  We introduce a method to solve the MaxCut problem efficiently based on
quantum imaginary time evolution (QITE). We employ a linear Ansatz for unitary
updates and an initial state involving no entanglement, as well as an
imaginary-time-dependent Hamiltonian interpolating between a given graph and a
subgraph with two edges excised. We apply the method to thousands of randomly
selected graphs with up to fifty vertices. We show that our algorithm exhibits
a 93% and above performance converging to the maximum solution of the MaxCut
problem for all considered graphs. Our results compare favorably with the
performance of classical algorithms, such as the greedy and Goemans-Williamson
algorithms. We also discuss the overlap of the final state of the QITE
algorithm with the ground state as a performance metric, which is a quantum
feature not shared by other classical algorithms. This metric can be improved
by introducing higher-order Ansaetze and entangled initial states.
