### Abstract

A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a superposition of logical qubits of the related graph code. By using the relation, we first discuss that a local complementation which has been used for a graph state can be useful for searching locally equivalent stabilizer codes, and second provide a method to find a stabilizer group of a graph code.

Original language | English |
---|---|

Pages (from-to) | 237-250 |

Number of pages | 14 |

Journal | Quantum Information and Computation |

Volume | 16 |

Issue number | 3-4 |

Publication status | Published - 2016 Mar 1 |

### Fingerprint

### Keywords

- Graph code
- Graph state
- Local complementation
- Stabilizer formalism

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics
- Nuclear and High Energy Physics

### Cite this

*Quantum Information and Computation*,

*16*(3-4), 237-250.

**On the relation between a graph code and a graph state.** / Hwang, Yongsoo; Heo, Jun.

Research output: Contribution to journal › Article

*Quantum Information and Computation*, vol. 16, no. 3-4, pp. 237-250.

}

TY - JOUR

T1 - On the relation between a graph code and a graph state

AU - Hwang, Yongsoo

AU - Heo, Jun

PY - 2016/3/1

Y1 - 2016/3/1

N2 - A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a superposition of logical qubits of the related graph code. By using the relation, we first discuss that a local complementation which has been used for a graph state can be useful for searching locally equivalent stabilizer codes, and second provide a method to find a stabilizer group of a graph code.

AB - A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a superposition of logical qubits of the related graph code. By using the relation, we first discuss that a local complementation which has been used for a graph state can be useful for searching locally equivalent stabilizer codes, and second provide a method to find a stabilizer group of a graph code.

KW - Graph code

KW - Graph state

KW - Local complementation

KW - Stabilizer formalism

UR - http://www.scopus.com/inward/record.url?scp=84953883915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84953883915&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84953883915

VL - 16

SP - 237

EP - 250

JO - Quantum Information and Computation

JF - Quantum Information and Computation

SN - 1533-7146

IS - 3-4

ER -