A Linear Time Algorithm for Quantum 2-SAT

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.

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Abstract
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].
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Proceedings Title
Proceedings of the 31st Conference on Computational Complexity (CCC 2016)
Volume
50
Page
27:1-17:21
Conference
31st Conference on Computational Complexity (CCC 2016)
Conference Location
Tokyo, Japan
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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
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
@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)} }
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.
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.
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.

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