Abstract: Embodiments implement iterative quantum annealing to provide a solution of an optimization. An annealing engine is located upstream of a quantum annealer (or a digital annealer, simulated annealer, or classical solver). The annealing engine is configured to process an initial solution to an original Quadratic Unconstrained Binary Optimization (QUBO) model, and thereby construct a second QUBO model. The second model is then fed to the quantum annealer, which returns a computed solution. The annealing engine constructs an intermediate solution from the computed solution and the second QUBO model. If the annealing engine determines a stopping criterion is satisfied by the intermediate solution, a final solution is constructed therefrom.