Triorthogonal Codes and Self-dual Codes

TL;DR

This paper introduces an algorithm to construct binary triorthogonal matrices from self-dual codes, generalizes classical coding techniques to this setting, and provides propagation rules, advancing quantum error correction methods.

Contribution

It presents a novel algorithm linking self-dual codes to triorthogonal matrices and extends classical coding techniques to this quantum context.

Findings

Algorithm for constructing triorthogonal matrices from self-dual codes

Generalization of shortening and extending techniques

Development of simple propagation rules

Abstract

Triorthogonal matrices were introduced in Quantum Information Theory in connection with distillation of magic states (Bravyi and Haah (2012)). We give an algorithm to construct binary triorthogonal matrices from binary self-dual codes. Further, we generalize to this setting the classical coding techniques of shortening and extending. We also give some simple propagation rules.