# On the relation between a graph code and a graph state

Yongsoo Hwang, Jun Heo

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 237-250 14 Quantum Information and Computation 16 3-4 Published - 2016 Mar 1

### Fingerprint

Graph in graph theory
Complementation
Qubit
Simple Graph
Superposition

### 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

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

In: Quantum Information and Computation, Vol. 16, No. 3-4, 01.03.2016, p. 237-250.

Research output: Contribution to journalArticle

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