A Scheme of Concatenated Quantum Code to Protect against both Computational Error and an Erasure

TL;DR

This paper proposes a concatenated quantum coding scheme that simultaneously protects quantum information against computational errors and a single erasure, combining graph codes and GHZ state encoding.

Contribution

It introduces a novel concatenated quantum code scheme integrating graph codes and GHZ states for dual error and erasure protection.

Findings

Effective encoding and decoding procedures are described.

The scheme provides protection against both errors and a single erasure.

The approach enhances quantum error correction capabilities.

Abstract

We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used encoding and decoding via scheme of GHZ states for protection against the occurrence of one quantum erasure.