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arXiv:2504.21135 · IEEE High Performance Extreme Computing Conference

QAOA Parameter Transferability for Maximum Independent Set using Graph Attention Networks

Hanjing Xu, Xiaoyuan Liu, Alex Pothen, Ilya Safro

Published Sep 15, 2025• 0 citations
arXivHTMLPDF

Abstract

The quantum approximate optimization algorithm (QAOA) is one of the promising variational approaches of quantum computing to solve combinatorial optimization problems. In QAOA, variational parameters need to be optimized by solving a series of nonlinear, nonconvex optimization programs. In this work, we propose a QAOA parameter transfer scheme using Graph Attention Networks (GAT) to solve Maximum Independent Set (MIS) problems. We prepare optimized parameters for graphs of 12 and 14 vertices and use GATs to transfer their parameters to larger graphs. Additionally, we design a hybrid distributed resource-aware algorithm for MIS (HyDRA-MIS), which decomposes large problems into smaller ones that can fit onto noisy intermediate-scale quantum (NISQ) computers. We integrate our GAT-based parameter transfer approach to HyDRA-MIS and demonstrate competitive results compared to KaMIS, a state-of-the-art classical MIS solver, on graphs with several thousands vertices.Reproducibility: Our source code and data are available at https://github.com/jxsoortha/QAOA-Parameter-Transfer-via-GAT.

DOI
10.1109/hpec67600.2025.11196625

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The quantum approximate optimization algorithm (QAOA) is one of the promising variational approaches of quantum computing to solve combinatorial optimization problems. In QAOA, variational parameters need to be optimized by solving a series of nonlinear, nonconvex optimization programs. In this work, we propose a QAOA parameter transfer scheme using Graph Attention Networks (GAT) to solve Maximum Independent Set (MIS) problems. We prepare optimized parameters for graphs of 12 and 14 vertices and use GATs to transfer their parameters to larger graphs. Additionally, we design a hybrid distributed resource-aware algorithm for MIS (HyDRA-MIS), which decomposes large problems into smaller ones that can fit onto noisy intermediate-scale quantum (NISQ) computers. We integrate our GAT-based parameter transfer approach to HyDRA-MIS and demonstrate competitive results compared to KaMIS, a state-of-the-art classical MIS solver, on graphs with several thousands vertices.Reproducibility: Our source code and data are available at https://github.com/jxsoortha/QAOA-Parameter-Transfer-via-GAT.
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.
The quantum approximate optimization algorithm (QAOA) is widely recognized for its potential to deliver quantum advantage in combinatorial optimization tasks. As a hybrid classical-quantum algorithm, it achieves an approximate solution to the combinatorial optimization problem by preparing a specific quantum state via a classical optimization of the quantum circuit parameters. A key property of QAOA is the observed concentration and transferability of optimal parameters across distinct problem instances, linked to local graph characteristics such as subgraph types (lightcones) and node degrees (parity) [1]. However, quantum noise poses a critical challenge in the current NISQ era, hindering the performance of QAOA, particularly for large system sizes. In this follow-up study, we investigate the resilience of parameter transferability under noisy conditions. Leveraging zero-noise extrapolation (ZNE), we evaluate the transferability's robustness across various random graphs under different noise levels. Our analysis reveals that the transferability of optimal parameters from smaller ‘donor’ graphs to larger ‘acceptor’ graphs retains its effectiveness, even under substantial noise when combined with ZNE. Importantly, by illustrating that QAOA parameter transferability can still be exploited effectively among NISQ devices, we offer a pragmatic approach to enhance the algorithm's performance. Our research reinforces the promise of QAOA for large-scale applications under the practical challenges of quantum noise.
The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of quantum computing, denominated Noisy Intermediate-Scale Quantum (NISQ) era, has introduced algorithms and methods that are able to harness the computational power of current quantum computers with advantages over classical computers (referred to as quantum advantage). Achieving quantum advantage is of particular relevance for the combinatorial optimization domain, since it often implies solving an NP-Hard optimization problem. Moreover, combinatorial problems are highly relevant for practical application areas, such as operations research, or resource allocation problems. Among quantum computing methods, Variational Quantum Algorithms (VQA) have emerged as one of the strongest candidates towards reaching practical applicability of NISQ systems. This paper explores the current state and recent developments of VQAs, emphasizing their applicability to combinatorial optimization. We identify the Quantum Approximate Optimization Algorithm (QAOA) as the leading candidate for these problems. Furthermore, we implement QAOA circuits with varying depths to solve the MaxCut problem on graphs with 10 and 20 nodes, demonstrating the potential and challenges of using VQAs in practical optimization tasks. We release our code, dataset and optimized circuit parameters under https://github.com/DanielFPerez/VQA-for-MaxCut.
Solving combinatorial optimization problems (COPs) is a promising application of quantum computation, with the Quantum Approximate Optimization Algorithm (QAOA) being one of the most studied quantum algorithms for solving them. However, multiple factors make the parameter search of the QAOA a hard optimization problem. In this work, we study transfer learning (TL), a methodology to reuse pre-trained QAOA parameters of one problem instance into different COP instances. This methodology can be used to alleviate the necessity of classical optimization to find good parameters for individual problems. To this end, we select small cases of the traveling salesman problem (TSP), the bin packing problem (BPP), the knapsack problem (KP), the weighted maximum cut (MaxCut) problem, the maximal independent set (MIS) problem, and portfolio optimization (PO), and find optimal βββ and γγγ parameters for p layers. We compare how well the parameters found for one problem adapt to the others. Among the different problems, BPP is the one that produces the best transferable parameters, maintaining the probability of finding the optimal solution above a quadratic speedup over random guessing for problem sizes up to 42 qubits and p = 10 layers. Using the BPP parameters, we perform experiments on IonQ Harmony and Aria, Rigetti Aspen-M-3, and IBM Brisbane of MIS instances for up to 18 qubits. The results indicate that IonQ Aria yields the best overlap with the ideal probability distribution. Additionally, we show that cross-platform TL is possible using the D-Wave Advantage quantum annealer with the parameters found for BPP. We show an improvement in performance compared to the default protocols for MIS with up to 170 qubits. Our results suggest that there are QAOA parameters that generalize well for different COPs and annealing protocols.
Quantum technology enters in the new era of Noisy Intermediate-Scale Quantum (NISQ) with 50-100 qubits quantum computers already available. It is now important to compare quantum methods with the classical approach to solve optimization problems in order to determine if there is a potential speed-up and what quantum technologies will be able to perform. The Quantum Approximate optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. We provide the method to apply QAOA on a shortest path problem and a study of the performance of this quantum method by using heuristic strategies based on observed patterns in optimal parameters. First, we will present the state of the art of quantum hybrid algorithms and technologies. Then we will discuss the effect of the shape of the graph, the number of valid solutions, and the number of nodes of the graph we consider on the quality of the QAOA’s results and on the patterns in optimal variational parameters.
Learning the problem structure at multiple levels of coarseness to inform the decomposition-based hybrid quantum-classical combinatorial optimization solvers is a promising approach to scaling up variational approaches. We introduce a multilevel algorithm reinforced with the spectral graph representation learning-based accelerator to tackle large-scale graph maximum cut instances and fused with several versions of the quantum approximate optimization algorithm (QAOA) and QAOA-inspired algorithms. The graph representation learning model utilizes the idea of QAOA variational parameters concentration and substantially improves the performance of QAOA. We demonstrate the potential of using multilevel QAOA and representation learning-based approaches on extensive graphs by achieving high-quality solutions much faster. Reproducibility: Our source code and results are available at https://github.com/bachbao/MLQAOA.