Quantum Deletion Codes derived from Classical Deletion Codes (Extended Abstract)

@article{Hagiwara2022QuantumDC,
  title={Quantum Deletion Codes derived from Classical Deletion Codes (Extended Abstract)},
  author={Manabu Hagiwara},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.05699}
}
  • M. Hagiwara
  • Published 11 August 2022
  • Computer Science
  • ArXiv
This manuscript is an extended abstract version of the paper entitled “Quantum Deletion Codes derived from Classical Deletion Codes.” The paper contributes to the fundamental theory for quantum deletion error-correcting codes. The paper proposes a code construction condition for a partition of classical deletion error-correcting codes to derive quantum deletion error-correcting codes. The construction methods in this paper give examples of quantum codes that can correct single-quantum deletion… 
[PDF] Semantic Reader

34 References

Single Quantum Deletion Error-Correcting Codes

  • Ayumu NakayamaM. Hagiwara
  • Computer Science
    2020 International Symposium on Information Theory and Its Applications (ISITA)
  • 2020
It is proved that quantum deletion error-correcting codes can be constructed by two sets that satisfy the conditions, and problems that correct the deletion errors for quantum states are reduced to problems that find the sets satisfying the condition.

Permutation-Invariant Quantum Codes for Deletion Errors

This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes include examples of quantum codes that…

A Four-Qubits Code that is a Quantum Deletion Error-Correcting Code with the Optimal Length

It is proven that the length of any single deletion error-correcting codes is greater than or equal to 4, and the code provided is optimal for the code length.

The four qubits deletion code is the first quantum insertion code

The first quantum insertion code is provided, whose encoding is the same as the four-qubits deletion code, known as the theoretically shortest deletion code.

New Instances of Quantum Error-Correcting Codes for Single Deletion Errors

  • Taro Shibayama
  • Computer Science
    2020 International Symposium on Information Theory and Its Applications (ISITA)
  • 2020
This paper constructs new infinite series of quantum error-correcting codes for single deletion errors by using two sets of binary sequences that satisfy three conditions.

Permutation-invariant quantum coding for quantum deletion channels

  • Yingkai Ouyang
  • Computer Science
    2021 IEEE International Symposium on Information Theory (ISIT)
  • 2021
This work derives corresponding coding bounds for permutationinvariant quantum codes under quantum deletions from a specific family of N -qubit permutation-invariants quantum codes, which are called shifted gnu codes and can be performed in O(N) and O( N).

Constructios of l-adic t-deletion-correcting quantum codes

Two systematic constructions of deletion-correcting codes for protecting quantum inforomation are proposed, one of which allows conversion of stabilizer-based quantum codes to deletion-Correcting codes, and entanglement.

Equivalence of Quantum Single Insertion and Single Deletion Error-Correctabilities, and Construction of Codes and Decoders

The solution in Shibayama and Ouyang’s sense is provided in the single-error under the assumption of the purity of quantum codeword states; a class of codes that can correct both single deletion and single insertion is provided.

Optimal k-Deletion Correcting Codes

This work presents a k-deletion correcting code that has redundancy 8k log n + o(log n) and encoding/decoding algorithms of complexity O(n2k+1) for constant k and presents a solution to this longstanding open problem.

Bosonic quantum codes for amplitude damping

This work demonstrates alternative codes that correct just amplitude damping errors that allow, for example, a $t=1$, $k=1$ code using effectively $n=4.6$.