QURIOSO: Quantum gate parameter predictIon through quantum-enhanced long-short term memory

In Variational Quantum Algorithms (VQAs), circuit parameters are typically re-optimized from scratch for each new dataset, an approach that becomes inefficient in continuous computation settings where data arrive incrementally and statistical properties evolve over time. This limitation is exacerbated on noisy intermediate-scale quantum (NISQ) devices, where optimization is costly and prone to barren plateaus. To overcome these challenges, we introduce QURIOSO (QUantum gate parameteR predictIOn through quantum-enhanced long-Short term memOry), a machine learning framework that replaces repeated optimization with parameter prediction. QURIOSO learns trajectories of PQC parameters from past data and forecasts parameters for new data using either classical or quantum-enhanced LSTM architectures. We redesign quantum LSTM cells by employing Y-axis controlled rotations for amplitude modulation and full entanglement generation, enabling richer transformations than conventional phase-based designs. The framework operates in two modes: direct parameter transfer to unseen data and prediction-driven initialization to accelerate subsequent optimization. Validation on real-world binary classification tasks with hybrid classical–quantum models shows that quantum-enhanced LSTMs frequently outperform classical counterparts, highlighting their ability to preserve non-linearity through quantum encoding and measurement, and demonstrating the effectiveness of QURIOSO in generalizing across parameter trajectories within continuous quantum learning scenarios.