  We use Quantum Imaginary Time Evolution (QITE) to solve polynomial
unconstrained binary optimization (PUBO) problems. We show that a linear Ansatz
yields good results for a wide range of PUBO problems, often outperforming
standard classical methods, such as the Goemans-Williamson (GW) algorithm. We
obtain numerical results for the Low Autocorrelation Binary Sequences (LABS)
and weighted MaxCut combinatorial optimization problems, thus extending an
earlier demonstration of successful application of QITE on MaxCut for
unweighted graphs. We find the performance of QITE on the LABS problem with a
separable Ansatz comparable with p=10 QAOA, and do not see a significant
advantage with an entangling Ansatz. On weighted MaxCut, QITE with a separable
Ansatz often outperforms the GW algorithm on graphs up to 150 vertices.
