Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines

Abstract

Quantum Extreme Learning Machine (QELM) is an emerging hybrid quantum machine learning framework that leverages quantum system dynamics to enhance classical models. However, QELM can suffer from the exponential concentration problem, where excessive entanglement reduces model expressivity. In this work, we gain insight into this challenge and demonstrate how tensor network methods specifically, the Time Dependent Variational Principle (TDVP) with Matrix Product States (MPS) can efficiently simulate quantum systems while controlling entanglement and mitigating exponential concentration. Using numerical experiments on the Modified National Institute of Standards and Technology (MNIST) dataset, we show that time-evolving an MPS system modeled as a chain of Rydberg atoms produces high-quality data embeddings with low classical computational overhead. Our findings indicate that exact simulation of quantum dynamics is not necessary for strong machine learning performance; even approximate quantum embeddings can yield competitive results. Furthermore, we observe that both increased disorder in the quantum state achieved by tuning Hamiltonian parameters and careful control of entanglement directly correlate with improved model accuracy, highlighting the importance of these factors in optimizing QELM performance.