### 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 |
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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 |

### 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

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## Cite this

Hwang, Y., & Heo, J. (2016). On the relation between a graph code and a graph state.

*Quantum Information and Computation*,*16*(3-4), 237-250.