Benchmarking Quantum Neural Networks Developed for MBHB Coalescence in the Context of LISA Space Mission

Machine learning (ML) techniques are increasingly explored to analyse gravitational wave (GW) data expected from the Laser Interferometer Space Antenna (LISA). At the same time, advances in quantum computing have stimulated interest in quantum machine learning as a potential alternative to conventional approaches. We investigate the applicability of quantum, hybrid quantum-classical, and classical ML models to two tasks relevant for LISA observations of massive black hole binaries: GW signal detection and merger prediction. Using the Sangria dataset from the LISA Data Challenge, we benchmark several quantum architectures, including variational quantum classifiers (VQCs), post VQC hybrid models, quantum kernel methods, data reuploading classifiers, and quantum long short-term memory (QLSTM) networks, against classical support vector machines, multilayer perceptrons, recurrent neural networks, and LSTM networks. The models are trained on labelled data derived from the Sangria training dataset and evaluated on the corresponding blind dataset. For signal detection, several quantum models match or outperform classical baselines. In particular, the best performing hybrid post VQC architecture correctly identifies all signal samples in the blind dataset, while the standard VQC and data reuploading classifier achieve competitive detection rates. For merger detection and coalescence time estimation, however, the standard VQC emerges as the most reliable model, successfully localising all detected merger events with the lowest localisation errors. We further analyse the trade-offs between predictive performance, model complexity, and quantum circuit resources. Our results indicate that, although no universal quantum advantage is observed, selected quantum models can provide practical benefits for specific GW analysis tasks and represent promising candidates for future LISA data analysis pipelines.