Codeword-stabilized quantum codes on subsystems

Jeonghwan Shin, Jun Heo, Todd A. Brun

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Codeword-stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and nonadditive quantum codes. Standard codeword-stabilized quantum codes encode quantum information into subspaces. The more general notion of encoding quantum information into a subsystem is known as an operator (or subsystem) quantum error-correcting code. Most operator codes studied to date are based in the usual stabilizer formalism. We introduce operator quantum codes based on the codeword-stabilized quantum code framework. Based on the necessary and sufficient conditions for operator quantum error correction, we derive an error-correction condition for operator codeword-stabilized quantum codes. Based on this condition, the word operators of a operator codeword-stabilized quantum code are constructed from a set of classical binary errors induced by generators of the gauge group. We use this scheme to construct examples of both additive and nonadditive codes that encode quantum information into a subsystem.

Original languageEnglish
Article number042318
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume86
Issue number4
DOIs
Publication statusPublished - 2012 Oct 15

Fingerprint

operators
error correcting codes
coding
generators
formalism

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Codeword-stabilized quantum codes on subsystems. / Shin, Jeonghwan; Heo, Jun; Brun, Todd A.

In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 86, No. 4, 042318, 15.10.2012.

Research output: Contribution to journalArticle

@article{4b3a0c65f3544e9ea5864f3fddaa185c,
title = "Codeword-stabilized quantum codes on subsystems",
abstract = "Codeword-stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and nonadditive quantum codes. Standard codeword-stabilized quantum codes encode quantum information into subspaces. The more general notion of encoding quantum information into a subsystem is known as an operator (or subsystem) quantum error-correcting code. Most operator codes studied to date are based in the usual stabilizer formalism. We introduce operator quantum codes based on the codeword-stabilized quantum code framework. Based on the necessary and sufficient conditions for operator quantum error correction, we derive an error-correction condition for operator codeword-stabilized quantum codes. Based on this condition, the word operators of a operator codeword-stabilized quantum code are constructed from a set of classical binary errors induced by generators of the gauge group. We use this scheme to construct examples of both additive and nonadditive codes that encode quantum information into a subsystem.",
author = "Jeonghwan Shin and Jun Heo and Brun, {Todd A.}",
year = "2012",
month = "10",
day = "15",
doi = "10.1103/PhysRevA.86.042318",
language = "English",
volume = "86",
journal = "Physical Review A - Atomic, Molecular, and Optical Physics",
issn = "1050-2947",
publisher = "American Physical Society",
number = "4",

}

TY - JOUR

T1 - Codeword-stabilized quantum codes on subsystems

AU - Shin, Jeonghwan

AU - Heo, Jun

AU - Brun, Todd A.

PY - 2012/10/15

Y1 - 2012/10/15

N2 - Codeword-stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and nonadditive quantum codes. Standard codeword-stabilized quantum codes encode quantum information into subspaces. The more general notion of encoding quantum information into a subsystem is known as an operator (or subsystem) quantum error-correcting code. Most operator codes studied to date are based in the usual stabilizer formalism. We introduce operator quantum codes based on the codeword-stabilized quantum code framework. Based on the necessary and sufficient conditions for operator quantum error correction, we derive an error-correction condition for operator codeword-stabilized quantum codes. Based on this condition, the word operators of a operator codeword-stabilized quantum code are constructed from a set of classical binary errors induced by generators of the gauge group. We use this scheme to construct examples of both additive and nonadditive codes that encode quantum information into a subsystem.

AB - Codeword-stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and nonadditive quantum codes. Standard codeword-stabilized quantum codes encode quantum information into subspaces. The more general notion of encoding quantum information into a subsystem is known as an operator (or subsystem) quantum error-correcting code. Most operator codes studied to date are based in the usual stabilizer formalism. We introduce operator quantum codes based on the codeword-stabilized quantum code framework. Based on the necessary and sufficient conditions for operator quantum error correction, we derive an error-correction condition for operator codeword-stabilized quantum codes. Based on this condition, the word operators of a operator codeword-stabilized quantum code are constructed from a set of classical binary errors induced by generators of the gauge group. We use this scheme to construct examples of both additive and nonadditive codes that encode quantum information into a subsystem.

UR - http://www.scopus.com/inward/record.url?scp=84867553580&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867553580&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.86.042318

DO - 10.1103/PhysRevA.86.042318

M3 - Article

AN - SCOPUS:84867553580

VL - 86

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 4

M1 - 042318

ER -