Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes

TL;DR

This paper introduces an efficient heuristic decoding scheme for foliated quantum codes, enabling improved fault-tolerant quantum error correction in quantum networks and computation.

Contribution

It presents a novel message passing decoding method for foliated quantum codes and demonstrates its effectiveness on turbo and bicycle codes.

Findings

High numerical performance thresholds achieved

Effective decoding for turbo and bicycle codes

Construction schedule for code states provided

Abstract

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.