QAOA-Driven PMU placement optimization with graph learning-based parameter initialization refinement

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.