# Integrating Quantum-Classical Attention in Patch Transformers for Enhanced Time Series Forecasting

arXiv: https://arxiv.org/abs/2504.00068 · HTML: https://mlsanity.com/paper/2504.00068/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [AutoFormer: Searching Transformers for Visual Recognition](https://mlsanity.com/paper/2107.00651/) (2021)
- [ETSformer: Exponential Smoothing Transformers for Time-series Forecasting](https://mlsanity.com/paper/2202.01381/) (2022)
- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Time Series Prediction using Deep Learning Methods in Healthcare](https://mlsanity.com/paper/2108.13461/) (2021)
- [Systematic Literature Review: Quantum Machine Learning and its applications](https://mlsanity.com/paper/2201.04093/) (2022)
- [QSAN: A Near-term Achievable Quantum Self-Attention Network](https://mlsanity.com/paper/2207.07563/) (2022)
- [QKSAN: A Quantum Kernel Self-Attention Network](https://mlsanity.com/paper/2308.13422/) (2023)
- [Pay Attention to Evolution: Time Series Forecasting with Deep Graph-Evolution Learning](https://mlsanity.com/paper/2008.12833/) (2020)
- [Transferable Time-Series Forecasting under Causal Conditional Shift](https://mlsanity.com/paper/2111.03422/) (2021)
- [Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecasting](https://mlsanity.com/paper/2412.08851/) (2024)
- [Improved Financial Forecasting via Quantum Machine Learning](https://mlsanity.com/paper/2306.12965/) (2023)
- [EDformer: Embedded Decomposition Transformer for Interpretable Multivariate Time Series Predictions](https://mlsanity.com/paper/2412.12227/) (2024)

## Built on by (most cited first, 1 of 1)

- [A Quantum-Classical Hybrid Framework for Multivariate Time-Series Forecasting Complexity-Fidelity Trade-offs and Limitations](https://mlsanity.com/paper/2607.16358/) (2026)

## Abstract (arXiv)

QCAAPatchTF is a quantum attention network integrated with an advanced patch-based transformer, designed for multivariate time series forecasting, classification, and anomaly detection. Leveraging quantum superpositions, entanglement, and variational quantum eigensolver principles, the model introduces a quantum-classical hybrid self-attention mechanism to capture multivariate correlations across time points. For multivariate long-term time series, the quantum self-attention mechanism can reduce computational complexity while maintaining temporal relationships. It then applies the quantum-classical hybrid self-attention mechanism alongside a feed-forward network in the encoder stage of the advanced patch-based transformer. While the feed-forward network learns nonlinear representations for each variable frame, the quantum self-attention mechanism processes individual series to enhance multivariate relationships. The advanced patch-based transformer computes the optimized patch length by dividing the sequence length into a fixed number of patches instead of using an arbitrary set of values. The stride is then set to half of the patch length to ensure efficient overlapping representations while maintaining temporal continuity. QCAAPatchTF achieves state-of-the-art performance in both long-term and short-term forecasting, classification, and anomaly detection tasks, demonstrating state-of-the-art accuracy and efficiency on complex real-world datasets.