doi-asserted-by":"crossref","unstructured":"Khairy, S., Shaydulin, R., Cincio, L., Alexeev, Y., Balaprakash, P.: Reinforcement-learning-based variational quantum circuits optimization for combinatorial problems. ArXiv (2019)","DOI":"10.1609\/aaai.v34i03.5616"},{"key":"18_CR31","doi-asserted-by":"publisher","first-page":"229","DOI":"10.4204\/EPTCS.318.14","volume":"318","author":"A Kissinger","year":"2020","unstructured":"Kissinger, A., van de Wetering, J.: PyZX: large scale automated diagrammatic reasoning. Electron. Proc. Theor. Comput. Sci. 318, 229\u2013241 (2020). https:\/\/doi.org\/10.4204\/EPTCS.318.14","journal-title":"Electron. Proc. Theor. Comput. Sci."},{"issue":"2","key":"18_CR32","doi-asserted-by":"publisher","first-page":"022406","DOI":"10.1103\/PhysRevA.102.022406","volume":"102","author":"A Kissinger","year":"2020","unstructured":"Kissinger, A., van de Wetering, J.: Reducing T-count with the ZX-calculus. Phys. Rev. A 102(2), 022406 (2020). https:\/\/doi.org\/10.1103\/PhysRevA.102.022406","journal-title":"Phys. Rev. A"},{"issue":"1","key":"18_CR33","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/0004-3702(85)90084-0","volume":"27","author":"RE Korf","year":"1985","unstructured":"Korf, R.E.: Depth-first iterative-deepening: an optimal admissible tree search. Artif. Intell. 27(1), 97\u2013109 (1985). https:\/\/doi.org\/10.1016\/0004-3702(85)90084-0","journal-title":"Artif. Intell."},{"key":"18_CR34","unstructured":"Kotzig, A.: Eulerian lines in finite 4-valent graphs and their transformations. Theory Graphs 219\u2013230 (1968)"},{"issue":"3","key":"18_CR35","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1109\/TCAD.2007.911334","volume":"27","author":"D Maslov","year":"2008","unstructured":"Maslov, D., Dueck, G.W., Miller, D.M., Negrevergne, C.: Quantum circuit simplification and level compaction. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 27(3), 436\u2013444 (2008). https:\/\/doi.org\/10.1109\/TCAD.2007.911334","journal-title":"IEEE Trans. Comput. Aided Des. Integr. Circuits Syst."},{"key":"18_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/978-3-319-99498-7_12","volume-title":"Reversible Computation","author":"G Meuli","year":"2018","unstructured":"Meuli, G., Soeken, M., De Micheli, G.: SAT-based CNOT, T quantum circuit synthesis. In: Kari, J., Ulidowski, I. (eds.) RC 2018. LNCS, vol. 11106, pp. 175\u2013188. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-99498-7_12"},{"key":"18_CR37","unstructured":"Nam, Y., Ross, N.J., Su, Y., Childs, A.M., Maslov, D.: GitHub - meamy\/t-par: a quantum circuit optimizer based on sum-over-paths representations (2019). https:\/\/github.com\/meamy\/t-par"},{"key":"18_CR38","doi-asserted-by":"crossref","unstructured":"N\u00e4gele, M., Marquardt, F.: Optimizing ZX-diagrams with deep reinforcement learning (2023)","DOI":"10.1088\/2632-2153\/ad76f7"},{"key":"18_CR39","unstructured":"Riu, J., Nogu\u00e9, J., Vilaplana, G., Garcia-Saez, A., Estarellas, M.P.: Reinforcement learning based quantum circuit optimization via ZX-calculus (2023)"},{"key":"18_CR40","doi-asserted-by":"publisher","unstructured":"Staudacher, K., Guggemos, T., Grundner-Culemann, S., Gehrke, W.: Reducing 2-QuBit gate count for ZX-calculus based quantum circuit optimization. In: Electronic Proceedings in Theoretical Computer Science, vol.\u00a0394, pp. 29\u201345 (2023). https:\/\/doi.org\/10.4204\/EPTCS.394.3","DOI":"10.4204\/EPTCS.394.3"},{"issue":"2","key":"18_CR41","doi-asserted-by":"publisher","first-page":"025004","DOI":"10.1088\/2058-9565\/aaa331","volume":"3","author":"D Venturelli","year":"2018","unstructured":"Venturelli, D., Do, M., Rieffel, E., Frank, J.: Compiling quantum circuits to realistic hardware architectures using temporal planners. Quantum Sci. Technol. 3(2), 025004 (2018). https:\/\/doi.org\/10.1088\/2058-9565\/aaa331","journal-title":"Quantum Sci. Technol."},{"key":"18_CR42","doi-asserted-by":"publisher","unstructured":"Winderl, D., Huang, Q., Mendl, C.B.: A recursively partitioned approach to architecture-aware ZX Polynomial synthesis and optimization. In: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 837\u2013847 (2023). https:\/\/doi.org\/10.1109\/QCE57702.2023.00098","DOI":"10.1109\/QCE57702.2023.00098"},{"key":"18_CR43","unstructured":"Zhang, F., Chen, J.: Optimizing T gates in Clifford+T circuit as \\$$$\\pi $$\/4\\$ rotations around Paulis (2019)"}],"container-title":["Communications in Computer and Information Science","Optimization and Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-13589-6_18","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T05:22:04Z","timestamp":1767331324000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-13589-6_18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032135889","9783032135896"],"references-count":43,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-13589-6_18","relation":{},"ISSN":["1865-0929","1865-0937"],"issn-type":[{"value":"1865-0929","type":"print"},{"value":"1865-0937","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"3 January 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"OLA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Optimization and Learning","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Dubai","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Arab Emirates","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 April 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25 April 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ola2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ola2025.sciencesconf.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}