  In this work, we present a Gauss-Newton based quantum algorithm (GNQA) for
combinatorial optimization problems that, under optimal conditions, rapidly
converges towards one of the optimal solutions without being trapped in local
minima or plateaus. Quantum optimization algorithms have been explored for
decades, but more recent investigations have been on variational quantum
algorithms, which often suffer from the aforementioned problems. Our approach
mitigates those by employing a tensor product state that accurately represents
the optimal solution, and an appropriate function for the Hamiltonian,
containing all the combinations of binary variables. Numerical experiments
presented here demonstrate the effectiveness of our approach, and they show
that GNQA outperforms other optimization methods in both convergence properties
and accuracy for all problems considered here. Finally, we briefly discuss the
potential impact of the approach to other problems, including those in quantum
chemistry and higher order binary optimization.
