2026-08-17T01:16:26Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:5836 2024-03-06T10:37:11Z ddc:004 open_access

A Linear Time Algorithm for Quantum 2-SAT de Beaudrap, Niel Gharibian, Sevag quantum 2-SAT transfer matrix strongly connected components limited backtracking local Hamiltonian 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]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Niel de Beaudrap and Sevag Gharibian 2016 Is Part Of LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2016.27 urn:nbn:de:0030-drops-58363 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.27 eng https://creativecommons.org/licenses/by/3.0/legalcode