Topological Order — Ground State Degeneracy
Kitaev toric code: GSD = 4^g on genus-g surface, anyonic excitations
Surface
Genus g:
1
Lattice size L:
6
Anyon density:
0.05
GSD = 4^g
4
Kitaev toric code on T² (g=1)
A_s = ∏_{e∈star(s)} σ_e^x
B_p = ∏_{e∈∂p} σ_e^z
GSD = 4^g (non-local encoding!)
Euler: χ = 2-2g = V-E+F