# Machine Learning Phase Transitions with a Quantum Processor

## TL;DR

This paper introduces a quantum algorithm combining quantum simulation and machine learning to classify phases of matter efficiently, overcoming classical simulation limitations and achieving high accuracy on quantum models.

## Contribution

It presents a novel variational quantum classifier using tensor network-inspired states and a quantum neural network, advancing quantum phase classification methods.

## Key findings

- Achieved 99% accuracy on the transverse field Ising model.
- Achieved 94% accuracy on the XXZ model.
- Proposed tensor network-inspired variational states and a quantum neural network.

## Abstract

Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods$-$such as Monte Carlo$-$which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented method recovers. Finally, we propose a nearest-neighbour (checkerboard) quantum neural network. This majority vote quantum classifier is successfully trained to recognize phases of matter with $99\%$ accuracy for the transverse field Ising model and $94\%$ accuracy for the XXZ model. These findings suggest that our merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.