Ternary logic design in topological quantum computing

A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to decoherence effect, superposition a state gets destroyed by interaction with environment. is real challenge completely isolate system make it free decoherence. This problem be circumvented use topological phases matter. These have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When order exchange matters, then non-Abelian Majorana fermions in superconductors some Hall states Such matter ground degeneracy. fusion two or more result several gates implemented braiding fault-tolerance achieved through degrees freedom non-local, hence inaccessible local perturbations. In this paper, Hilbert space for qubit discussed. Ising Fibonacci anyonic models binary briefly given. Ternary logic compact their counterparts naturally arise type model metaplectic mathematical model, matrices anyons, deformation recoupling theory. We proposed that existing ternary arithmetic realized charge measurement