  We present a quantum adiabatic algorithm for a set of quantum
2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability
(2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is
similar to that of a Heisenberg chain. All the solutions of the given Q2SAT
problem span the subspace of the degenerate ground states. The Hamiltonian is
adiabatically evolved so that the system stays in the degenerate subspace. Our
numerical results suggest that the time complexity of our algorithm is
$O(n^{3.9})$ for yielding non-trivial solutions for problems with the number of
clauses $m=dn(n-1)/2\ (d\lesssim 0.1)$. We discuss the advantages of our
algorithm over the known quantum and classical algorithms.
