Geometry and Curvature of Spin Networks

Understand

A measure for the maximum quantum information transfer capacity (ITC) between nodes of a spin network is defined, and shown to induce a metric on a space of equivalence classes of nodes for homogeneous chains with XX and Heisenberg couplings.

• The geometry and curvature of spin chains with respect of this metric are studied and compared to the physical network geometry.
• For general networks hierarchical clustering is used to elucidate the proximity of nodes with regard to the maximum ITC.
• Finally, it is shown how minimal control can be used to overcome intrinsic limitations and speed up information transfer.