A Hybrid Quantum-Classical Framework for Financial Volatility Forecasting Based on Quantum Circuit Born Machines

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Abstract

Accurate forecasting of financial market volatility is crucial for risk management, option pricing, and portfolio optimization. Traditional econometric models and classical machine learning methods face challenges in handling the inherent non-linear and non-stationary characteristics of financial time series. In recent years, the rapid development of quantum computing has provided a new paradigm for solving complex optimization and sampling problems. This paper proposes a novel hybrid quantum-classical computing framework aimed at combining the powerful representation capabilities of classical neural networks with the unique advantages of quantum models. For the specific task of financial market volatility forecasting, we designed and implemented a hybrid model based on this framework, which combines a Long Short-Term Memory (LSTM) network with a Quantum Circuit Born Machine (QCBM). The LSTM is responsible for extracting complex dynamic features from historical time series data, while the QCBM serves as a learnable prior module, providing the model with a high-quality prior distribution to guide the forecasting process. We evaluated the model on two real financial datasets consisting of 5-minute high-frequency data from the Shanghai Stock Exchange (SSE) Composite Index and CSI 300 Index. Experimental results show that, compared to a purely classical LSTM baseline model, our hybrid quantum-classical model demonstrates significant advantages across multiple key metrics, including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and QLIKE loss, proving the great potential of quantum computing in enhancing the capabilities of financial forecasting models. More broadly, the proposed hybrid framework offers a flexible architecture that may be adapted to other machine learning tasks involving high-dimensional, complex, or non-linear data distributions.