An Application of Quantum Machine Learning on Quantum Correlated Systems: Quantum Convolutional Neural Network as a Classifier for Many-Body Wavefunctions from the Quantum Variational Eigensolver

TL;DR

This paper demonstrates that a quantum convolutional neural network trained on wavefunctions from a variational quantum eigensolver can accurately classify phases in a quantum many-body system, aiding the identification of quantum critical points.

Contribution

It introduces the application of a quantum convolutional neural network to classify phases of matter in quantum systems using wavefunctions from the variational quantum eigensolver.

Findings

QCNN accurately distinguishes paramagnetic and ferromagnetic phases.

QCNN predicts phases near the quantum critical point.

Training on wavefunctions away from criticality enables phase identification.

Abstract

Machine learning has been applied on a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems for the identification of phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present here the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions which correspond to the paramagnetic phase and the ferromagnetic phase of the TFIM with good accuracy. The QCNN can be trained to predict the corresponding phase of wavefunctions around the putative quantum critical point, even though it is trained by wavefunctions far away from it. This provides a basis for exploiting the QCNN to identify the quantum critical point.