Accelerating Feedback-based Algorithms for Quantum Optimization Using Gradient Descent

TL;DR

This paper introduces a hybrid gradient-based approach to enhance feedback-driven quantum optimization algorithms, notably QAOA, achieving faster convergence while maintaining low training overhead and stability.

Contribution

It proposes a layer-wise gradient estimation technique to accelerate Quantum Lyapunov Control in QAOA, improving convergence speed and robustness.

Findings

Significantly faster convergence demonstrated in numerical experiments.

Maintains low training overhead and stability guarantees.

Effective across various problem instances.

Abstract

Feedback-based methods have gained significant attention as an alternative training paradigm for the Quantum Approximate Optimization Algorithm (QAOA) in solving combinatorial optimization problems such as MAX-CUT. In particular, Quantum Lyapunov Control (QLC) employs feedback-driven control laws that guarantee monotonic non-decreasing objective values, can substantially reduce the training overhead of QAOA, and mitigate barren plateaus. However, these methods might require long control sequences, leading to sub-optimal convergence rates. In this work, we propose a hybrid method that incorporates per-layer gradient estimation to accelerate the convergence of QLC while preserving its low training overhead and stability guarantees. By leveraging layer-wise gradient information, the proposed approach selects near-optimal control parameters, resulting in significantly faster convergence and improved robustness. We validate the effectiveness of the method through extensive numerical experiments across a range of problem instances and optimization settings.