%A Kardashin,Andrey
%A Uvarov,Alexey
%A Biamonte,Jacob
%D 2021
%J Frontiers in Physics
%C
%F
%G English
%K Quantum computing,Quantum algorithms and circuits,tensor network algorithms,machine learning,Quantum information,Ground state - properties
%Q
%R 10.3389/fphy.2020.586374
%W
%L
%M
%P
%7
%8 2021-March-01
%9 Original Research
%#
%! NA
%*
%<
%T Quantum Machine Learning Tensor Network States
%U https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.586374
%V 8
%0 JOURNAL ARTICLE
%@ 2296-424X
%X Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar toolsâ€”called tensor network methodsâ€”form the backbone of modern numerical methods used to simulate many-body physics and have a further range of applications in machine learning. Finding and contracting tensor network states is a computational task, which may be accelerated by quantum computing. We present a quantum algorithm that returns a classical description of a rank-r tensor network state satisfying an area law and approximating an eigenvector given black-box access to a unitary matrix. Our work creates a bridge between several contemporary approaches, including tensor networks, the variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and quantum computation.