The recent interest in learning-augmented algorithms has motivated us to explore their applicability in quantum computing, specifically during the noisy intermediate-scale quantum (NISQ) era. This paper introduces a learning-augmented algorithm-like approach to enhance the Quantum Approximate Optimization Algorithm (QAOA) for max-cut problems, by improving initial parameter estimation. We trained a random forest regression model on the optimal solution parameters from various max-cut graphs, and then used this model to guess better initial parameters for previously unseen graphs. Experimental results demonstrate that our approach reduces the number of iterations of quantum computation required, thereby reducing noise and error. These findings indicate that integrating learning-augmented algorithm techniques can enhance the computational feasibility of solving QAOA problems in the NISQ era.
The recent interest in learning-augmented algorithms has motivated us to explore their applicability in quantum computing, specifically during the noisy intermediate-scale quantum (NISQ) era. This paper introduces a learning-augmented algorithm-like approach to enhance the Quantum Approximate Optimization Algorithm (QAOA) for max-cut problems, by improving initial parameter estimation. We trained a random forest regression model on the optimal solution parameters from various max-cut graphs, and then used this model to guess better initial parameters for previously unseen graphs. Experimental results demonstrate that our approach reduces the number of iterations of quantum computation required, thereby reducing noise and error. These findings indicate that integrating learning-augmented algorithm techniques can enhance the computational feasibility of solving QAOA problems in the NISQ era.
The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems that are classically intractable. Careful parameter initialization in QAOA can reduce the number of quantum circuit evaluations required, making it more feasible to run on noisy intermediate-scale quantum (NISQ) devices. In this work, We focus on MaX-Cut, a classic NP-hard optimization problem, and propose a conditional variational autoencoder (CVAE) scheme for generating initial QAOA parameters for the Max-Cut problems based on input graph structures. The CVAE, trained on optimal parameters from 270 ten-node graphs, produces multiple parameter candidates conditioned on 27-dimensional feature vectors that incorporate spectral properties as well as learned embeddings. We evaluate and compare two strategies: direct initialization using the highestconfidence prediction, and dynamic injection which monitors optimization progress and intervenes when needed. On 89 test graphs, the dynamic injection strategy increased successful convergence cases from 41 to 49, reduced mean iteration count by 4.94.
In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.
Abstract Quantum computing has recently emerged as a promising approach to solve complex combinatorial optimization problems beyond the reach of classical algorithms. This study explores the integration of machine learning techniques with the Quantum Approximate Optimization Algorithm (QAOA) to improve its effectiveness in graph-based optimization tasks, with a particular focus on the Max-Cut problem. We propose a hybrid framework that utilizes a neural network to dynamically adjust QAOA parameters, leveraging historical data to enhance performance. We conduct a comparative analysis between the machine learning-augmented QAOA and a traditional QAOA implementation. Through extensive simulations on random graphs with up to 2000 nodes, the machine learning-enhanced QAOA demonstrates superior performance, reducing training loss significantly and achieving a final loss of approximately 3.112 x 10-33 compared to 2.34 x 10-15 for the standard QAOA. Statistical analysis reveals a moderate negative correlation between training epochs and loss, highlighting the benefits of continued training while acknowledging other influencing factors. This research highlights the potential of combining quantum algorithms with machine learning to solve real-world optimization problems, offering promising applications in fields such as logistics, finance, and network design.
In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.
In the Noisy Intermediate-Scale Quantum (NISQ) era, the Quantum Approximate Optimization Algorithm (QAOA) has attracted significant attention as an algorithm for solving combinatorial optimization problems that are classically intractable. Various modifications and training strategies have been proposed to enhance the performance of QAOA. However, as the circuit depth increases, existing methods encounter greater training difficulty and reach a barren plateau in performance improvements. In this paper, we propose the Smart Insert Layerwise QAOA (SIL QAOA) to overcome these challenges. In SIL QAOA, at each stage, a new layer is inserted into all possible positions; each circuit is independently optimized, and the parameter set from the circuit yielding the highest expectation value is adopted as the initial parameter for the next stage. Applying the proposed method to the MaxCut problem, we achieved up to approximately 11% higher approximation ratios compared to conventional Layerwise learning QAOA, while successfully mitigating early performance saturation observed at shallow depths. These results demonstrate the superior performance improvement capability of SIL QAOA. Furthermore, we also discuss its potential applicability to more complex optimization problems and deeper variational quantum circuits in future work.
The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It has been observed that the optimal parameters obtained from one instance of a COP can be transferred to another instance, resulting in generally good solutions for the latter. In this work, we propose a refinement scheme in which only a subset of QAOA layers is optimized following parameter transfer, with a focus on the Max-Cut problem. Our motivation is to reduce the complexity of the loss landscape when optimizing all the layers of high-depth QAOA circuits, as well as to reduce the optimization time. We investigate the potential hierarchical roles of different layers and analyze how the approximation ratio scales with increasing problem size. Our findings indicate that the selective layer optimization scheme offers a favorable trade-off between solution quality and computational time, and can be more beneficial than full optimization at a lower optimization time.