Two infinite families of nonadditive quantum error-correcting codes

TL;DR

This paper introduces two infinite families of nonadditive quantum error-correcting codes that outperform stabilizer codes in size, with a stabilizer-like structure allowing straightforward encoding circuit design.

Contribution

It explicitly constructs two infinite families of genuine nonadditive 1-error correcting quantum codes with larger coding subspaces than optimal stabilizer codes, characterized by a stabilizer-like structure.

Findings

Coding subspaces are 50% larger than optimal stabilizer codes.

Codes can be characterized by a stabilizer-like structure.

Encoding circuits are straightforward to design.

Abstract

We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear programming bound. All these nonadditive codes can be characterized by a stabilizer-like structure and thus their encoding circuits can be designed in a straightforward manner.