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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

Fuzzy Clustering-based Transferability of QAOA Parameters for Solving Vertex Cover Problems

Giovanni Acampora, Angela Chiatto, Autilia Vitiello

Published Jul 6, 2025• 1 citation
Publisher

Abstract

Optimization problems are fundamental to real-world applications, driving the need for increasingly advanced computational techniques. One promising methodology is the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical approach that maximizes the probability of obtaining sub-optimal solutions for combinatorial problems by tuning quantum gate parameters with a classical optimizer. Despite its success, QAOA still faces practical challenges, particularly in terms of training efficiency and computational cost. This paper introduces a fuzzy clustering-based approach to transfer QAOA parameters from instances of a relatively simpler problem to instances of different, more complex problems. Experimental results demonstrate both the effectiveness and efficiency of this approach in solving the Vertex Cover problem, thereby offering a viable alternative to conventional parameter tuning methods.

DOI
10.1109/fuzz62266.2025.11152203

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Optimization problems are fundamental to real-world applications, driving the need for increasingly advanced computational techniques. One promising methodology is the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical approach that maximizes the probability of obtaining sub-optimal solutions for combinatorial problems by tuning quantum gate parameters with a classical optimizer. Despite its success, QAOA still faces practical challenges, particularly in terms of training efficiency and computational cost. This paper introduces a fuzzy clustering-based approach to transfer QAOA parameters from instances of a relatively simpler problem to instances of different, more complex problems. Experimental results demonstrate both the effectiveness and efficiency of this approach in solving the Vertex Cover problem, thereby offering a viable alternative to conventional parameter tuning methods.
The Quantum Approximate Optimization Algorithm (QAOA) has become one of the most widely used components in the development of modern quantum applications. It works on the paradigm of quantum variational circuits, where a quantum circuit is trained - by repeatedly adjusting circuit parameters - to adequately solve a combinatorial optimization problem. This training process, based on classical optimization algorithms, represents a significant computational bottleneck for QAOA, as it requires repeated calls to the quantum device to evaluate the cost function of the problem to solve. Therefore, there is a strong need to eliminate this computationally expensive task and identify an alternative strategy to compute good parameters for QAOA. This paper synergistically exploits the parameter concentration property of QAOA and the Fuzzy C-Means algorithm to achieve this goal. Experimental results show that the proposed approach can support QAOA to maintain high performance in solving well-known optimization problems such as MAXCUT, requiring a reduced computational effort for the parameter tuning phase.
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.
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.
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization problem is achieved by preparing a quantum state through the optimization of quantum circuit parameters. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. In this work we show clustering of optimal QAOA parameters around specific values; consequently, successful transferability of parameters between different QAOA 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). We apply this approach to several instances of random graphs with a varying number of nodes as well as parity and show that one can use optimal donor graph QAOA parameters as near-optimal parameters for larger acceptor graphs with comparable approximation ratios. This work presents a pathway to identifying classes of combinatorial optimization instances for which variational quantum algorithms such as QAOA can be substantially accelerated.
The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality solutions within reasonable timeframes. This study investigates the potential of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical method, to solve TSP under realistic constraints. We adopt a QUBO-based formulation of TSP that integrates real-world logistical constraints reflecting operational conditions, such as vehicle capacity, road accessibility, and time windows, while ensuring compatibility with the limitations of current quantum hardware. Our experiments are conducted in a simulated environment using high-performance computing (HPC) resources to assess QAOA's performance across different problem sizes and quantum circuit depths. In order to improve scalability, we propose clustering QAOA (Cl-QAOA), a hybrid approach combining classical machine learning with QAOA. This method decomposes large TSP instances into smaller sub-problems, making quantum optimization feasible even on devices with a limited number of qubits. The results offer a comprehensive evaluation of QAOA's strengths and limitations in solving constrained TSP scenarios. This study advances quantum optimization and lays groundwork for future large-scale applications.
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization problem is achieved by preparing a quantum state through the optimization of quantum circuit parameters. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. In this work we show clustering of optimal QAOA parameters around specific values; consequently, successful transferability of parameters between different QAOA 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). We apply this approach to several instances of random graphs with a varying number of nodes as well as parity and show that one can use optimal donor graph QAOA parameters as near-optimal parameters for larger acceptor graphs with comparable approximation ratios. This work presents a pathway to identifying classes of combinatorial optimization instances for which variational quantum algorithms such as QAOA can be substantially accelerated.