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Genetic Algorithm-based QAOA Training improved with Fuzzy Clustering

Giovanni Acampora, Angela Chiatto, Autilia Vitiello

Published Mar 17, 2025• 0 citations
Publisher

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is emerging as a key method in quantum optimization. Operating within the framework of variational quantum circuits, QAOA entails training a parameterized quantum circuit through classical optimizers to effectively address combinatorial optimization problems. In this context, evolutionary algorithms such as genetic algorithms are emerging as suitable methodologies to search the optimal parameters for QAOA circuits. However, unfortunately, the training process results in a computationally intensive task, and, as a consequence, it is crucial to explore innovative strategies to address this issue. This work introduces a novel approach based on Fuzzy C-means algorithm to opportunely initialize the population of the genetic algorithms employed as optimizers for QAOA and, as a consequence, enhance the training. Experimental results demonstrate that the proposed approach significantly improves the performance of genetic algorithms-based training for QAOA.

DOI
10.1109/mcii64973.2025.11032773

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The Quantum Approximate Optimization Algorithm (QAOA) is emerging as a key method in quantum optimization. Operating within the framework of variational quantum circuits, QAOA entails training a parameterized quantum circuit through classical optimizers to effectively address combinatorial optimization problems. In this context, evolutionary algorithms such as genetic algorithms are emerging as suitable methodologies to search the optimal parameters for QAOA circuits. However, unfortunately, the training process results in a computationally intensive task, and, as a consequence, it is crucial to explore innovative strategies to address this issue. This work introduces a novel approach based on Fuzzy C-means algorithm to opportunely initialize the population of the genetic algorithms employed as optimizers for QAOA and, as a consequence, enhance the training. Experimental results demonstrate that the proposed approach significantly improves the performance of genetic algorithms-based training for QAOA.
The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum optimization technique used for solving combinatorial optimization problems. However, in constrained binary optimization, QAOA’s reliance on equal initial probabilities for all solutions can lead to suboptimal outcomes. To enhance the performance of QAOA in this context, we propose a novel approach that combines QAOA with genetic algorithms. In this hybrid approach, the results obtained from QAOA serve as the initial population for a genetic algorithm. We apply this methodology to address the k-heaviest subgraph problem, a critical challenge in quantum computing research. Our experiments, conducted on benchmark datasets, demonstrate a significant improvement in solution quality.
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.
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.
Recently, Variational Quantum Circuits (VQCs) are attracting considerable attention among quantum algorithms thanks to their robustness to the noise characterizing the current quantum devices. In detail, VQCs involve parameterized quan-tum circuits to be trained by means of a classical optimizer that makes queries to the quantum device. VQCs play a key role in several applications including quantum classifiers where the Hilbert space is used as feature space. Currently, the most used classical optimizer to learn V QCs is the gradient descent method. However, the so-called barren plateaus issue causes gradients of cost functions to become exceedingly small as the dimension of the classification problem is increased. As consequence, gradient descent method could be not efficient in real-world classification problems. This paper proposes to apply Genetic Algorithms (GAs) to train VQCs used as quantum classifiers. As shown in the experiments, the application of GAs results in accurate solutions obtained with a reduced number of queries to quantum devices.
Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quantum-classical algorithm that combines a parameterized quantum state evolution with a classical optimization routine to approximately solve combinatorial problems. The quality of the solution obtained by QAOA within a fixed budget of calls to the quantum computer depends on the performance of the classical optimization routine used to optimize the variational parameters. In this work, we propose an approach based on reinforcement learning (RL) to train a policy network that can be used to quickly find high-quality variational parameters for unseen combinatorial problem instances. The RL agent is trained on small problem instances which can be simulated on a classical computer, yet the learned RL policy is generalizable and can be used to efficiently solve larger instances. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our trained RL policy can reduce the optimality gap by a factor up to 8.61 compared with other off-the-shelf optimizers tested.
Variational Quantum Circuits (VQCs) are viable alternatives for implementing quantum circuits in current quantum processors. VQCs are reduced circuits with parameters that are trained to minimize a loss function for a given problem. In this work, we propose an approach to optimize the parameters of a VQC using Genetic Algorithms (GAs). We explored different GA configurations, on 3 databases - Sonar, Cancer and Banknotes datasets, comparing the proposed approach with 2 classical optimizers based on gradient descent. The results show that genetic algorithms can effectively optimize the weights of variational circuits to achieve high classification accuracy with convergence speed up to 7.3 times (in Sonar Database), 4.8 times (Cancer Database), and 3.7 times (Banknote Database) compared with the traditional optimizers. The experimental results indicate that the genetic algorithm achieves performance metrics that are significantly superior or at least comparable to those obtained by gradient descent-based optimizers, demonstrating the potential and robustness of evolutionary strategies in training variational quantum circuits.