Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation

TL;DR

This paper introduces a second-order approximation feedback law for quantum optimization, significantly reducing circuit depth and improving convergence speed, making the method more suitable for noisy quantum devices.

Contribution

It proposes a novel second-order feedback law that accelerates convergence and reduces circuit depth in feedback-based quantum optimization algorithms.

Findings

Significant reduction in circuit depth, over an order of magnitude.

Linear scaling of circuit depth with problem size.

Enhanced suitability for noisy quantum hardware.

Abstract

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.