Quantum Phase Recognition using Quantum Tensor Networks

TL;DR

This paper explores a quantum machine learning approach using tensor network-inspired variational circuits for image classification and quantum phase recognition, achieving high accuracy on complex quantum models.

Contribution

It introduces a quantum tensor network-based variational ansatz for supervised learning, demonstrating high accuracy in quantum phase recognition tasks.

Findings

Achieved ≥98% test accuracy in quantum phase recognition

Studied the impact of tensor network layers on model expressibility

Applied MERA and TTN inspired circuits to quantum classification

Abstract

Machine learning (ML) has recently facilitated many advances in solving problems related to many-body physical systems. Given the intrinsic quantum nature of these problems, it is natural to speculate that quantum-enhanced machine learning will enable us to unveil even greater details than we currently have. With this motivation, this paper examines a quantum machine learning approach based on shallow variational ansatz inspired by tensor networks for supervised learning tasks. In particular, we first look at the standard image classification tasks using the Fashion-MNIST dataset and study the effect of repeating tensor network layers on ansatz's expressibility and performance. Finally, we use this strategy to tackle the problem of quantum phase recognition for the transverse-field Ising and Heisenberg spin models in one and two dimensions, where we were able to reach $\geq 98\%$ test-set accuracies with both multi-scale entanglement renormalization ansatz (MERA) and tree tensor network (TTN) inspired parametrized quantum circuits.