{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T10:00:25Z","timestamp":1776333625587,"version":"3.51.2"},"publisher-location":"Cham","reference-count":25,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032227737","type":"print"},{"value":"9783032227744","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\/978-3-032-22774-4_8","type":"book-chapter","created":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T09:21:23Z","timestamp":1776331283000},"page":"149-169","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["QEMI: A Quantum Software Stacks Testing Framework via Equivalence Modulo Inputs"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-7821-6879","authenticated-orcid":false,"given":"Junjie","family":"Luo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2775-9633","authenticated-orcid":false,"given":"Shangzhou","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6560-5102","authenticated-orcid":false,"given":"Fuyuan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8083-4352","authenticated-orcid":false,"given":"Jianjun","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,17]]},"reference":[{"key":"8_CR1","doi-asserted-by":"publisher","unstructured":"Canonne, C.L.: A Survey on Distribution Testing: Your Data is Big. But is it Blue? No.\u00a09 in Graduate Surveys, Theory of Computing Library (2020). https:\/\/doi.org\/10.4086\/toc.gs.2020.009, http:\/\/www.theoryofcomputing.org\/library.html","DOI":"10.4086\/toc.gs.2020.009"},{"key":"8_CR2","unstructured":"Corporation, M.: Q# api reference (2025), https:\/\/learn.microsoft.com\/en-us\/qsharp\/api\/, accessed: 2025-07-04"},{"key":"8_CR3","doi-asserted-by":"publisher","unstructured":"Dai, A., Ying, M.: Qreach: A reachability analysis tool for quantum markov chains. In: Computer Aided Verification: 36th International Conference, CAV 2024, Montreal, QC, Canada, July 24\u201327, 2024, Proceedings, Part III. p. 520\u2013532. Springer-Verlag, Berlin, Heidelberg (2024). https:\/\/doi.org\/10.1007\/978-3-031-65633-0_23, https:\/\/doi.org\/10.1007\/978-3-031-65633-0_23","DOI":"10.1007\/978-3-031-65633-0_23"},{"key":"8_CR4","doi-asserted-by":"publisher","unstructured":"Developers, C.: Cirq. Zenodo (Apr 2025). https:\/\/doi.org\/10.5281\/ZENODO.4062499, https:\/\/zenodo.org\/doi\/10.5281\/zenodo.4062499","DOI":"10.5281\/ZENODO.4062499"},{"key":"8_CR5","unstructured":"Diakonikolas, I., Kane, D.M.: A new approach for testing properties of discrete distributions. CoRR abs\/1601.05557 (2016), http:\/\/arxiv.org\/abs\/1601.05557"},{"key":"8_CR6","doi-asserted-by":"crossref","unstructured":"Good, I.J.: Some terminology and notation in information theory (1956), https:\/\/api.semanticscholar.org\/CorpusID:121348458","DOI":"10.1049\/pi-c.1956.0024"},{"key":"8_CR7","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search (1996), https:\/\/arxiv.org\/abs\/quant-ph\/9605043","DOI":"10.1145\/237814.237866"},{"key":"8_CR8","doi-asserted-by":"crossref","unstructured":"Hellinger, E.: Neue begr\u00fcndung der theorie quadratischer formen von unendlichvielen ver\u00e4nderlichen. Journal f\u00fcr die reine und angewandte Mathematik 136, 210\u2013271 (1909), http:\/\/eudml.org\/doc\/149313","DOI":"10.1515\/crll.1909.136.210"},{"key":"8_CR9","doi-asserted-by":"publisher","unstructured":"Hu, T., Ye, G., Tang, Z., Tan, S.H., Wang, H., Li, M., Wang, Z.: Upbeat: Test input checks of q# quantum libraries. In: Proceedings of the 33rd ACM SIGSOFT International Symposium on Software Testing and Analysis. p. 186\u2013198. ISSTA 2024, Association for Computing Machinery, New York, NY, USA (2024). https:\/\/doi.org\/10.1145\/3650212.3652120, https:\/\/doi.org\/10.1145\/3650212.3652120","DOI":"10.1145\/3650212.3652120"},{"key":"8_CR10","unstructured":"Intel Corporation: Yarpgen: Yet another random program generator. https:\/\/github.com\/intel\/yarpgen (2018), accessed: 2025-06-30"},{"key":"8_CR11","unstructured":"Iwumbwe, I., Liu, B.Z., Wickerson, J.: QuteFuzz: Fuzzing quantum compilers using randomly generated circuits with control flow and subcircuits. In: PLanQC \u201925: Programming Languages for Quantum Computing Workshop, co-located with POPL 2025. ACM SIGPLAN (2025)"},{"key":"8_CR12","unstructured":"Javadi-Abhari, A., Treinish, M., Krsulich, K., Wood, C.J., Lishman, J., Gacon, J., Martiel, S., Nation, P.D., Bishop, L.S., Cross, A.W., Johnson, B.R., Gambetta, J.M.: Quantum computing with qiskit (2024), https:\/\/arxiv.org\/abs\/2405.08810"},{"key":"8_CR13","unstructured":"Kolmogorov, A.N.: Sulla determinazione empirica di una legge di distribuzione. Giornale dell\u2019Istituto Italiano degli Attuari 4(1), 83\u201391 (1933)"},{"key":"8_CR14","doi-asserted-by":"publisher","unstructured":"Le, V., Afshari, M., Su, Z.: Compiler validation via equivalence modulo inputs. SIGPLAN Not. 49(6), 216\u2013226 (Jun 2014). https:\/\/doi.org\/10.1145\/2666356.2594334, https:\/\/doi.org\/10.1145\/2666356.2594334","DOI":"10.1145\/2666356.2594334"},{"key":"8_CR15","doi-asserted-by":"publisher","unstructured":"Lidbury, C., Lascu, A., Chong, N., Donaldson, A.F.: Many-core compiler fuzzing. SIGPLAN Not. 50(6), 65\u201376 (Jun 2015). https:\/\/doi.org\/10.1145\/2813885.2737986, https:\/\/doi.org\/10.1145\/2813885.2737986","DOI":"10.1145\/2813885.2737986"},{"key":"8_CR16","doi-asserted-by":"publisher","unstructured":"Luo, S., Zhang, Q.: Informational distance on quantum-state space. Phys. Rev. A 69, 032106 (Mar 2004). https:\/\/doi.org\/10.1103\/PhysRevA.69.032106, https:\/\/link.aps.org\/doi\/10.1103\/PhysRevA.69.032106","DOI":"10.1103\/PhysRevA.69.032106"},{"key":"8_CR17","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press (2010)"},{"key":"8_CR18","doi-asserted-by":"publisher","unstructured":"Paltenghi, M., Pradel, M.: Morphq: Metamorphic testing of the qiskit quantum computing platform. In: Proceedings of the 45th International Conference on Software Engineering. p. 2413\u20132424. ICSE \u201923, IEEE Press (2023). https:\/\/doi.org\/10.1109\/ICSE48619.2023.00202, https:\/\/doi.org\/10.1109\/ICSE48619.2023.00202","DOI":"10.1109\/ICSE48619.2023.00202"},{"key":"8_CR19","doi-asserted-by":"publisher","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing 26(5), 1484\u20131509 (Oct 1997). https:\/\/doi.org\/10.1137\/s0097539795293172, http:\/\/dx.doi.org\/10.1137\/S0097539795293172","DOI":"10.1137\/s0097539795293172"},{"key":"8_CR20","doi-asserted-by":"publisher","unstructured":"Shore, J., Johnson, R.: Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Transactions on Information Theory 26(1), 26\u201337 (1980). https:\/\/doi.org\/10.1109\/TIT.1980.1056144","DOI":"10.1109\/TIT.1980.1056144"},{"key":"8_CR21","doi-asserted-by":"publisher","unstructured":"Sivarajah, S., Dilkes, S., Cowtan, A., Simmons, W., Edgington, A., Duncan, R.: t|ket$$\\rangle $$: a retargetable compiler for nisq devices. Quantum Science and Technology 6(1), 014003 (nov 2020). https:\/\/doi.org\/10.1088\/2058-9565\/ab8e92, https:\/\/dx.doi.org\/10.1088\/2058-9565\/ab8e92","DOI":"10.1088\/2058-9565\/ab8e92"},{"key":"8_CR22","unstructured":"Smirnov, N.V.: On the estimation of the discrepancy between empirical curves of distributions for two independent samples. Moscow University Mathematics Bulletin 2, 3\u201326 (1939)"},{"key":"8_CR23","doi-asserted-by":"publisher","unstructured":"Svore, K., Geller, A., Troyer, M., Azariah, J., Granade, C., Heim, B., Kliuchnikov, V., Mykhailova, M., Paz, A., Roetteler, M.: Q#: Enabling Scalable Quantum Computing and Development with a High-level DSL. In: Proceedings of the Real World Domain Specific Languages Workshop 2018. RWDSL2018, ACM (Feb 2018). https:\/\/doi.org\/10.1145\/3183895.3183901, http:\/\/dx.doi.org\/10.1145\/3183895.3183901","DOI":"10.1145\/3183895.3183901"},{"key":"8_CR24","doi-asserted-by":"publisher","unstructured":"Wang, J., Zhang, Q., Xu, G.H., Kim, M.: Qdiff: differential testing of quantum software stacks. In: Proceedings of the 36th IEEE\/ACM International Conference on Automated Software Engineering. p. 692\u2013704. ASE \u201921, IEEE Press (2022). https:\/\/doi.org\/10.1109\/ASE51524.2021.9678792, https:\/\/doi.org\/10.1109\/ASE51524.2021.9678792","DOI":"10.1109\/ASE51524.2021.9678792"},{"key":"8_CR25","doi-asserted-by":"publisher","unstructured":"Yang, X., Chen, Y., Eide, E., Regehr, J.: Finding and understanding bugs in c compilers. In: Proceedings of the 32nd ACM SIGPLAN Conference on Programming Language Design and Implementation. p. 283\u2013294. PLDI \u201911, Association for Computing Machinery, New York, NY, USA (2011). https:\/\/doi.org\/10.1145\/1993498.1993532, https:\/\/doi.org\/10.1145\/1993498.1993532","DOI":"10.1145\/1993498.1993532"}],"container-title":["Lecture Notes in Computer Science","Fundamental Approaches to Software Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-22774-4_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T09:21:32Z","timestamp":1776331292000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-22774-4_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032227737","9783032227744"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-22774-4_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"17 April 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FASE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Fundamental Approaches to Software Engineering","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Turin","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 April 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 April 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fase2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/etaps.org\/2026\/conferences\/fase\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}