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

This paper proposes and evaluates a hybrid classical-quantum neural network (HQNN-FSP) for financial stock market prediction, introducing a novel quantum ansatz and two optimization strategies to demonstrate the potential of quantum-assisted learning in capturing complex temporal dependencies and improving regression-based forecasting.

Original authors: Prashant Kumar Choudhary, Nouhaila Innan, Muhammad Shafique, Rajeev Singh

Published 2026-10-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Prashant Kumar Choudhary, Nouhaila Innan, Muhammad Shafique, Rajeev Singh

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The stock market is a vast, shifting landscape where prices rise and fall based on a tangled web of human emotion, global events, and economic data. For decades, investors and analysts have relied on computers to make sense of this chaos, using mathematical models to spot patterns in past prices and guess where the market might go next. These traditional computer programs are powerful, but they often struggle when the market behaves unpredictably or when the rules of the game change suddenly. They can get stuck on noise, mistaking random fluctuations for real trends, or fail to remember important lessons from the distant past. As the world's financial systems grow more complex, researchers have begun to look toward a different kind of computing power: quantum mechanics. This is the branch of physics that governs the behavior of the tiniest particles in the universe, where things can exist in multiple states at once and become deeply linked to one another in ways that seem impossible in our everyday world. The question driving a new line of inquiry is whether these strange quantum properties can help computers understand the stock market better than the classical machines we use today.

A team of researchers from India and the United Arab Emirates has taken a significant step in answering that question by building a new kind of prediction tool that mixes the old with the new. They created a system that combines standard, reliable computer models with a specialized quantum processor. Instead of asking a quantum computer to do everything from scratch, which is currently difficult due to the fragile nature of quantum hardware, they designed a hybrid approach. In this setup, a classical computer first digests the raw data, organizing it and pulling out the most important signals. It then hands this refined information over to a quantum circuit, which uses the unique rules of quantum physics to find deeper, more subtle connections that the classical computer might have missed. The researchers tested this system on historical stock data, specifically looking at the trading history of Wipro, a major technology company, along with several technical indicators that traders use to gauge market momentum.

The study explored two different ways to make this partnership work. In the first method, the classical computer acted as a filter, cleaning up the data and identifying key trends before passing them to the quantum system for a final analysis. In the second method, the two systems worked together in a single, unified loop, learning from each other simultaneously as they adjusted their internal settings to improve their predictions. The team ran thousands of simulations to see how well these hybrid models performed compared to using a quantum system alone or a classical system alone. They found that the hybrid approaches were consistently more accurate than the quantum-only version. By letting the classical computer handle the heavy lifting of data organization, the quantum part was able to focus on the complex patterns that truly mattered, resulting in fewer mistakes when predicting future prices.

However, the results also revealed the current limits of this technology. While the hybrid models were better than the quantum-only version, they still could not match the performance of the most advanced classical computer models available today. The researchers observed that all the models, including their own hybrid creations, struggled when the market underwent a sudden, sharp drop. When the price trend changed abruptly, the systems often failed to adjust quickly enough, continuing to predict based on the old pattern. This suggests that while the quantum component adds a new layer of insight, it is not yet a magic bullet that can instantly solve the problem of market volatility. The study also highlighted a trade-off between accuracy and speed. As the researchers added more quantum bits, the basic units of information in the quantum system, to their models, the predictions became slightly more accurate, but the time required to train the system grew significantly longer.

The researchers also looked closely at how their models made decisions. By using a technique that tracks which pieces of information influenced the final prediction the most, they confirmed that the system was paying attention to the right things. The model relied heavily on specific financial indicators, such as measures of market momentum and trend strength, rather than just random noise. This gives the system a level of transparency that is often missing in complex computer models, allowing analysts to understand why a prediction was made. The study concludes that while hybrid quantum-classical models are not yet ready to replace the tools used by professional traders, they represent a promising path forward. They show that by carefully combining the strengths of classical computing with the unique capabilities of quantum mechanics, it is possible to build systems that are more robust and insightful than either could be on its own. As quantum hardware continues to improve and become more stable, these hybrid systems may eventually play a transformative role in how we understand and navigate the financial world.

Technical Summary: HQNN-FSP

Problem Statement
Financial time-series forecasting remains a challenging task due to complex temporal dependencies, high volatility, non-linearity, and sensitivity to macroeconomic and geopolitical factors. While traditional Machine Learning (ML) models, such as Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) networks, have been widely used, they face limitations including overfitting, inadequate generalization in dynamic market conditions, and difficulty capturing long-range dependencies. Furthermore, classical models often struggle to capture intricate correlations in non-stationary markets. This study explores whether hybrid quantum-classical approaches can leverage quantum resources—specifically superposition and entanglement—to improve feature representation and learning for stock market regression tasks.

Methodology
The authors propose HQNN-FSP, a hybrid framework integrating classical deep learning with Quantum Neural Networks (QNNs). The methodology encompasses the following components:

Data Preparation: The study utilizes historical stock prices (Open, Close, High, Low) augmented with technical indicators: Relative Strength Index (RSI), Moving Average Convergence Divergence (MACD), and Average Directional Index (ADX). Features are selected using SelectKBest and normalized using MinMaxScaler.
Model Architectures: Three distinct architectures are evaluated:
1. CustomQNN: A standalone Quantum Neural Network based on a Parameterized Quantum Circuit (PQC) inspired by a Hamiltonian formulation. It uses angle encoding (single-qubit $R_Y$ and $R_Z$ gates) to map classical data to quantum states, followed by a custom ansatz featuring parameterized rotations and entangling operations (CNOT and CZ gates) to capture non-trivial dependencies.
2. HybridQNN1 (Sequential): A pipeline where a classical deep learning model (LSTM) first extracts temporal features from the data. These features are then encoded into quantum states and processed by a QNN regressor.
3. HybridQNN2 (Joint): An end-to-end framework where classical (LSTM) and quantum (PQC) components are trained simultaneously. Raw features are processed in parallel by both modules, and their outputs are fused in a dedicated layer before a final prediction. This allows for joint optimization of all parameters via backpropagation.
Training and Optimization: The models are trained using the ADAM optimizer with a learning rate schedule. To ensure temporal integrity, the study employs TimeSeriesSplit and k-fold cross-validation. Early stopping and batch normalization are used to prevent overfitting. The experiments are conducted on a quantum simulator (QULACS) and a High-Performance Computing cluster (PARAM Shivay).

Key Contributions

Hybrid Architecture Development: The paper proposes a seamless integration of custom-designed QNNs with classical architectures (RNN, LSTM, BiLSTM, GRU).
Custom QNN Regressor: Introduction of a QNN regressor utilizing a novel, customized ansatz and parameterized quantum circuits specifically optimized for financial time-series forecasting.
Dual Optimization Strategies: The exploration of two hybrid configurations: sequential feature extraction followed by quantum modeling (HybridQNN1) and joint optimization of classical and quantum parameters (HybridQNN2).
Systematic Evaluation: Comprehensive hyperparameter tuning and error analysis using TimeSeriesSplit, k-fold cross-validation, and Root Mean Square Error (RMSE) metrics.

Results

Performance Comparison: Hybrid models (HybridQNN1 and HybridQNN2) consistently outperformed the standalone CustomQNN, achieving lower RMSE values. Among the quantum-enhanced methods, HybridQNN2 achieved the lowest RMSE across all qubit configurations (3, 4, and 5 qubits).
Error Analysis: Gaussian fit and violin plot analyses revealed that hybrid models exhibited narrower error distributions centered near zero compared to the broader variance of the standalone QNN, indicating greater stability.
Classical vs. Hybrid: While hybrid models improved upon standalone quantum models, classical models (LSTM, RNN, BiLSTM, GRU) still achieved the lowest overall RMSE and required significantly less training time.
Qubit Impact: Increasing the qubit count generally improved accuracy for hybrid models but increased computational costs. Notably, HybridQNN1 showed a sharp rise in training time with 5 qubits, whereas HybridQNN2 remained relatively more efficient.
Market Regimes: All models, including hybrids, struggled to adapt to abrupt market shifts (regime changes), particularly during sharp downward trends, highlighting a limitation in responsiveness to rapid dynamics.

Significance and Claims
The paper claims that hybrid quantum-classical models offer a promising avenue for financial forecasting by leveraging quantum-enhanced feature spaces to improve pattern recognition, particularly under volatile conditions. The integration of domain-specific technical indicators (RSI, MACD) via SHAP analysis was found to significantly influence predictive output.

However, the authors maintain a modest stance regarding current capabilities. They acknowledge that while hybridization mitigates some limitations of standalone quantum models (such as high error variance), these models do not yet surpass state-of-the-art classical deep learning approaches in terms of RMSE or computational efficiency. The study concludes that hybrid models represent a viable path toward quantum-enhanced predictive analytics, but their practical deployment in financial markets requires further optimization in circuit design, noise resilience, and hardware scalability to narrow the performance gap with classical methods.

Technical Summary: HQNN-FSP

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