We study a quantum algorithm that consists of a simple quantum Markov
process, and we analyze its behavior on restricted versions of Quantum 2-SAT.
We prove that the algorithm solves this decision problem with high probability
for n qubits, L clauses, and promise gap c in time O(n^2 L^2 c^{-2}). If the
Hamiltonian is additionally polynomially gapped, our algorithm efficiently
produces a state that has high overlap with the satisfying subspace. The Markov
process we study is a quantum analogue of Sch\"oning's probabilistic algorithm
for k-SAT
