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

2026-03-10

AI Summary

This work proposes a hybrid quantum-classical framework for financial volatility forecasting that integrates long short-term memory (LSTM) networks with a quantum circuit Born machine (QCBM). Addressing the challenges posed by the nonlinearity and non-stationarity of financial time series, the LSTM component captures temporal dynamics, while the QCBM serves as a learnable prior module to model high-quality probability distributions. The two components are jointly optimized through an end-to-end hybrid training strategy. To the best of our knowledge, this is the first application of QCBM to financial volatility prediction, offering a generalizable architecture extensible to other complex tasks. Empirical evaluations on high-frequency data from the SSE Composite Index and CSI 300 demonstrate significant improvements over classical LSTM baselines across multiple metrics—including MSE, RMSE, and QLIKE—thereby validating the efficacy of quantum-enhanced modeling in financial forecasting.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• financial volatility forecasting
• non-linear time series
• non-stationary data
• quantum computing
• hybrid modeling

Innovation

• Quantum-Classical Hybrid
• Quantum Circuit Born Machine
• Financial Volatility Forecasting
• LSTM
• Quantum Machine Learning