Hybrid quantum tensor networks for aeroelastic applications

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.

Tensor networks for quantum machine learning

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems that classical computers are unable to solve efficiently. Their nature at the interface between physics and machine learning makes tensor networks easily deployable on quantum computers. In this review article, we shed light on one of the major architectures considered to be predestined for variational quantum machine learning. In particular, we discuss how layouts like MPS, PEPS, TTNs and MERA can be mapped to a quantum computer, how they can be used for machine learning and data encoding and which implementation techniques improve their performance.