# Hybrid quantum tensor networks for aeroelastic applications

arXiv: https://arxiv.org/abs/2508.05169 · HTML: https://mlsanity.com/paper/2508.05169/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [PED-ANOVA: Efficiently Quantifying Hyperparameter Importance in Arbitrary Subspaces](https://mlsanity.com/paper/2304.10255/) (2023)
- [A Multi-Scale Tensor Network Architecture for Classification and Regression](https://mlsanity.com/paper/2001.08286/) (2020)
- [Tensor Network alternating linear scheme for MIMO Volterra system identification](https://mlsanity.com/paper/1607.00127/) (2016)
- [Classification of the Fashion-MNIST Dataset on a Quantum Computer](https://mlsanity.com/paper/2403.02405/) (2024)

## Abstract (arXiv)

We investigate the application of hybrid quantum tensor networks to aeroelastic problems, harnessing the power of Quantum Machine Learning (QML). By combining tensor networks with variational quantum circuits, we demonstrate the potential of QML to tackle complex time series classification and regression tasks. Our results showcase the ability of hybrid quantum tensor networks to achieve high accuracy in binary classification. Furthermore, we observe promising performance in regressing discrete variables. While hyperparameter selection remains a challenge, requiring careful optimisation to unlock the full potential of these models, this work contributes significantly to the development of QML for solving intricate problems in aeroelasticity. We present an end-to-end trainable hybrid algorithm. We first encode time series into tensor networks to then utilise trainable tensor networks for dimensionality reduction, and convert the resulting tensor to a quantum circuit in the encoding step. Then, a tensor network inspired trainable variational quantum circuit is applied to solve either a classification or a multivariate or univariate regression task in the aeroelasticity domain.