标题： 基于自编码器与多并行化量子长短期记忆和门控循环单元混合方法的非线性高维系统时间序列预测 显示英文标题

标题： 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

摘要： 一种针对高维空间数据的时间序列预测方法被提出。 该方法包括最优选择稀疏传感器位置以高效表示空间域，这些位置的时间序列预测，以及通过学习的解码器从预测值估计整个空间分布。 传感器位置是使用基于组合优化的方法选择的。 引入多并行量子长短期记忆（MP-QLSTM）和门控循环单元（MP-QGRU）通过使用与单元状态维度相同数量的变分量子电路（VQCs）扩展QLSTM模型，从而提高时间序列预测性能。 与原始的QLSTM不同，我们的方法在每个VQC中完全测量所有量子比特，最大化表示能力。 MP-QLSTM和MP-QGRU的测试损失比经典LSTM和GRU低约1.5%。 MP-QLSTM的均方百分比误差为0.256%，相对于使用半导体压力传感器独立测量的数值，证明了该方法在高维预测任务中的准确性和有效性。 显示英文摘要

摘要： 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.