title: Tensor networks and quantum error correction.
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.
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, 08860 Barcelona, Spain and Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse, 1, 85748 Garching, Germany and Département de Physique, Université de Sherbrooke, Québec J1K 2R1, Canada.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Ferris
authors.affiliation: Département de Physique, Université de Sherbrooke, Québec J1K 2R1, Canada.
authors.forename: David
authors.initials: D
authors.lastname: Poulin