HQNN-FSP: A Hybrid Classical-Quantum Neural Network for Regression-Based Financial Stock Market Prediction

TL;DR

The paper tackles stock price forecasting by introducing hybrid quantum-classical architectures that integrate a customized QNN regressor with classical deep learning components. It presents a Hamiltonian-based PQC with angle encoding and two integration schemes, HybridQNN1 and HybridQNN2, augmented by domain-specific indicators RSI, MACD, and ADX. The models are evaluated with TimeSeriesSplit and k-fold cross-validation using the ADAM optimizer and RMSE as the metric, and results show that HybridQNN2 achieves the lowest RMSE among quantum methods while offering improved stability over standalone QNNs, though classical baselines still perform best overall. The work demonstrates the practical potential of quantum-assisted learning for financial time-series forecasting and outlines concrete avenues for improving scalability, noise resilience, and integration with real quantum hardware.

Abstract

Financial time-series forecasting remains a challenging task due to complex temporal dependencies and market fluctuations. This study explores the potential of hybrid quantum-classical approaches to assist in financial trend prediction by leveraging quantum resources for improved feature representation and learning. A custom Quantum Neural Network (QNN) regressor is introduced, designed with a novel ansatz tailored for financial applications. Two hybrid optimization strategies are proposed: (1) a sequential approach where classical recurrent models (RNN/LSTM) extract temporal dependencies before quantum processing, and (2) a joint learning framework that optimizes classical and quantum parameters simultaneously. Systematic evaluation using TimeSeriesSplit, k-fold cross-validation, and predictive error analysis highlights the ability of these hybrid models to integrate quantum computing into financial forecasting workflows. The findings demonstrate how quantum-assisted learning can contribute to financial modeling, offering insights into the practical role of quantum resources in time-series analysis.

Figures (11)

• Figure 1: Stock price forecasting plot displaying historical prices (blue), a predicted trend (red) with a 95% confidence interval (shaded), and a clear train/test split. The observed increasing volatility highlights the challenges of financial forecasting and underscores the need for robust hybrid quantum-classical models.
• Figure 2: Schematic illustrating key challenges in classical modeling, motivating the exploration of quantum approaches. (a) Overfitting in classical models: A low-degree polynomial fit (pink) captures noise rather than the true trend, highlighting the limitations of classical curve-fitting techniques. (b) Failure to model long-term dependencies: While both classical LSTM (red) and quantum RNN (blue) models extend trends, neither fully captures complex dependencies, suggesting the need for improved architectures. (c) Poor generalization in non-stationary markets: Forecasts struggle in volatile regimes, where classical models show some alignment with the true trend, but quantum predictions exhibit larger deviations, raising questions about their robustness. (d) Quantum feature space: Nonlinear transformations in classical feature spaces can mimic certain quantum effects, yet the potential for quantum-enhanced representations remains an open question. Together, these findings highlight the need for further investigation into whether quantum models can provide genuine advantages beyond classical methods. The visualizations presented are conceptual representations rather than outputs from actual quantum models.
• Figure 3: Overview of the proposed hybrid quantum-classical methodology.
• Figure 4: Angle encoding circuit, where each qubit $q_i$ is encoded using a parameterized $R_Y$ gate with angle $\arcsin(f(x_i))$ followed by an $R_Z$ gate with angle $\arccos(g(x_i))$, mapping the classical input $x_i$ into a quantum state via nonlinear transformations.
• Figure 5: Customized quantum ansatz utilized in QNN (also in HybridQNN2). The circuit integrates parameterized single-qubit rotations and entangling operations to enhance feature representation and learning capacity.