# A Hybrid Quantum Circuit Born Machine Framework for Financial Volatility Forecasting: Quantum-Assisted Training and Classical Inference

arXiv: https://arxiv.org/abs/2603.09789 · HTML: https://mlsanity.com/paper/2603.09789/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Listening to Chaotic Whispers: A Deep Learning Framework for News-oriented Stock Trend Prediction](https://mlsanity.com/paper/1712.02136/) (2017)
- [Foundations for Near-Term Quantum Natural Language Processing](https://mlsanity.com/paper/2012.03755/) (2020)
- [Quantum versus Classical Generative Modelling in Finance](https://mlsanity.com/paper/2008.00691/) (2020)
- [Multi-Transformer: A New Neural Network-Based Architecture for Forecasting S&P Volatility](https://mlsanity.com/paper/2109.12621/) (2021)
- [HQNN-FSP: A Hybrid Classical-Quantum Neural Network for Regression-Based Financial Stock Market Prediction](https://mlsanity.com/paper/2503.15403/) (2025)
- [QADQN: Quantum Attention Deep Q-Network for Financial Market Prediction](https://mlsanity.com/paper/2408.03088/) (2024)
- [Contextual Quantum Neural Networks for Stock Price Prediction](https://mlsanity.com/paper/2503.01884/) (2025)
- [Quantum vs. Classical Machine Learning: A Benchmark Study for Financial Prediction](https://mlsanity.com/paper/2601.03802/) (2026)
- [From GARCH to Neural Network for Volatility Forecast](https://mlsanity.com/paper/2402.06642/) (2024)
- [Quantum Temporal Convolutional Neural Networks for Cross-Sectional Equity Return Prediction: A Comparative Benchmark Study](https://mlsanity.com/paper/2512.06630/) (2025)
- [Hybrid Quantum-Classical Ensemble Learning for S&P 500 Directional Prediction](https://mlsanity.com/paper/2512.15738/) (2025)

## Abstract (arXiv)

Accurate financial volatility forecasting is crucial but challenged by the non-linear, highly correlated nature of market data. Recently, quantum computing has emerged as a promising paradigm for solving complex high-dimensional sampling problems. To harness this, we propose a novel hybrid framework combining the temporal representation power of classical neural networks with the distribution-learning capabilities of quantum models. Specifically, we integrate a Long Short-Term Memory (LSTM) network with a Quantum Circuit Born Machine (QCBM). The LSTM extracts dynamic features, while the QCBM acts as a learnable generative prior modeling complex market distributions to guide forecasting. Evaluated on 5-minute high-frequency data from the SSE Composite and CSI 300 indices, our model significantly outperforms a classical LSTM baseline across MSE, RMSE, and QLIKE metrics. Furthermore, by introducing a stochastic ``Drop-Prior" mechanism during training, the LSTM implicitly distills structured information from the quantum prior. This establishes a pragmatic paradigm of ``quantum-assisted training with classical-efficient inference", whereby the model retains its quantum-enhanced accuracy even when the quantum module is entirely disabled during deployment. This demonstrates a practical pathway for leveraging quantum computing to enhance classical models without real-time quantum inference latency.