  We investigate the performance of a quantum algorithm for solving classical
3-SAT problems. A cycle of post-selected measurements drives the computer's
register monotonically toward a steady state which is correlated to the
classical solution(s). An internal parameter $\theta$ determines both the
degree of correlation and the success probability, thus controlling the
algorithm's runtime. Optionally this parameter can be gradually evolved during
the algorithm's execution to create a Zeno-like effect; this can be viewed as
an adiabatic evolution of a Hamiltonian which remains frustration-free at all
points, and we lower-bound the corresponding gap. In exact numerical
simulations of small systems up to 34 qubits our approach competes favourably
with a high-performing classical 3-SAT solver, which itself outperforms a
brute-force application of Grover's search.
