Character Varieties and Algebraic Surfaces for the Topology of Quantum Computing

It is shown that the representation theory of some finitely presented groups thanks to their SL2(C) character variety related algebraic surfaces. We make use Enriques–Kodaira classification surfaces and topological tools such explicit. study connection varieties quantum computing (TQC) as an alternative concept anyons. The Hopf link H, whose a Del Pezzo surface fH (the trace commutator), kernel our view TQC. Qutrit two-qubit magic state computing, derived from trefoil knot in previous work, may be seen TQC link. two-generator Bianchi groups, well fundamental group for singular fibers E˜6 D˜4 contain fH. A birationally equivalent K3 another compound varieties.