{"keyword":["search complexity","local Hamiltonian","Quantum SAT","algebraic geometry"],"oa":"1","place":"Dagstuhl, Germany","volume":117,"abstract":[{"lang":"eng","text":"The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k >= 3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been well-studied for special tractable cases, as well as from a parameterized complexity perspective, much less is known in similar settings for k-QSAT. Here, we study the open problem of computing satisfying assignments to k-QSAT instances which have a \"matching\" or \"dimer covering\"; this is an NP problem whose decision variant is trivial, but whose search complexity remains open. Our results fall into three directions, all of which relate to the \"matching\" setting: (1) We give a polynomial-time classical algorithm for k-QSAT when all qubits occur in at most two clauses. (2) We give a parameterized algorithm for k-QSAT instances from a certain non-trivial class, which allows us to obtain exponential speedups over brute force methods in some cases by reducing the problem to solving for a single root of a single univariate polynomial. (3) We conduct a structural graph theoretic study of 3-QSAT interaction graphs which have a \"matching\". We remark that the results of (2), in particular, introduce a number of new tools to the study of Quantum SAT, including graph theoretic concepts such as transfer filtrations and blow-ups from algebraic geometry; we hope these prove useful elsewhere."}],"doi":"10.4230/LIPIcs.MFCS.2018.38","status":"public","author":[{"first_name":"Marco","last_name":"Aldi","full_name":"Aldi, Marco"},{"full_name":"de Beaudrap, Niel","last_name":"de Beaudrap","first_name":"Niel"},{"first_name":"Sevag","orcid":"0000-0002-9992-3379","id":"71541","last_name":"Gharibian","full_name":"Gharibian, Sevag"},{"first_name":"Seyran","last_name":"Saeedi","full_name":"Saeedi, Seyran"}],"_id":"8162","intvolume":" 117","publication_identifier":{"unknown":["978-3-95977-086-6"]},"year":"2018","conference":{"name":"43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)","location":"Liverpool, UK"},"type":"conference","page":"38:1-38:16","publication":"43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)","date_created":"2019-03-01T11:34:41Z","department":[{"_id":"623"},{"_id":"7"}],"citation":{"bibtex":"@inproceedings{Aldi_de Beaudrap_Gharibian_Saeedi_2018, place={Dagstuhl, Germany}, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={On Efficiently Solvable Cases of Quantum k-SAT}, volume={117}, DOI={10.4230/LIPIcs.MFCS.2018.38}, booktitle={43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, publisher={Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik}, author={Aldi, Marco and de Beaudrap, Niel and Gharibian, Sevag and Saeedi, Seyran}, editor={Potapov, Igor and Spirakis, Paul and Worrell, James}, year={2018}, pages={38:1-38:16}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }","chicago":"Aldi, Marco, Niel de Beaudrap, Sevag Gharibian, and Seyran Saeedi. “On Efficiently Solvable Cases of Quantum K-SAT.” In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), edited by Igor Potapov, Paul Spirakis, and James Worrell, 117:38:1-38:16. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018. https://doi.org/10.4230/LIPIcs.MFCS.2018.38.","ama":"Aldi M, de Beaudrap N, Gharibian S, Saeedi S. On Efficiently Solvable Cases of Quantum k-SAT. In: Potapov I, Spirakis P, Worrell J, eds. 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Vol 117. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik; 2018:38:1-38:16. doi:10.4230/LIPIcs.MFCS.2018.38","short":"M. Aldi, N. de Beaudrap, S. Gharibian, S. Saeedi, in: I. Potapov, P. Spirakis, J. Worrell (Eds.), 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2018, p. 38:1-38:16.","ieee":"M. Aldi, N. de Beaudrap, S. Gharibian, and S. Saeedi, “On Efficiently Solvable Cases of Quantum k-SAT,” in 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Liverpool, UK, 2018, vol. 117, p. 38:1-38:16, doi: 10.4230/LIPIcs.MFCS.2018.38.","apa":"Aldi, M., de Beaudrap, N., Gharibian, S., & Saeedi, S. (2018). On Efficiently Solvable Cases of Quantum k-SAT. In I. Potapov, P. Spirakis, & J. Worrell (Eds.), 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018) (Vol. 117, p. 38:1-38:16). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2018.38","mla":"Aldi, Marco, et al. “On Efficiently Solvable Cases of Quantum K-SAT.” 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), edited by Igor Potapov et al., vol. 117, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018, p. 38:1-38:16, doi:10.4230/LIPIcs.MFCS.2018.38."},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik","user_id":"71541","editor":[{"full_name":"Potapov, Igor","last_name":"Potapov","first_name":"Igor"},{"last_name":"Spirakis","full_name":"Spirakis, Paul","first_name":"Paul"},{"full_name":"Worrell, James","last_name":"Worrell","first_name":"James"}],"series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","main_file_link":[{"open_access":"1","url":"http://drops.dagstuhl.de/opus/volltexte/2018/9620/"}],"publication_status":"published","date_updated":"2023-02-28T11:01:16Z","language":[{"iso":"eng"}],"title":"On Efficiently Solvable Cases of Quantum k-SAT","external_id":{"arxiv":["1712.09617"]}}