Class of codes correcting absorptions and emissions

TL;DR

This paper introduces a broad family of quantum error-correcting codes, called AE codes, capable of correcting multiple types of quantum errors including emissions and absorptions, with practical constructions and mappings from existing codes.

Contribution

The authors develop simplified error correction conditions for AE codes, demonstrate mappings from permutation-invariant and spin codes to AE codes, and construct efficient examples in low angular momentum systems.

Findings

AE codes correct errors up to arbitrary fixed order

Permutation-invariant codes can be transformed into AE codes

Constructed efficient AE codes in low angular momentum systems

Abstract

We construct a general family of quantum codes that protect against all emission, absorption, dephasing, and raising/lowering errors up to an arbitrary fixed order. Such codes are known in the literature as absorption-emission (AE) codes. We derive simplified error correction conditions for a general AE code and show that any permutation-invariant code that corrects $\le t$ errors can be mapped to an AE code that corrects up to order-$t$ transitions. Carefully tuning the parameters of permutationally invariant codes, we construct several examples of efficient AE codes, hosted in systems with low total angular momentum. Our results also imply that spin codes can be mapped to AE codes, enabling us to characterize logical operators for certain subclasses of such codes.