The Phasor Measurement Unit (PMU) plays a crucial role in the real-time monitoring of power systems. Investigating the optimal PMU placement can not only provide full system observability but also reduce unnecessary installation costs. However, as a typical combinatorial optimization problem, determining the optimal PMU installation strategy is NP-hard and would cost significant computational resources for classical computers. In this work, a graph learning based acceleration strategy for the Quantum Approximation Optimization Algorithm (QAOA) is developed to effectively identify the optimal PMU placement. The proposed graph learning method will distill knowledge from the power grid to better initialize the QAOA parameter, boosting the overall implementation speed of QAOA. Empirical results indicate that our graph learning strategy can provide a 5% to 8% speedup to the QAOA execution. This work aims to provide a cornerstone in accelerated quantum computing to solve real-world power system applications.
The Phasor Measurement Unit (PMU) plays a crucial role in the real-time monitoring of power systems. Investigating the optimal PMU placement can not only provide full system observability but also reduce unnecessary installation costs. However, as a typical combinatorial optimization problem, determining the optimal PMU installation strategy is NP-hard and would cost significant computational resources for classical computers. In this work, a graph learning based acceleration strategy for the Quantum Approximation Optimization Algorithm (QAOA) is developed to effectively identify the optimal PMU placement. The proposed graph learning method will distill knowledge from the power grid to better initialize the QAOA parameter, boosting the overall implementation speed of QAOA. Empirical results indicate that our graph learning strategy can provide a 5% to 8% speedup to the QAOA execution. This work aims to provide a cornerstone in accelerated quantum computing to solve real-world power system applications.
With the significant expansion of renewable energy integration, the scale of the power grid also increases rapidly. To effectively monitor the operational state of large-scale power grids, optimizing the placement of Phasor Measurement Units (PMUs) is a critical research focus. Optimizing PMU Placement (OPP) is a typical combinatorial optimization problem with NP-hard complexity, which brings substantial challenges to classical computers. The sheer scale of modern grids forces classical solvers into prohibitive runtimes and sub-optimal local minima, degrading both execution speed and solution quality. Recent advances in quantum computing have opened new opportunities for tackling combinatorial optimization problems, particularly through the Quantum Approximate Optimization Algorithm (QAOA). However, QAOA operates as a hybrid quantum–classical framework, where determining the optimal parameters depends on a classical optimization process that remains computationally challenging and inherently NP-hard. On the other hand, in the Noisy Intermediate-Scale Quantum (NISQ) era, obtaining optimal optimization results typically requires a large number of quantum measurement shots. In this work, we propose a graph-learning-based strategy to provide QAOA with guided parameter initialization, enabling effective operation under limited quantum resources, particularly when the number of available measurement shots is restricted. Both the OPP problem and the channel-limitation task are investigated, where the proposed graph-learning-based parameter predictor enhances QAOA performance on both tasks, improving both the approximation ratio and computational efficiency. Furthermore, due to the complexity of the channel-limitation task and the scarcity of its pretraining data, a transfer learning strategy is employed to leverage knowledge from the original OPP task, where QAOA parameter datasets are more readily available to train the graph learning framework for the QAOA parameter predictor. The transfer learning approach also outperforms both random initialization and graph learning trained solely on the channel-limitation dataset in terms of the approximation ratio and the time efficiency. In general, this work is aimed at providing a new benchmark for solving complicated real-world power system optimization problems in the current NISQ era.
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 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.
We propose a machine learning based approach to accelerate quantum approximate optimization algorithm (QAOA) implementation which is a promising quantum-classical hybrid algorithm to prove the so-called quantum supremacy. In QAOA, a parametric quantum circuit and a classical optimizer iterates in a closed loop to solve hard combinatorial optimization problems. The performance of QAOA improves with increasing number of stages (depth) in the quantum circuit. However, two new parameters are introduced with each added stage for the classical optimizer increasing the number of optimization loop iterations. We note a correlation among parameters of the lower-depth and the higher-depth QAOA implementations and, exploit it by developing a machine learning model to predict the gate parameters close to the optimal values. As a result, the optimization loop converges in a fewer number of iterations. We choose graph MaxCut problem as a prototype to solve using QAOA. We perform a feature extraction routine using 100 different QAOA instances and develop a training data-set with 13, 860 optimal parameters. We present our analysis for 4 flavors of regression models and 4 flavors of classical optimizers. Finally, we show that the proposed approach can curtail the number of optimization iterations by on average 44.9% (up to 65.7%) from an analysis performed with 264 flavors of graphs.
The integration of quantum algorithms into machine learning pipelines offers a promising direction for addressing complex combinatorial optimization problems inherent in graph-structured data. This study investigates the use of the Quantum Approximate Optimization Algorithm (QAOA) as a quantum subroutine within a hybrid quantum–classical framework to enhance machine learning solutions for graph-based tasks. QAOA is employed to solve NP-hard graph optimization problems such as Max-Cut, graph coloring, and community detection, which are reformulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. The solutions provided by QAOA are then incorporated into machine learning models, such as Graph Neural Networks (GNNs) or clustering algorithms, as enriched features or optimized graph partitions. The hybrid approach is evaluated on benchmark datasets, demonstrating competitive accuracy and improved scalability in certain problem instances compared to purely classical methods. The findings highlight the potential of leveraging near-term quantum hardware for augmenting classical learning systems in domains such as logistics, social network analysis, and computational biology.
Graph-based combinatorial optimization problems are computationally challenging for classical optimization techniques due to their NP-hard nature. This paper proposes a novel Quantum-Assisted Hybrid Optimization Algorithm (QAHOA) that integrates the Quantum Approximate Optimization Algorithm (QAOA), spectral graph theory, and classical optimization strategies for graph-based combinatorial optimization. The developed framework uses spectral initialization via the graph Laplacian Fiedler vector to provide structurally informed starting variational parameters, aiming to stabilize the parameter search space and improve convergence trajectories under noisy conditions. The mathematical framework, alongside a convergence analysis to first-order stationary points, is provided to establish theoretical baseline properties. Evaluated on synthetic Erdős–Rényi random graph instances, the current study serves as a preliminary, small-to-medium-scale proof-of-concept. Controlled evaluations demonstrate that the proposed QAHOA achieves marginal yet stable and statistically significant improvements in mean cut values and approximation ratios over classical Greedy heuristics, Simulated Annealing, the standard QAOA, and Warm-Start QAOA. Formal paired hypothesis testing mathematically verifies the stability of the framework, while preliminary 4-qubit hardware executions demonstrate baseline architectural compatibility under physical NISQ noise channels.