Tensor Networks and Quantum Error Correction
arXiv:1312.4578 · doi:10.1103/PhysRevLett.113.030501
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.
Accepted in Phys. Rev. Lett. 8 pages, 9 figures