Codeword Stabilized Quantum Codes

TL;DR

This paper introduces a unifying framework for quantum error correcting codes that includes both stabilizer and nonadditive codes, leading to the discovery of new codes with better parameters and methods for constructing encoding circuits.

Contribution

It provides a comprehensive framework for quantum code design, enabling the creation of superior codes and systematic encoding circuit construction.

Findings

Discovered new quantum codes ((10,18,3)) and ((10,20,3)).

Unified approach encompasses all known code types.

Method for constructing encoding circuits for all codes in the framework.

Abstract

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with superior parameters to any previously known. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework.