Towards quantum machine learning with tensor networks

Huggins, William; Patil, Piyush; Mitchell, Bradley; Whaley, K. Birgitta; Stoudenmire, E. Miles

doi:10.1088/2058-9565/aaea94

Title: Towards quantum machine learning with tensor networks

Abstract

Machine learning is a promising application of quantum computing, but challenges remain for implementation today because near-term devices have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks, that could already have benefits with such near-term devices. The result is a unified framework in which classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes in which, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. Here, we demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a hybrid quantum-classical optimization procedure that could be carried out on quantum hardware today, and testing the noise resilience of the trained model.

Authors:

^[1]; Patil, Piyush ^[1]; Mitchell, Bradley ^[1];

^[1]; Stoudenmire, E. Miles ^[2]

Univ. of California, Berkeley, CA (United States)
Flatiron Inst., New York, NY (United States)

Publication Date:: Wed Jan 09 00:00:00 EST 2019

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Institutes of Health (NIH)

OSTI Identifier:: 1604671

Grant/Contract Number:: AC02-05CH11231; S1OD023532

Resource Type:: Accepted Manuscript

Journal Name:: Quantum Science and Technology

Additional Journal Information:: Journal Volume: 4; Journal Issue: 2; Journal ID: ISSN 2058-9565

Publisher:: IOPscience

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Huggins, William, Patil, Piyush, Mitchell, Bradley, Whaley, K. Birgitta, and Stoudenmire, E. Miles. Towards quantum machine learning with tensor networks.  United States: N. p., 2019. 
Web.  doi:10.1088/2058-9565/aaea94.

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                    Huggins, William, Patil, Piyush, Mitchell, Bradley, Whaley, K. Birgitta, & Stoudenmire, E. Miles. Towards quantum machine learning with tensor networks.  United States.  https://doi.org/10.1088/2058-9565/aaea94

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                    Huggins, William, Patil, Piyush, Mitchell, Bradley, Whaley, K. Birgitta, and Stoudenmire, E. Miles. Wed .  
"Towards quantum machine learning with tensor networks".  United States.  https://doi.org/10.1088/2058-9565/aaea94.  https://www.osti.gov/servlets/purl/1604671.

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@article{osti_1604671,

  title        = {Towards quantum machine learning with tensor networks},

  author       = {Huggins, William and Patil, Piyush and Mitchell, Bradley and Whaley, K. Birgitta and Stoudenmire, E. Miles},

  abstractNote = {Machine learning is a promising application of quantum computing, but challenges remain for implementation today because near-term devices have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks, that could already have benefits with such near-term devices. The result is a unified framework in which classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes in which, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. Here, we demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a hybrid quantum-classical optimization procedure that could be carried out on quantum hardware today, and testing the noise resilience of the trained model.},

  doi          = {10.1088/2058-9565/aaea94},

  journal      = {Quantum Science and Technology},

  number       = 2,

  volume       = 4,

  place        = {United States},

  year         = {Wed Jan 09 00:00:00 EST 2019},

  month        = {Wed Jan 09 00:00:00 EST 2019}

}

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Title: Towards quantum machine learning with tensor networks

Abstract

Citation Formats

Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice journal, January 2000

The density-matrix renormalization group in the age of matrix product states journal, January 2011

Implementation of the simultaneous perturbation algorithm for stochastic optimization journal, July 1998

Learning relevant features of data with multi-scale tensor networks journal, April 2018

Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines journal, August 2018

Characterizing quantum supremacy in near-term devices journal, April 2018

Class of Quantum Many-Body States That Can Be Efficiently Simulated journal, September 2008

Demonstration of a quantum error detection code using a square lattice of four superconducting qubits journal, April 2015

Unsupervised Generative Modeling Using Matrix Product States journal, July 2018

No Signaling and Quantum Key Distribution journal, June 2005

Tensor Network States and Geometry journal, June 2011

The theory of variational hybrid quantum-classical algorithms journal, February 2016

A variational eigenvalue solver on a photonic quantum processor journal, July 2014

A practical introduction to tensor networks: Matrix product states and projected entangled pair states journal, October 2014

A New Scheme for the Tensor Representation journal, October 2009

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law journal, December 2009

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer journal, October 1997

Gradient-based learning applied to document recognition journal, January 1998

Preparing Projected Entangled Pair States on a Quantum Computer journal, March 2012

Thermodynamic Limit of Density Matrix Renormalization journal, November 1995

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems journal, March 2008

Efficient Classical Simulation of Slightly Entangled Quantum Computations journal, October 2003

Preparing topological projected entangled pair states on a quantum computer journal, September 2013

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law text, January 2009

The density-matrix renormalization group in the age of matrix product states text, January 2010

Preparing projected entangled pair states on a quantum computer text, January 2011

Tensor network states and geometry text, January 2011

Characterizing Quantum Supremacy in Near-Term Devices text, January 2016

Unsupervised Generative Modeling Using Matrix Product States text, January 2017

Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines text, January 2017

Efficient classical simulation of slightly entangled quantum computations text, January 2003

Finitely correlated states on quantum spin chains journal, March 1992

A New Scheme for the Tensor Representation journal, October 2009

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems journal, March 2008

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law text, January 2009

Tensor network states and geometry text, January 2011

Efficient classical simulation of slightly entangled quantum computations text, January 2003

A fast quantum mechanical algorithm for database search preprint, January 1996

Tensor-Based Algorithms for Image Classification journal, November 2019

Parameterized quantum circuits as machine learning models journal, October 2019

Quantum convolutional neural networks journal, August 2019

Learning and inference on generative adversarial quantum circuits journal, May 2019

Matrix Product State–Based Quantum Classifier journal, July 2019

Variational quantum eigensolver with fewer qubits journal, September 2019

Generative tensor network classification model for supervised machine learning journal, February 2020

Hierarchical quantum classifiers journal, December 2018

Learning and Inference on Generative Adversarial Quantum Circuits text, January 2018

Variational Quantum Eigensolver with Fewer Qubits text, January 2019

Parameterized quantum circuits as machine learning models text, January 2019

Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice
journal, January 2000

The density-matrix renormalization group in the age of matrix product states
journal, January 2011

Implementation of the simultaneous perturbation algorithm for stochastic optimization
journal, July 1998

Learning relevant features of data with multi-scale tensor networks
journal, April 2018

Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines
journal, August 2018

Characterizing quantum supremacy in near-term devices
journal, April 2018

Class of Quantum Many-Body States That Can Be Efficiently Simulated
journal, September 2008

Demonstration of a quantum error detection code using a square lattice of four superconducting qubits
journal, April 2015

Unsupervised Generative Modeling Using Matrix Product States
journal, July 2018

No Signaling and Quantum Key Distribution
journal, June 2005

Tensor Network States and Geometry
journal, June 2011

The theory of variational hybrid quantum-classical algorithms
journal, February 2016

A variational eigenvalue solver on a photonic quantum processor
journal, July 2014

A practical introduction to tensor networks: Matrix product states and projected entangled pair states
journal, October 2014

A New Scheme for the Tensor Representation
journal, October 2009

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
journal, December 2009

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
journal, October 1997

Gradient-based learning applied to document recognition
journal, January 1998

Preparing Projected Entangled Pair States on a Quantum Computer
journal, March 2012

Thermodynamic Limit of Density Matrix Renormalization
journal, November 1995

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
journal, March 2008

Efficient Classical Simulation of Slightly Entangled Quantum Computations
journal, October 2003

Preparing topological projected entangled pair states on a quantum computer
journal, September 2013

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
text, January 2009

The density-matrix renormalization group in the age of matrix product states
text, January 2010

Preparing projected entangled pair states on a quantum computer
text, January 2011

Tensor network states and geometry
text, January 2011

Characterizing Quantum Supremacy in Near-Term Devices
text, January 2016

Unsupervised Generative Modeling Using Matrix Product States
text, January 2017

Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines
text, January 2017

Efficient classical simulation of slightly entangled quantum computations
text, January 2003

Finitely correlated states on quantum spin chains
journal, March 1992

A New Scheme for the Tensor Representation
journal, October 2009

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
journal, March 2008

Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
text, January 2009

Tensor network states and geometry
text, January 2011

Efficient classical simulation of slightly entangled quantum computations
text, January 2003

A fast quantum mechanical algorithm for database search
preprint, January 1996

Tensor-Based Algorithms for Image Classification
journal, November 2019

Parameterized quantum circuits as machine learning models
journal, October 2019

Quantum convolutional neural networks
journal, August 2019

Learning and inference on generative adversarial quantum circuits
journal, May 2019

Matrix Product State–Based Quantum Classifier
journal, July 2019

Variational quantum eigensolver with fewer qubits
journal, September 2019

Generative tensor network classification model for supervised machine learning
journal, February 2020

Hierarchical quantum classifiers
journal, December 2018

Learning and Inference on Generative Adversarial Quantum Circuits
text, January 2018

Variational Quantum Eigensolver with Fewer Qubits
text, January 2019

Parameterized quantum circuits as machine learning models
text, January 2019