Quantum Optimisation Algorithms Converge Faster with New Feedback and Gradient Technique

Feedback-based algorithms represent a promising avenue for training the Quantum Approximate Optimization Algorithm (QAOA) to tackle complex combinatorial optimisation problems like MAX-CUT. Masih Mozakka and Mohsen Heidari, both from the Luddy School of Informatics, Computing, and Engineering at Indiana University Bloomington, demonstrate a novel hybrid approach to accelerate Quantum Lyapunov Control (QLC). Their work addresses the challenge of slow convergence often seen in feedback-driven methods, while retaining QLC’s benefits of reduced training overhead and stability. By incorporating per-layer gradient estimation, the researchers achieve significantly faster convergence and improved robustness, representing a substantial step towards practical quantum optimisation solutions. By incorporating this classical optimisation technique, the team significantly reduced the time needed for the algorithm to converge on a solution while maintaining the inherent stability of the feedback control mechanism. This innovation is particularly relevant for tackling combinatorial optimisation challenges such as MAX-CUT, where finding the best solution from a vast number of possibilities is computationally demanding. Existing feedback-based methods have previously struggled with slow convergence rates and the need for deep quantum circuits, a significant hurdle for implementation on current quantum hardware. The new hybrid method demonstrably improves upon these limitations, offering a pathway towards more efficient and scalable quantum optimisation. The core of this advancement lies in the strategic combination of feedback control and gradient descent. QLC utilizes feedback laws derived from a Lyapunov function, guaranteeing monotonic improvement of the objective function without requiring a traditional classical optimisation loop. However, the researchers recognised that supplementing this with per-layer gradient estimation could further refine the control parameters, leading to faster convergence.

This research not only accelerates existing quantum optimisation techniques but also paves the way for tackling increasingly complex problems with near-term quantum devices. Across a range of test instances, the proposed hybrid method achieved a 2.7x improvement in convergence speed compared to standard QLC. This acceleration was consistently observed, demonstrating the effectiveness of incorporating per-layer gradient descent into the feedback loop. The implementation of layer-wise gradient estimation allowed for the selection of near-optimal control parameters, directly contributing to this faster convergence. Further analysis revealed that the performance of this GD-QLC approach is remarkably robust to variations in parameter settings. Experiments demonstrated stable performance even with up to 5 per-layer gradient descent iterations, indicating a broad tolerance for hyperparameter choices. The choice of timestep, ∆t, also exhibited minimal impact on algorithmic performance, with well-behaved control parameters observed across a wide range of values. Results showed that the proposed approach maintains monotonic objective improvement even with significant deviations in control parameters, confirming its inherent stability. The effectiveness of the hybrid approach was validated through extensive numerical experiments on diverse problem instances, including MAX-CUT, MAX-CLIQUE, and MIN-CLIQUE problems. These experiments consistently showed that GD-QLC not only converges faster but also achieves comparable or superior results to standard QLC in terms of the final objective value. Recent work has demonstrated the promise of feedback-based methods, particularly QLC, in navigating the notoriously difficult landscapes plagued by barren plateaus. This new hybrid method, intelligently combining feedback control with layer-wise gradient estimation, represents a significant step towards practical implementation. It’s not merely about achieving faster convergence, but about doing so without sacrificing the inherent stability that makes feedback-based QAOA so attractive. The ability to accelerate the learning process while maintaining robustness is crucial; a fast but unreliable algorithm is of limited value. This work subtly shifts the focus from simply avoiding barren plateaus to actively and efficiently traversing the optimisation landscape. The implications extend beyond theoretical improvements; faster training translates directly to reduced demands on expensive quantum hardware, bringing the prospect of solving real-world combinatorial optimisation problems, from logistics and finance to materials discovery, closer to reality. However, the method’s performance will undoubtedly vary depending on the specific problem instance and the underlying quantum hardware. Future research must explore the scalability of this approach, investigating how it performs on larger, more complex problems and across different quantum architectures. 👉 More information 🗞 Accelerating Feedback-based Algorithms for Quantum Optimization Using Gradient Descent 🧠 ArXiv: https://arxiv.org/abs/2602.12387 Tags: