Holonomic quantum computation associated with a defect structure of conical graphene

A possibility of holonomic quantum computation based on the defect-mediated properties of graphite cones is discussed. Using a geometric description for the conical graphene, we demonstrate how one can construct the most important one-qubit quantum gates without invoking the adiabatic approximation. The control parameter which defines a particular qubit configuration is directly linked with the number of removed sectors in the graphene layer needed to create a particular conical configuration.