Time-series forecasting for nonlinear high-dimensional system using hybrid method combining autoencoder and multi-parallelized quantum long short-term memory and gated recurrent unit

A time-series forecasting method for high-dimensional spatial data is proposed. The method involves optimal selection of sparse sensor positions to efficiently represent the spatial domain, time-series forecasting at these positions, and estimation of the entire spatial distribution from the forecasted values via a learned decoder. Sensor positions are selected using a method based on combinatorial optimization. Introducing multi-parallelized quantum long short-term memory (MP-QLSTM) and gated recurrent unit (MP-QGRU) improves time-series forecasting performance by extending QLSTM models using the same number of variational quantum circuits (VQCs) as the cell state dimensions. Unlike the original QLSTM, our method fully measures all qubits in each VQC, maximizing the representation capacity. MP-QLSTM and MP-QGRU achieve approximately 1.5% lower test loss than classical LSTM and GRU. The root mean squared percentage error of MP-QLSTM is 0.256% against the values measured independently using semiconductor pressure sensors, demonstrating the method's accuracy and effectiveness for high-dimensional forecasting tasks.