Graphical description of the action of local Clifford transformations on graph states

By Maarten Van den Nest, Jeroen Dehaene, B. De Moor. 2003

346 citations recorded by the source corpus.

We translate the action of local Clifford operations on graph states into transformations on their associated graphs, i.e., we provide transformation rules, stated in purely graph theoretical terms, which completely characterize the evolution of graph states under local Clifford operations. As we will show, there is essentially one basic rule, successive application of which generates the orbit of any graph state under local unitary operations within the Clifford group.

Subfields: Atomic and Molecular Physics, and Optics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/88436ee23020a3c3de29e25d1dae1c1fe8e691b5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Nicolas C. Menicucci
2. Steven T. Flammia
3. Peter van Loock
4. Miriam Backens
5. Claude Fabre
6. Nicolas Treps
7. Kyungjoo Noh
8. A. J. Ramsay

In Spectroscopy

1. Peter van Loock
2. Nicolas C. Menicucci
3. Steven T. Flammia

Citations in the corpus

• Graphical calculus for Gaussian pure states (2010, methodology): “A similar connection between complete graphs and star graphs is known for qubit cluster states [33, 34].”
• The ZX-calculus is complete for stabilizer quantum mechanics (2013, background): “Furthermore, any stabilizer state is equivalent to some graph state under local Clifford operations, which are tensor products of single qubit Clifford operators [13].”