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.

References in corpus (47)

• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Probing many-body dynamics on a 51-atom quantum simulator
• Efficient classical simulation of slightly entangled quantum computations
• Recent Advances in Physical Reservoir Computing: A Review
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Power of data in quantum machine learning
• Time-evolution methods for matrix-product states
• A rigorous and robust quantum speed-up in supervised machine learning
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Towards Quantum Machine Learning with Tensor Networks
• Information-theoretic bounds on quantum advantage in machine learning
• Time integration of tensor trains
• Lecture Notes of Tensor Network Contractions
• Opportunities in Quantum Reservoir Computing and Extreme Learning Machines
• Quantum reservoir computing with a single nonlinear oscillator
• On entropy growth and the hardness of simulating time evolution
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Time dynamics with matrix product states: Many-body localization transition of large systems revisited
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Information Processing Capacity of Spin-Based Quantum Reservoir Computing Systems
• Potential and limitations of quantum extreme learning machines
• Scalable photonic platform for real-time quantum reservoir computing
• Tensor network based machine learning of non-Markovian quantum processes
• Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments
• Performance of the time-dependent variational principle for matrix product states in long-time evolution of a pure state
• A machine learning approach to dynamical properties of quantum many-body systems
• Tensor networks for quantum machine learning
• Feedback-driven quantum reservoir computing for time-series analysis
• Tensor networks for unsupervised machine learning
• Interpretable Quantum Advantage in Neural Sequence Learning
• Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
• On fundamental aspects of quantum extreme learning machines
• Tensor networks for interpretable and efficient quantum-inspired machine learning
• Harnessing Quantum Extreme Learning Machines for image classification
• Tensor networks for quantum computing
• Entanglement in the quantum phases of an unfrustrated Rydberg atom array
• Simple Hamiltonian dynamics is a powerful quantum processing resource
• Geometric phase and multipartite entanglement of Rydberg atom chains