Codeword Stabilized Quantum Codes for Asymmetric Channels

TL;DR

This paper extends the codeword stabilized quantum code framework to asymmetric error models, enabling the discovery of new quantum codes for amplitude and phase damping noise with improved parameters.

Contribution

It introduces a method to adapt CWS quantum codes to asymmetric channels and exhaustively searches for optimal codes up to length 9, finding many new codes including nonadditive and degenerate ones.

Findings

Discovered numerous new quantum codes with good parameters.

Developed an exhaustive search method for codes up to length 9.

Identified codes that correct multiple amplitude damping errors.

Abstract

We discuss a method to adapt the codeword stabilized (CWS) quantum code framework to the problem of finding asymmetric quantum codes. We focus on the corresponding Pauli error models for amplitude damping noise and phase damping noise. In particular, we look at codes for Pauli error models that correct one or two amplitude damping errors. Applying local Clifford operations on graph states, we are able to exhaustively search for all possible codes up to length $9$. With a similar method, we also look at codes for the Pauli error model that detect a single amplitude error and detect multiple phase damping errors. Many new codes with good parameters are found, including nonadditive codes and degenerate codes.