Stabilizer Quantum Codes: A Unified View based on Forney-style Factor Graphs

TL;DR

This paper presents a unified graphical model framework for stabilizer quantum error-correcting codes using Forney-style factor graphs, enabling efficient decoding and unifying previous constructions.

Contribution

It extends duality results for Forney-style factor graphs to stabilizer label codes, providing a simple design rule that unifies earlier stabilizer code constructions.

Findings

Unified graphical model framework for stabilizer QECCs

Extended duality results for Forney-style factor graphs

A simple design rule for stabilizer label codes

Abstract

Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure that enables efficient and close-to-optimal iterative decoding. In this paper we focus on stabilizer QECCs, a class of QECCs whose construction is rendered non-trivial by the fact that the stabilizer label code, a code that is associated with a stabilizer QECC, has to satisfy a certain self-orthogonality condition. In order to design graphical models of stabilizer label codes that satisfy this condition, we extend a duality result for Forney-style factor graphs (FFGs) to the stabilizer label code framework. This allows us to formulate a simple FFG design rule for constructing stabilizer label codes, a design rule that unifies several earlier stabilizer label code constructions.