Quantum Time-index Models with Reservoir for Time Series Forecasting

The time-index models are a class of time series forecasting models that map time-index features to forecasts in continuous space. Compared to the historical-value models, the time-index models can avoid the effect of data sampling frequency and are usually more expressive. However, the vanilla deep time-index model is weak in modeling the high-frequency components of time series and often requires the introduction of many parameters to enhance the modeling capability. Moreover, the time-index model learns only a mapping relationship and ignores the sequence relationship between temporal features, leading to a weak extrapolation capability in the forecast horizon. In this paper, inspired by the ability of quantum implicit neural representations to model the high-frequency components of signals with fewer parameters, we propose Quantum Time-Index Models with Reservoir (QuantumTime). Specifically, we introduce variational quantum circuits to address the challenge of representing high-frequency components in time series. Then, we introduce a reservoir that empowers QuantumTime with powerful extrapolation capabilities by exploiting the rich dynamical properties of reservoir computing. Ultimately, experiments conducted on chaotic datasets and various real-world datasets demonstrate that QuantumTime achieves highly competitive results compared to the state-of-the-art deep time-index model while reducing training parameters by at least 95%. Our approach provides a paradigm for utilizing potential quantum advantage in practical tasks.