Quantum Reupload Units: A Scalable and Expressive Approach for Time Series Learning

We propose a single-qubit Quantum Machine Learning (QML) model for time series forecasting, built around the concept of a Quantum Reupload Unit (QRU), a hardwareefficient quantum circuit architecture with shallow depth. The proposed model demonstrates enhanced predictive power compared to variational methods such as quantum circuits (VQC), parameterized quantum circuits (PQC), and quantum residual blocks (QRB). The proposed QRU outperforms classical learning models such as Recurrent Neural Networks (RNNs) and Long-Short Term Memory (LSTM) with the same number of parameters. The novelty of this approach is its ability to model temporal patterns without relying on an extensive memory state, which reduces resource demands while preserving forecast accuracy. The expressivity of the model is evaluated through Fourier spectral decomposition. We analyze the trainability of our model using the absorption witness metric. We benchmarked the proposed model on the Mackey-Glass chaotic time series and the real-world river level dataset from TAIAO. The proposed model consistently exhibits enhanced expressivity over both of the datasets. These results highlight the significance of QRUs as promising candidates for learning models that can be conveniently deployed on noisy intermediate-scale quantum (NISQ) hardware.