Excitations paquet operators: Sp=l Ze ∈p vertex operators IIE e∈0 X anti-commutes with two plaque operators iX, Sp)=0= Sp(XlG))=-XlalG +|++ excitation is 4 above ground state +++
plaquet operators: vertex operators: anti-commutes with two plaquet operators − − excitation is above ground state Excitations
excitations particles come in pairs(particle/antiparticle) at end of "error" chains two types of particles, X-type(live on vertices of dual lattice) Z-type (live on vertices of the lattice)
excitations particles come in pairs (particle/antiparticle) at end of “error” chains two types of particles, X-type (live on vertices of dual lattice) Z-type (live on vertices of the lattice)
Topological qubit and operation Encode two qubits into the ground state gap 1 Z1 22+2122z+Z X X X1Z1X1Z1=-1
Topological qubit and operation
Topological protection Encode two qubits into the ground state gap HC Perturbation theory ∑E+∑ 00U But for m≤ 0 V"2)-(;V")=0
Encode two qubits into the ground state gap Perturbation theory: But for Topological protection
Abelian anyons B'A ground> aground> -BCA Igroyhd>=BAC Ground>=-BA Ground> Phase
Phase: Abelian anyons