TY - CONF
AB - 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].
AU - de Beaudrap, Niel
AU - Gharibian, Sevag
ED - Raz, Ran
ID - 8159
KW - quantum 2-SAT
KW - transfer matrix
KW - strongly connected components
KW - limited backtracking
KW - local Hamiltonian
SN - 978-3-95977-008-8
T2 - Proceedings of the 31st Conference on Computational Complexity (CCC 2016)
TI - A Linear Time Algorithm for Quantum 2-SAT
VL - 50
ER -