AUTHOR=Kardashin Andrey , Uvarov Alexey , Biamonte Jacob 

TITLE=Quantum Machine Learning Tensor Network States

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.586374

DOI=10.3389/fphy.2020.586374

ISSN=2296-424X

ABSTRACT=Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---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 quantum computers might be used to accelerate.  We present a quantum algorithm which 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 (QAOA), and quantum computation.