{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T16:20:24Z","timestamp":1781108424891,"version":"3.54.1"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030908690","type":"print"},{"value":"9783030908706","type":"electronic"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-90870-6_2","type":"book-chapter","created":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T00:06:44Z","timestamp":1636502804000},"page":"23-39","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Model Checking for Verification of Quantum Circuits"],"prefix":"10.1007","author":[{"given":"Mingsheng","family":"Ying","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,11,10]]},"reference":[{"key":"2_CR1","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1142\/S0219749908003530","volume":"6","author":"P Baltazar","year":"2008","unstructured":"Baltazar, P., Chadha, R., Mateus, P.: Quantum computation tree logic: model checking and complete calculus. Int. J. Quant. Inf. 6, 219\u201336 (2008)","journal-title":"Int. J. Quant. Inf."},{"key":"2_CR2","doi-asserted-by":"publisher","first-page":"823","DOI":"10.2307\/1968621","volume":"37","author":"G Birkhoff","year":"1936","unstructured":"Birkhoff, G., von Neumann, J.: The logic of quantum mechanics. Ann. Math. 37, 823\u2013843 (1936)","journal-title":"Ann. Math."},{"key":"2_CR3","doi-asserted-by":"publisher","first-page":"080502","DOI":"10.1103\/PhysRevLett.114.080502","volume":"114","author":"A Bocharov","year":"2015","unstructured":"Bocharov, A., Roetteler, M., Svore, K.M.: Efficient synthesis of universal repeat-until-success quantum circuits. Phys. Rev. Lett. 114, 080502 (2015)","journal-title":"Phys. Rev. Lett."},{"key":"2_CR4","doi-asserted-by":"crossref","unstructured":"Boule, M., Chenard, J.-S., Zilic, Z.: Assertion checkers in verification, silicon debug and in-field diagnosis. In: 8th IEEE International Symposium on Quality Electronic Design, pp. 613\u2013620 (2007)","DOI":"10.1109\/ISQED.2007.38"},{"key":"2_CR5","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1109\/43.275352","volume":"13","author":"JR Burch","year":"1994","unstructured":"Burch, J.R., Clarke, E.D., Long, D.E., McMillan, K.L., Dill, D.L.: Symbolic model checking for sequential circuit verification. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 13, 401\u2013424 (1994)","journal-title":"IEEE Trans. Comput. Aided Des. Integr. Circ. Syst."},{"key":"2_CR6","doi-asserted-by":"crossref","unstructured":"Burgholzer, L., Wille, R.: Advanced equivalence checking for quantum circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 40(9), 1810\u20131824 (2021)","DOI":"10.1109\/TCAD.2020.3032630"},{"key":"2_CR7","unstructured":"Corcoles, A.D., et al.: Exploiting dynamic quantum circuits in a quantum algorithm with superconducting qubits, arXiv: 2102:01682"},{"key":"2_CR8","first-page":"73","volume":"8","author":"TA Davidson","year":"2011","unstructured":"Davidson, T.A., Gay, S.J., Mlnarik, H., Nagarajan, R., Papanikolaou, N.: Model checking for communicating quantum processes. Int. J. Unconv. Comput. 8, 73\u201398 (2011)","journal-title":"Int. J. Unconv. Comput."},{"key":"2_CR9","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1016\/j.jcss.2013.04.002","volume":"79","author":"Y Feng","year":"2013","unstructured":"Feng, Y., Yu, N.K., Ying, M.S.: Model checking quantum Markov chains. J. Comput. Syst. Sci. 79, 1181\u20131198 (2013)","journal-title":"J. Comput. Syst. Sci."},{"key":"2_CR10","doi-asserted-by":"crossref","unstructured":"D Foster, H., Marschner, E.: Assertion-based verification, In: Lavagno, L., Martin, G.M., Markov, I.L., Scheffer, L.K. (eds.) Electronic Design Automation for IC System Design, Verification, and Testing, pp. 441-460. CRC Press (2016)","DOI":"10.1201\/b19569-18"},{"key":"2_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/978-3-540-70545-1_51","volume-title":"Computer Aided Verification","author":"SJ Gay","year":"2008","unstructured":"Gay, S.J., Nagarajan, R., Papanikolaou, N.: QMC: a model checker for quantum systems. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 543\u2013547. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-70545-1_51"},{"key":"2_CR12","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1007\/s00220-008-0698-8","volume":"287","author":"JE Gough","year":"2008","unstructured":"Gough, J.E., James, M.R.: Quantum feedback network: Hamiltonian formulation. Commun. Math. Phys. 287, 1109\u20131132 (2008). https:\/\/doi.org\/10.1007\/s00220-008-0698-8","journal-title":"Commun. Math. Phys."},{"key":"2_CR13","doi-asserted-by":"crossref","unstructured":"Guan, J., Wang, Q.S., Ying, M.S.: An HHL-based algorithm for computing hitting probabilities of quantum random walks, Quantum Information & Computation (2021)","DOI":"10.26421\/QIC21.5-6-4"},{"key":"2_CR14","doi-asserted-by":"publisher","first-page":"072105","DOI":"10.1063\/1.2953952","volume":"49","author":"S Gudder","year":"2008","unstructured":"Gudder, S.: Quantum Markov chains. J. Math. Phys. 49, 072105 (2008)","journal-title":"J. Math. Phys."},{"key":"2_CR15","doi-asserted-by":"crossref","unstructured":"H\u00e4ner, T., Steiger, D.S.: 0.5 petabyte simulation of a 45-qubit quantum circuit. In: Proceedings of the SC 2017, pp. 1\u201310 (2017)","DOI":"10.1145\/3126908.3126947"},{"key":"2_CR16","unstructured":"Hong, X., Zhou, X.Z., Li, S.J., Feng, Y., Ying, M.S.: A tensor network based decision diagram for representation of quantum circuits, arXiv: 2009.02618"},{"key":"2_CR17","unstructured":"Huang, C.J.: et al.: Classical simulation of quantum supremacy circuits, arXiv:2005.06787"},{"key":"2_CR18","doi-asserted-by":"publisher","first-page":"040502","DOI":"10.1103\/PhysRevLett.105.040502","volume":"105","author":"J Kerckhoff","year":"2010","unstructured":"Kerckhoff, J., Nurdin, H.I., Pavlichin, D.S., Mabuchi, H.: Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction. Phys. Rev. Lett. 105, 040502 (2010)","journal-title":"Phys. Rev. Lett."},{"key":"2_CR19","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1109\/TPDS.2019.2947511","volume":"31","author":"RL Li","year":"2020","unstructured":"Li, R.L., Wu, B.J., Ying, M.S., Sun, X.M., Yang, G.W.: Quantum supremacy circuit simulation on Sunway TaihuLight. IEEE Trans. Parallel Distrib. Syst. 31, 805\u2013816 (2020)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"2_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1007\/978-3-662-44584-6_33","volume-title":"CONCUR 2014 \u2013 Concurrency Theory","author":"Y Li","year":"2014","unstructured":"Li, Y., Ying, M.: (Un)decidable problems about reachability of quantum systems. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 482\u2013496. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-44584-6_33"},{"key":"2_CR21","unstructured":"Pednault, E., et al.: Breaking the 49-qubit barrier in the simulation of quantum circuits, arXiv:1710.05867"},{"key":"2_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/978-3-642-36315-3_15","volume-title":"Reversible Computation","author":"J Seiter","year":"2013","unstructured":"Seiter, J., Soeken, M., Wille, R., Drechsler, R.: Property checking of quantum circuits using quantum multiple-valued decision diagrams. In: Gl\u00fcck, R., Yokoyama, T. (eds.) RC 2012. LNCS, vol. 7581, pp. 183\u2013196. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-36315-3_15"},{"key":"2_CR23","doi-asserted-by":"publisher","first-page":"5270","DOI":"10.1098\/rsta.2011.0526","volume":"370","author":"N Tezak","year":"2012","unstructured":"Tezak, N., Niederberger, A., Pavlichin, D.S., Sarma, G., Mabuchi, H.: Specification of photonic circuits using quantum hardware description language. Philos. Trans. R. Soc. A 370, 5270\u20135290 (2012)","journal-title":"Philos. Trans. R. Soc. A"},{"key":"2_CR24","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1023\/B:QINP.0000022725.70000.4a","volume":"2","author":"GF Viamontes","year":"2004","unstructured":"Viamontes, G.F., Markov, I.L., Hayes, J.P.: Improving gate-level simulation of quantum circuits. Quantum Inf. Process. 2, 347\u2013379 (2004). https:\/\/doi.org\/10.1023\/B:QINP.0000022725.70000.4a","journal-title":"Quantum Inf. Process."},{"key":"2_CR25","doi-asserted-by":"crossref","unstructured":"Viamontes, G.F., Markov, I.L., Hayes, J.P.: Checking equivalence of quantum circuits and states. In: Proceedings of the ICCAD 2007, pp. 69\u201374 (2007)","DOI":"10.1109\/ICCAD.2007.4397246"},{"key":"2_CR26","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/j.ic.2017.01.007","volume":"255","author":"L Vigano","year":"2017","unstructured":"Vigano, L., Volpe, M., Zorzi, M.: A branching distributed temporal logic for reasoning about entanglement-free quantum state transformations. Inf. Comput. 255, 311\u2013333 (2017)","journal-title":"Inf. Comput."},{"key":"2_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41534-019-0196-1","volume":"5","author":"B Villalonga","year":"2019","unstructured":"Villalonga, B., et al.: A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware. NPJ Quantum Inf. 5, 1\u201316 (2019). Art. no. 86","journal-title":"NPJ Quantum Inf."},{"key":"2_CR28","unstructured":"Wang ,Q.S., Ying, M.S.: Equivalence checking of sequential quantum circuits, arXiv:1811.07722"},{"key":"2_CR29","volume-title":"Foundations of Quantum Programming","author":"MS Ying","year":"2016","unstructured":"Ying, M.S.: Foundations of Quantum Programming. Morgan Kaufmann, Cambridge, MA, USA (2016)"},{"key":"2_CR30","doi-asserted-by":"crossref","unstructured":"Ying, M.S., Duan, R.Y., Feng, Y., Ji, Z.F.: Predicate transformer semantics of quantum programs. In: Mackie, I., Gay, S. (eds.) Semantic Techniques in Quantum Computation, pp. 311\u2013360. Cambridge University Press (2010)","DOI":"10.1017\/CBO9781139193313.009"},{"key":"2_CR31","doi-asserted-by":"publisher","DOI":"10.1017\/9781108613323","volume-title":"Model Checking Quantum Systems: Principles and Algorithms","author":"MS Ying","year":"2021","unstructured":"Ying, M.S., Feng, Y.: Model Checking Quantum Systems: Principles and Algorithms. Cambridge University Press, Cambridge, UK (2021)"},{"key":"2_CR32","unstructured":"Ying, M.S., Ji, Z.F.: Symbolic verification of quantum circuits, arXiv: 2010.03032"},{"key":"2_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2629680","volume":"15","author":"MS Ying","year":"2014","unstructured":"Ying, M.S., Li, Y.J., Yu, N.K., Feng, Y.: Model-checking linear-time properties of quantum systems. ACM Trans. Comput. Logic 15, 1\u201331 (2014). Art. no. 22","journal-title":"ACM Trans. Comput. Logic"},{"key":"2_CR34","doi-asserted-by":"crossref","unstructured":"Ying, M.S., Ying, S.G., Wu, X.D.: Invariants of quantum programs: characterisations and generation. In: POPL 2017, pp. 818\u2013832 (2017)","DOI":"10.1145\/3093333.3009840"},{"key":"2_CR35","doi-asserted-by":"publisher","first-page":"1679","DOI":"10.1016\/j.scico.2013.03.016","volume":"78","author":"MS Ying","year":"2013","unstructured":"Ying, M.S., Yu, N.K., Feng, Y., Duan, R.Y.: Verification of quantum programs. Sci. Comput. Program. 78, 1679\u20131700 (2013)","journal-title":"Sci. Comput. Program."},{"key":"2_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1007\/978-3-642-40184-8_24","volume-title":"CONCUR 2013 \u2013 Concurrency Theory","author":"S Ying","year":"2013","unstructured":"Ying, S., Feng, Y., Yu, N., Ying, M.: Reachability probabilities of Quantum Markov chains. In: D\u2019Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013. LNCS, vol. 8052, pp. 334\u2013348. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40184-8_24"},{"key":"2_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/978-3-642-32940-1_7","volume-title":"CONCUR 2012 \u2013 Concurrency Theory","author":"N Yu","year":"2012","unstructured":"Yu, N., Ying, M.: Reachability and termination analysis of concurrent quantum programs. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 69\u201383. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-32940-1_7"},{"key":"2_CR38","unstructured":"Yu, N.K.: Quantum temporal logic, arXiv:1908.00158"}],"container-title":["Lecture Notes in Computer Science","Formal Methods"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-90870-6_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T00:06:58Z","timestamp":1636502818000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-90870-6_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030908690","9783030908706"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-90870-6_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"10 November 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Formal Methods","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 November 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 November 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fm2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/formalmethods2021.csp.escience.cn\/dct\/page\/1","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"131","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"40","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"31% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"9","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Additionally, this includes 4 invited full papers.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}