Quantum Classical Ridgelet Neural Network For Time Series Model

TL;DR

This paper addresses time-series forecasting under nonlinear dynamics by fusing ridgelet transforms with a quantum processing unit. It introduces a hybrid classical-quantum model in which the ridgelet expansion $g_J(x)=\sum_{i=1}^J c_i a_i^{-1/2} \eta\left(\frac{x\cdot u_i - b_i}{a_i}\right)$ is mapped to a quantum circuit whose sequence of $R_y$ gates collapses to $U_J(x)=R_y(2 g_J(x))$, yielding a nonlinear activation. Theoretical development provides a single-qubit QRNN framework with $|\eta_{\mathrm{in}}(x)\rangle = R_y(\Psi(x))|0\rangle$ and $\langle Z\rangle^{(J)}_x = \cos(2 g_J(x))$, connecting ridgelet theory to quantum information processing. Empirical results on six stock time series from Yahoo Finance show QRNN achieving lower RMSE and MAE than classical and other quantum baselines, indicating practical potential for quantum-assisted finance forecasting.

Abstract

In this study, we present a quantum computing method that incorporates ridglet transforms into the quantum processing pipelines for time series data. Here, the Ridgelet neural network is integrated with a single-qubit quantum computing method, which improves feature extraction and forecasting capabilities. Furthermore, experimental results using financial time series data demonstrate the superior performance of our model compared to existing models.

Figures (2)

• Figure 1: APPL
• Figure 2: AMAZON