  Combinatorial optimization problems are one of the areas where near-term
noisy quantum computers may have practical advantage against classical
computers. Recently a novel feedback-based quantum optimization algorithm has
been proposed by Magann \textit{et al}. The method explicitly determines
quantum circuit parameters by feeding back measurement results thus avoids
classical parameter optimization that is known to cause significant trouble in
quantum approximate optimization algorithm, the well-studied near-term
algorithm. Meanwhile, a significant drawback of the feedback-based quantum
optimization is that it requires deep circuits, rendering the method unsuitable
to noisy quantum devices. In this study we propose a new feedback law for
parameter determination by introducing the second-order approximation with
respect to time interval, a hyperparameter in the feedback-based quantum
optimization. This allows one to take larger time interval, leading to
acceleration of convergence to solutions. In numerical simulations on the
maximum cut problem we demonstrate that our proposal significantly reduces
circuit depth, with its linear scaling with the problem size smaller by more
than an order of magnitude. We expect that the new feedback law proposed in
this work may pave the way for feedback-based quantum optimization with
near-term noisy quantum computers.
