Tensor networks for quantum machine learning

Abstract

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.

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• Dequantizing quantum machine learning models using tensor networks
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• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines
• Vertex Representation of Hyperbolic Tensor Networks
• QAS-QTNs: Curriculum Reinforcement Learning-Driven Quantum Architecture Search for Quantum Tensor Networks
• A Taxonomy of Real Faults in Hybrid Quantum-Classical Architectures
• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks
• Adaptive Interpolating Quantum Transform: A Quantum-Native Framework for Efficient Transform Learning
• Explaining Anomalies with Tensor Networks