Decoding schemes for foliated sparse quantum error-correcting codes
A. Bolt, David Poulin, Thomas M. Stace · Physical Review A · 2018
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error correcting codes into larger fault-tolerant networks. Here, we present an efficient heuristic decoding scheme for foliated quantum codes, based on message passing between primal and dual code ``sheets.'' We test this decoder on two different families of sparse quantum error correcting code: turbo codes and bicycle codes, and show reasonably high numerical performance thresholds. We also present a construction schedule for building such code states.