Accelerating Feedback-based Algorithms for Quantum Optimization Using Gradient Descent

2026-02-12

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Quantum Machine Learning
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• Quantum Optimization
• Feedback-based Algorithms
• Convergence Rate
• QAOA
• Quantum Lyapunov Control

Innovation

• Quantum Approximate Optimization Algorithm
• Quantum Lyapunov Control
• gradient descent
• feedback-based control
• layer-wise gradient estimation