We study parameter transferability for the Quantum Approximate Optimization Algorithm (QAOA) across multiple combinatorial optimization problem classes from a parameter generation perspective. Specifically, a meta-optimizer is trained on one problem class and deployed on another during test time. Prior work employs a Long Short-Term Memory network to emulate QAOA optimization trajectories, but the learned dynamics usually collapse to near-identical paths, limiting cross-problem transfer efficiency. In this paper, we present a problem-aware graph-conditioned meta-optimizer for QAOA that learns to generate parameter trajectories over a fixed horizon, providing strong initializations with only a few steps. The optimizer is conditioned on compact graph embeddings and trained end-to-end using differentiable feedback from the QAOA objective, avoiding the need for ground-truth angles. We evaluate across multiple graph problem classes, including MaxCut, Maximum Independent Set, Maximum Clique, and Minimum Vertex Cover. We report both solution quality and feasibility-aware metrics where constraints apply. Results across a comprehensive empirical study consisting of 64 settings show that the learned optimizer can reduce optimization effort and improve performance over standard initialization, while exhibiting transferable behavior across graph families and problem types.
We study parameter transferability for the Quantum Approximate Optimization Algorithm (QAOA) across multiple combinatorial optimization problem classes from a parameter generation perspective. Specifically, a meta-optimizer is trained on one problem class and deployed on another during test time. Prior work employs a Long Short-Term Memory network to emulate QAOA optimization trajectories, but the learned dynamics usually collapse to near-identical paths, limiting cross-problem transfer efficiency. In this paper, we present a problem-aware graph-conditioned meta-optimizer for QAOA that learns to generate parameter trajectories over a fixed horizon, providing strong initializations with only a few steps. The optimizer is conditioned on compact graph embeddings and trained end-to-end using differentiable feedback from the QAOA objective, avoiding the need for ground-truth angles. We evaluate across multiple graph problem classes, including MaxCut, Maximum Independent Set, Maximum Clique, and Minimum Vertex Cover. We report both solution quality and feasibility-aware metrics where constraints apply. Results across a comprehensive empirical study consisting of 64 settings show that the learned optimizer can reduce optimization effort and improve performance over standard initialization, while exhibiting transferable behavior across graph families and problem types.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading approach for solving combinatorial optimization problems on near-term quantum processors. However, finding good variational parameters remains a significant challenge due to the non-convex energy landscape, often resulting in slow convergence and poor solution quality. In this work, we propose a quantum meta-learning framework that trains advanced quantum sequence models to generate effective parameter initialization policies. We investigate four classical or quantum sequence models, including the Quantum Kernel-based Long Short-Term Memory (QK-LSTM), as learned optimizers in a "learning to learn" paradigm. Our numerical experiments on the Max-Cut problem demonstrate that the QK-LSTM optimizer achieves superior performance, obtaining the highest approximation ratios and exhibiting the fastest convergence rate across all tested problem sizes (n=10 to 13). Crucially, the QK-LSTM model achieves perfect parameter transferability by synthesizing a single, fixed set of near-optimal parameters, leading to a remarkable sustained acceleration of convergence even when generalizing to larger problems. This capability, enabled by the compact and expressive power of the quantum kernel architecture, underscores its effectiveness. The QK-LSTM, with only 43 trainable parameters, substantially outperforms the classical LSTM (56 parameters) and other quantum sequence models, establishing a robust pathway toward highly efficient parameter initialization for variational quantum algorithms in the NISQ era.
Approximate combinatorial optimisation has emerged as one of the most promising application areas for quantum computers, particularly those in the near term. In this work, we focus on the quantum approximate optimisation algorithm (QAOA) for solving the MaxCut problem. Specifically, we address two problems in the QAOA, how to initialise the algorithm, and how to subsequently train the parameters to find an optimal solution. For the former, we propose graph neural networks (GNNs) as a warm-starting technique for QAOA. We demonstrate that merging GNNs with QAOA can outperform both approaches individually. Furthermore, we demonstrate how graph neural networks enables warm-start generalisation across not only graph instances, but also to increasing graph sizes, a feature not straightforwardly available to other warm-starting methods. For training the QAOA, we test several optimisers for the MaxCut problem up to 16 qubits and benchmark against vanilla gradient descent. These include quantum aware/agnostic and machine learning based/neural optimisers. Examples of the latter include reinforcement and meta-learning. With the incorporation of these initialisation and optimisation toolkits, we demonstrate how the optimisation problems can be solved using QAOA in an end-to-end differentiable pipeline.
Quantum Approximate Optimization Algorithms (QAOA) promise efficient solutions to classically intractable combinatorial optimization problems by harnessing shallowdepth quantum circuits. Yet, their performance and scalability often hinge on effective parameter optimization, which remains nontrivial due to rugged energy landscapes and hardware noise. In this work, we introduce a quantum meta-learning framework that combines quantum neural networks, specifically Quantum Long Short-Term Memory (QLSTM) architectures, with QAOA. By training the QLSTM optimizer on smaller graph instances, our approach rapidly generalizes to larger, more complex problems, substantially reducing the number of iterations required for convergence. Through comprehensive benchmarks on Max-Cut and Sherrington-Kirkpatrick model instances, we demonstrate that QLSTM-based optimizers converge faster and achieve higher approximation ratios compared to classical baselines, thereby offering a robust pathway toward scalable quantum optimization in the NISQ era.
Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising candidates to achieve the quantum advantage in solving combinatorial optimization problems. The process of finding a good set of variational parameters in the QAOA circuit has proven to be challenging due to multiple factors, such as barren plateaus. As a result, there is growing interest in exploiting parameter transferability, where parameter sets optimized for one problem instance are transferred to another that could be more complex either to estimate the solution or to serve as a warm start for further optimization. But can we transfer parameters from one class of problems to another? Leveraging parameter sets learned from a well-studied class of problems could help navigate the less studied one, reducing optimization overhead and mitigating performance pitfalls. In this paper, we study whether pretrained QAOA parameters of MaxCut can be used as is or to warm start the Maximum Independent Set (MIS) circuits. Specifically, we design machine learning models to find good donor candidates optimized on MaxCut and apply their parameters to MIS acceptors. Our experimental results show that such parameter transfer can significantly reduce the number of optimization iterations required while achieving comparable approximation ratios. Reproducibility: Our results and code are available at: https://github.com/Nyquixt/Cross-Problem-PT-QAOA.
Abstract The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. Due to clustering of optimal QAOA parameters for MaxCut, successful parameter transferability between different MaxCut instances can be explained and predicted based on local properties of the graphs, including the type of subgraphs (lightcones) from which graphs are composed as well as the overall degree of nodes in the graph (parity). In this work, we apply five different graph embedding techniques to determine good donor candidates for parameter transferability, including parameter transferability between different classes of MaxCut instances. Using this technique, we effectively reduce the number of iterations required for parameter optimization, obtaining an approximate solution to the target problem with an order of magnitude speedup. This procedure also effectively removes the problem of encountering barren plateaus during the variational optimization of parameters. Additionally, our findings demonstrate that the transferred parameters maintain effectiveness when subjected to noise, supporting their use in real-world quantum applications. This work presents a framework for identifying classes of combinatorial optimization instances for which optimal donor candidates can be predicted such that QAOA can be substantially accelerated under both ideal and noisy conditions.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading variational framework for combinatorial optimization on noisy intermediate-scale quantum hardware, but its practical performance depends strongly on the classical optimizer used to train its variational parameters. This outer-loop optimization is often nonconvex, initialization-sensitive, and costly when repeated across large families of related problem instances. In this work, we propose a Transformer-based intrinsic optimization framework for QAOA, in which the optimizer itself is learned and embedded directly into the hybrid quantum-classical loop. The proposed graph-conditioned Transformer processes problem structure, current QAOA parameters, measurement feedback, and recent optimization history to predict the next variational-parameter update, thereby reformulating instance-wise classical optimization as an amortized learned policy. We develop a mathematical formulation of this intrinsic-optimization perspective and evaluate the method on QAOA-based MaxCut benchmarks across multiple problem settings, with comparisons against representative classical and learned optimization baselines. The results demonstrate that Transformer-based intrinsic optimization can provide a structured and transferable mechanism for improving the classical component of hybrid quantum optimization algorithms.