@ARTICLE{10.3389/fphy.2020.586374,
AUTHOR={Kardashin, Andrey and Uvarov, Alexey and Biamonte, Jacob },
TITLE={Quantum Machine Learning Tensor Network States},
JOURNAL={Frontiers in Physics},
VOLUME={8},
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 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.

}}