From graph states to two-graph states

The name `graph state' is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the two-graph state, this being a generalisation of the graph state and a two-graph representation of a stabilizer state. Mathematically, the two-graph state can be viewed as a simultaneous generalisation of a binary linear code and quadratic Boolean function. It describes precisely the coefficients of the pure quantum state vector resulting from the action of a member of the local Clifford group on a graph state, and comprises a graph which encodes the magnitude properties of the state, and a graph encoding its phase properties. This description facilitates a computationally efficient spectral analysis of the graph state with respect to operations from the local Clifford group on the state, as all operations can be realised graphically. By focusing...

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: Constanza Riera, Stéphane Jacob, Matthew G. Parker
• Keywords: Computer Graphics, DCC 2008, Graph State, Pure Quantum State, Quantum State Vector