[{"status":"public","_id":"8159","user_id":"71541","language":[{"iso":"eng"}],"place":"Dagstuhl, Germany","abstract":[{"text":"The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically motivated generalization of k-SAT to the quantum setting, defining the problem \"quantum k-SAT\". He showed that quantum 2-SAT is also solvable in polynomial time on a classical computer, in particular in deterministic time O(n^4), assuming unit-cost arithmetic over a field extension of the rational numbers, where n is number of variables. In this paper, we present an algorithm for quantum 2-SAT which runs in linear time, i.e. deterministic time O(n+m) for n and m the number of variables and clauses, respectively. Our approach exploits the transfer matrix techniques of Laumann et al. [QIC, 2010] used in the study of phase transitions for random quantum 2-SAT, and bears similarities with both the linear time 2-SAT algorithms of Even, Itai, and Shamir (based on backtracking) [SICOMP, 1976] and Aspvall, Plass, and Tarjan (based on strongly connected components) [IPL, 1979].","lang":"eng"}],"editor":[{"last_name":"Raz","first_name":"Ran","full_name":"Raz, Ran"}],"volume":50,"oa":1,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik","date_created":"2019-03-01T11:19:54Z","series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","keyword":["quantum 2-SAT","transfer matrix","strongly connected components","limited backtracking","local Hamiltonian"],"department":[{"_id":"596"}],"conference":{"name":"31st Conference on Computational Complexity (CCC 2016)","location":"Tokyo, Japan"},"publication_identifier":{"isbn":["978-3-95977-008-8"]},"extern":"1","title":"A Linear Time Algorithm for Quantum 2-SAT","external_id":{"arxiv":["1508.07338"]},"doi":"10.4230/LIPIcs.CCC.2016.27","intvolume":" 50","date_updated":"2020-05-07T05:30:55Z","main_file_link":[{"url":"http://drops.dagstuhl.de/opus/volltexte/2016/5836/","open_access":"1"}],"year":"2016","publication_status":"published","page":"27:1-17:21","author":[{"last_name":"de Beaudrap","first_name":"Niel","full_name":"de Beaudrap, Niel"},{"last_name":"Gharibian","first_name":"Sevag","id":"71541","full_name":"Gharibian, Sevag","orcid":"0000-0002-9992-3379"}],"citation":{"ieee":"N. de Beaudrap and S. Gharibian, “A Linear Time Algorithm for Quantum 2-SAT,” in *Proceedings of the 31st Conference on Computational Complexity (CCC 2016)*, Tokyo, Japan, 2016, vol. 50, pp. 27:1–17:21.","chicago":"Beaudrap, Niel de, and Sevag Gharibian. “A Linear Time Algorithm for Quantum 2-SAT.” In *Proceedings of the 31st Conference on Computational Complexity (CCC 2016)*, edited by Ran Raz, 50:27:1-17:21. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. https://doi.org/10.4230/LIPIcs.CCC.2016.27.","ama":"de Beaudrap N, Gharibian S. A Linear Time Algorithm for Quantum 2-SAT. In: Raz R, ed. *Proceedings of the 31st Conference on Computational Complexity (CCC 2016)*. Vol 50. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik; 2016:27:1-17:21. doi:10.4230/LIPIcs.CCC.2016.27","mla":"de Beaudrap, Niel, and Sevag Gharibian. “A Linear Time Algorithm for Quantum 2-SAT.” *Proceedings of the 31st Conference on Computational Complexity (CCC 2016)*, edited by Ran Raz, vol. 50, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016, pp. 27:1-17:21, doi:10.4230/LIPIcs.CCC.2016.27.","short":"N. de Beaudrap, S. Gharibian, in: R. Raz (Ed.), Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2016, pp. 27:1–17:21.","bibtex":"@inproceedings{de Beaudrap_Gharibian_2016, place={Dagstuhl, Germany}, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={A Linear Time Algorithm for Quantum 2-SAT}, volume={50}, DOI={10.4230/LIPIcs.CCC.2016.27}, booktitle={Proceedings of the 31st Conference on Computational Complexity (CCC 2016)}, publisher={Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik}, author={de Beaudrap, Niel and Gharibian, Sevag}, editor={Raz, RanEditor}, year={2016}, pages={27:1–17:21}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }","apa":"de Beaudrap, N., & Gharibian, S. (2016). A Linear Time Algorithm for Quantum 2-SAT. In R. Raz (Ed.), *Proceedings of the 31st Conference on Computational Complexity (CCC 2016)* (Vol. 50, pp. 27:1-17:21). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPIcs.CCC.2016.27"},"publication":"Proceedings of the 31st Conference on Computational Complexity (CCC 2016)","type":"conference"}]