Deflating quantum error-correcting codes

TL;DR

This paper introduces a novel technique called deflation for quantum stabilizer codes, allowing for more flexible and potentially improved code parameters compared to traditional puncturing and shortening methods.

Contribution

The authors develop a generalization of puncturing and shortening for quantum codes, demonstrating how deflation offers enhanced control over code parameters and can yield better results.

Findings

Deflation can reduce quantum code length while controlling parameters.

Deflation provides more flexibility than consecutive puncturing and shortening.

Better code parameters can be achieved through deflation.

Abstract

In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases where more than a single qudit is removed. We show that the parameters of the deflated quantum code can be controlled, and argue that a similar approach is not as beneficial when applied to classical linear codes. Furthermore, it is shown that deflation introduces additional freedom compared to applying just puncturing and shortening consecutively. We exemplify that it is possible to obtain better parameters by deflating a code rather than consecutively using puncturing and shortening.