# A Quantum-Classical Hybrid Framework for Multivariate Time-Series Forecasting Complexity-Fidelity Trade-offs and Limitations

arXiv: https://arxiv.org/abs/2607.16358 · HTML: https://mlsanity.com/paper/2607.16358/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 24 of 24)

- [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)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [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)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [AutoFormer: Searching Transformers for Visual Recognition](https://mlsanity.com/paper/2107.00651/) (2021)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Flowformer: Linearizing Transformers with Conservation Flows](https://mlsanity.com/paper/2202.06258/) (2022)
- [Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecasting](https://mlsanity.com/paper/2412.08851/) (2024)
- [Quantum Long Short-Term Memory (QLSTM) vs Classical LSTM in Time Series Forecasting: A Comparative Study in Solar Power Forecasting](https://mlsanity.com/paper/2310.17032/) (2023)
- [Quantum Adaptive Self-Attention for Quantum Transformer Models](https://mlsanity.com/paper/2504.05336/) (2025)
- [Rapid training of quantum recurrent neural networks](https://mlsanity.com/paper/2207.00378/) (2022)
- [Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Survey](https://mlsanity.com/paper/2407.17706/) (2024)
- [EDformer: Embedded Decomposition Transformer for Interpretable Multivariate Time Series Predictions](https://mlsanity.com/paper/2412.12227/) (2024)
- [Benchmarking Quantum and Classical Sequential Models for Urban Telecommunication Forecasting](https://mlsanity.com/paper/2508.04488/) (2025)
- [Multivariate Time Series Forecasting with Gate-Based Quantum Reservoir Computing on NISQ Hardware](https://mlsanity.com/paper/2510.13634/) (2025)
- [QuLTSF: Long-Term Time Series Forecasting with Quantum Machine Learning](https://mlsanity.com/paper/2412.13769/) (2024)
- [Integrating Quantum-Classical Attention in Patch Transformers for Enhanced Time Series Forecasting](https://mlsanity.com/paper/2504.00068/) (2025)
- [Quantum Temporal Fusion Transformer](https://mlsanity.com/paper/2508.04048/) (2025)
- [Quantum-Optimized Selective State Space Model for Efficient Time Series Prediction](https://mlsanity.com/paper/2509.00259/) (2025)

## Abstract (arXiv)

This paper presents a unified quantum-classical hybrid framework for multi-horizon time-series forecasting, introducing two model variants Quantum Reservoir Forecaster (QRC-F) and Variational Quantum Forecaster (VQF-F). The proposed framework investigates the complexity-fidelity trade-off of quantum forecasting under near-term NISQ hardware constraints. Continuous time-series signals are transformed into binary representations through uniform quantization and encoded into quantum states using angle encoding with parameterized RY rotation gates. Cross-channel entanglement layers capture dependencies among multiple variables. QRC-F utilizes a fixed random unitary quantum reservoir for stable, gradient-free temporal feature extraction, whereas VQF-F employs a trainable variational quantum circuit optimized through the parameter-shift rule to learn temporal and inter-variable patterns from Pauli expectation values. Both models replace computationally expensive quadratic self-attention with efficient linear transformations, reducing parameter complexity. A shared MIMO-based multi-horizon prediction head simultaneously generates forecasts across multiple horizons, avoiding error accumulation in recursive forecasting. Experimental evaluations on benchmark datasets, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, electricity, and exchange-rate, demonstrate that VQF-F achieves superior training stability and parameter efficiency, while QRC-F provides enhanced robustness and circuit fidelity under quantum noise. The results establish a practical quantum-native forecasting framework with strong potential for deployment on near-term NISQ devices.