Tensor Networks and Quantum Error Correction

Understand

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.