Correction of Data and Syndrome Errors by Stabilizer Codes

TL;DR

This paper introduces quantum data-syndrome (DS) codes that can correct errors in both data qubits and syndrome bits, enhancing the reliability of quantum error correction.

Contribution

It proposes the concept of quantum DS codes and provides CSS-type constructions, advancing error correction techniques in quantum computing.

Findings

Quantum DS codes can correct errors in data and syndrome bits.

Fundamental properties of quantum DS codes are characterized.

CSS-type constructions of quantum DS codes are developed.

Abstract

Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea of quantum data-syndrome (DS) codes that are capable of correcting both data qubits and syndrome bits errors. We study fundamental properties of quantum DS codes and provide several CSS-type code constructions of quantum DS codes.