High performance single-error-correcting quantum codes for amplitude damping

TL;DR

This paper introduces high-performance, nonadditive quantum amplitude damping codes that outperform existing codes for most block lengths, utilizing classical nonlinear and ternary codes with efficient encoding and decoding.

Contribution

The paper presents novel nonadditive quantum amplitude damping codes constructed from classical nonlinear and ternary codes, achieving better parameters than prior codes for lengths greater than 7.

Findings

Codes outperform additive codes in encoded dimension.

Construction methods include classical asymmetric and ternary codes.

Codes have efficient encoding and decoding circuits.

Abstract

We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear error-correcting codes for classical asymmetric channels, with which we systematically construct quantum amplitude damping codes with parameters better than any prior construction known for any block length n > 7 except n=2^r-1. We generalize this construction to employ classical codes over GF(3) with which we numerically obtain better performing codes up to length 14. Because the resulting codes are of the codeword stabilized (CWS) type, easy encoding and decoding circuits are available.