Branching MERA codes: A natural extension of classical and quantum polar codes

We introduce a new class of circuits for constructing efficiently decodable quantum and classical error-correction codes, based on a recently discovered contractible tensor network known as branching multi-scale entanglement renormalization ansatz [1]. We perform an in-depth study of a particular example that can be thought of as an extension to Arikan's polar code [2]-[4]. Notably, our numerical simulation show that these codes polarize the logical channels more strongly while retaining the log-linear decoding complexity using the successive cancellation decoder. These codes also display improved error-correcting capability with only a minor impact on decoding complexity. Efficient decoding is realized using powerful graphical calculus tools developed in the field of quantum many-body physics.