Exploring Tensor Network Algorithms as a Quantum-Inspired Method for Quantum Extreme Learning Machine

Quantum Extreme Learning Machine (QELM) has emerged as a promising hybrid quantum machine learning (QML) method that leverages the complex dynamics of quantum systems and classical machine learning models. Motivated by the development of this new QML method, we explore how quantum-inspired techniques like tensor networks (TNs), specifically the Time Dependent Variational Principle (TDVP) with Matrix Product State (MPS), can be used for the QELM algorithm. To demonstrate the utility of our quantum-inspired method, we performed numerical experiments on the MNIST dataset and compared the performance of our quantum-inspired QELM with different classical machine learning (ML) methods. The results reveal that high-quality embeddings can be generated by performing the time-evolution of MPS system consisting of one-dimensional chain of Rydberg atoms. This quantum-inspired method is highly scalable, enabling the simulation of 100 qubits with a low classical computing overhead. Finally, this study also underscores the potential of tensor networks as quantum-inspired algorithms to enhance the capability of quantum machine learning algorithms to study datasets with large numbers of features.