Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes

TL;DR

This paper introduces a new class of quantum error correcting subsystem codes derived from two classical linear codes, offering simpler error correction routines and reduced stabilizer measurements compared to traditional codes.

Contribution

It presents a novel construction of quantum subsystem codes from classical linear codes, improving error correction efficiency over existing subspace codes.

Findings

Codes reduce the number of stabilizer measurements needed.

Subsystem codes offer simpler error correction routines.

Construction generalizes Shor's codes.

Abstract

The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most general method for encoding quantum information is to encode it into a subsystem, there exists a novel form of quantum error correction beyond the traditional quantum error correcting subspace codes. These new quantum error correcting subsystem codes differ from subspace codes in that their quantum correcting routines can be considerably simpler than related subspace codes. Here we present a class of quantum error correcting subsystem codes constructed from two classical linear codes. These codes are the subsystem versions of the quantum error correcting subspace codes which are generalizations of Shor's original quantum error correcting subspace codes. For every Shor-type code, the codes we present give a considerable savings in the number of stabilizer measurements needed in their error recovery routines.