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Title: Towards quantum machine learning with tensor networks

Journal Article · · Quantum Science and Technology
ORCiD logo [1];  [1];  [1]; ORCiD logo [1];  [2]
  1. Univ. of California, Berkeley, CA (United States)
  2. Flatiron Inst., New York, NY (United States)
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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.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); National Institutes of Health (NIH)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1604671
Journal Information:
Quantum Science and Technology, Journal Name: Quantum Science and Technology Journal Issue: 2 Vol. 4; ISSN 2058-9565
Publisher:
IOPscienceCopyright Statement
Country of Publication:
United States
Language:
English

References (40)

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
Finitely correlated states on quantum spin chains journal March 1992
A New Scheme for the Tensor Representation journal October 2009
Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice journal January 2000
Tensor Network States and Geometry journal June 2011
The density-matrix renormalization group in the age of matrix product states journal January 2011
A practical introduction to tensor networks: Matrix product states and projected entangled pair states journal October 2014
A variational eigenvalue solver on a photonic quantum processor journal July 2014
Demonstration of a quantum error detection code using a square lattice of four superconducting qubits journal April 2015
Characterizing quantum supremacy in near-term devices journal April 2018
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems journal March 2008
The theory of variational hybrid quantum-classical algorithms journal February 2016
Learning relevant features of data with multi-scale tensor networks journal April 2018
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 journal December 2009
Class of Quantum Many-Body States That Can Be Efficiently Simulated journal September 2008
Preparing Projected Entangled Pair States on a Quantum Computer journal March 2012
Thermodynamic Limit of Density Matrix Renormalization journal November 1995
Efficient Classical Simulation of Slightly Entangled Quantum Computations journal October 2003
No Signaling and Quantum Key Distribution journal June 2005
Unsupervised Generative Modeling Using Matrix Product States journal July 2018
Gradient-based learning applied to document recognition journal January 1998
Implementation of the simultaneous perturbation algorithm for stochastic optimization journal July 1998
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer journal October 1997
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer journal January 1999
Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines journal August 2018
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

Cited By (12)

Hierarchical quantum classifiers journal December 2018
Quantum convolutional neural networks journal August 2019
Parameterized quantum circuits as machine learning models journal October 2019
Learning and inference on generative adversarial quantum circuits journal May 2019
Generative tensor network classification model for supervised machine learning journal February 2020
Variational quantum eigensolver with fewer qubits journal September 2019
Differentiable Programming Tensor Networks journal September 2019
Matrix Product State–Based Quantum Classifier journal July 2019
Tensor-Based Algorithms for Image Classification journal November 2019
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

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71 CLASSICAL AND QUANTUM MECHANICS
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