Graphical description of the action of Clifford operators on stabilizer states

Details Graphical description of the action of Clifford operators on stabilizer states Graphical description of the action of Clifford operators on stabilizer states

2007-03-30

arxiv.org/abs/quant-ph/0703278v2

Phys. Rev. A 77, 042307 (2008)

Physics

Quantum Physics

14 pages, 8 figures. Version 2 contains significant changes. Submitted to PRA

Scientific paper

10.1103/PhysRevA.77.042307

We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of solid and hollow nodes, with (undirected) edges between nodes and with loops and signs attached to individual nodes. We find that local Clifford transformations are completely described in terms of local complementation on nodes and along edges, loop complementation, and change of node type or sign. Additionally, we show that a small set of equivalence rules generates all graphs corresponding to a given stabilizer state; we do this by constructing an efficient procedure for testing the equality of any two stabilizer graphs.

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