Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

Nathaniel Wrobel; Anshumitra Baul; Ka Ming Tam; Juana Moreno

doi:10.3390/quantum4040042

Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

Nathaniel Wrobel, Anshumitra Baul, Ka Ming Tam, Juana Moreno

Research output: Contribution to journal › Article › peer-review

Abstract

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying 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 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 corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable 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. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.

Original language	English
Pages (from-to)	574-588
Number of pages	15
Journal	Quantum Reports
Volume	4
Issue number	4
DOIs	https://doi.org/10.3390/quantum4040042
State	Published - Dec 2022
Externally published	Yes

Funding

This manuscript is based on work supported by NSF DMR-1728457. This work involved use of the high-performance computational resources provided by the Louisiana Optical Network Initiative (http://www.loni.org (accessed on 1 December 2022)) and by HPC@LSU computing. JM and KMT are partially supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0017861. NW is supported by NSF OAC-1852454 with additional support from the Center for Computation & Technology at Louisiana State University.

Funders	Funder number
Center for Computation & Technology at Louisiana State University
National Science Foundation	DMR-1728457
U.S. Department of Energy
Office of Science
Basic Energy Sciences	DE-SC0017861, OAC-1852454

Keywords

convolutional neural network
quantum computing
quantum convolutional neural network
quantum machine learning
quantum neural network
quantum phase transition
transverse field Ising model
variational method
variational quantum eigensolver

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10.3390/quantum4040042

Cite this

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title = "Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver",

abstract = "Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying 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 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 corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding {\textquoteleft}phase{\textquoteright} of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.",

keywords = "convolutional neural network, quantum computing, quantum convolutional neural network, quantum machine learning, quantum neural network, quantum phase transition, transverse field Ising model, variational method, variational quantum eigensolver",

author = "Nathaniel Wrobel and Anshumitra Baul and Tam, {Ka Ming} and Juana Moreno",

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doi = "10.3390/quantum4040042",

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AU - Baul, Anshumitra

AU - Tam, Ka Ming

AU - Moreno, Juana

PY - 2022/12

Y1 - 2022/12

N2 - Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying 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 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 corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable 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. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.

AB - Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying 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 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 corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable 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. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.

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KW - quantum computing

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KW - quantum machine learning

KW - quantum neural network

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KW - variational method

KW - variational quantum eigensolver

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Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

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