Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
Graphical description of the action of local Clifford transformations on graph states
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abstract
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.
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2026 1verdicts
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The Structure of Circle Graph States
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.