10.4230/LIPIcs.CCC.2016.27
de Beaudrap, Niel
Niel
de Beaudrap
Gharibian, Sevag
Sevag
Gharibian0000-0002-9992-3379
A Linear Time Algorithm for Quantum 2-SAT
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
2016
2019-03-01T11:19:54Z
2020-05-07T05:30:55Z
conference
https://ris.uni-paderborn.de/record/8159
https://ris.uni-paderborn.de/record/8159.json
978-3-95977-008-8
1508.07338
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].