Permutation-Invariant Quantum Codes for Deletion Errors

TL;DR

This paper introduces permutation-invariant quantum codes capable of correcting multiple deletion errors and combined errors, marking a significant advancement in quantum error correction techniques.

Contribution

It provides the first construction of quantum codes that correct multiple deletions and combine multiple-qubit and deletion error correction.

Findings

First example of quantum codes correcting two or more deletions

Quantum codes correcting both multiple-qubit and deletion errors

Generalization of code construction methods

Abstract

This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion errors. Also, our codes give the first example of quantum codes that can correct both multiple-qubit errors and multiple-deletion errors. We also discuss a generalization of the construction of our codes at the end.