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Tuesday, March 08, 2016
3:00 PM - 4:00 PM
Annenberg 107

IQI Weekly Seminar

A linear time algorithm for quantum 2-SAT
Sevag Gharibian, Virginia Commonwealth University,

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].

This talk is based on joint work with Niel de Beaudrap (University of Oxford).
 
 
 

 

For more information, please contact Jackie O'Sullivan by phone at 626.395.4964 or by email at jackieos@caltech.edu.