Tensor Networks and Quantum Error Correction
Quantum Physics
2014-07-23 v3 Information Theory
math.IT
Abstract
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Keywords
Cite
@article{arxiv.1312.4578,
title = {Tensor Networks and Quantum Error Correction},
author = {Andrew J. Ferris and David Poulin},
journal= {arXiv preprint arXiv:1312.4578},
year = {2014}
}
Comments
Accepted in Phys. Rev. Lett. 8 pages, 9 figures