Why quantum simulation is important? Answer 2: simulate and build new virtual quantum materials Kitaev's models 3.5 ky/T P2 PI 05 H=∑(1-4s)+∑(1-B(p) ∑A topological quantum v=x, ),z:,/ computing
Why quantum simulation is important? Answer 2: simulate and build new virtual quantum materials. Kitaev’s models topological quantum computing
Physical Realizations for quantum simulation Atoms lons Electrons G B E H 2 lulia buluta and franco nor Science 326.108
Physical Realizations for quantum simulation Iulia Buluta and Franco Nori, Science 326,108
lI. Introduction to topological quantum computing based on Kitaev's group algebra quantum double) model
II. Introduction to topological quantum computing based on Kitaev’s group algebra (quantum double) model
A: Toric codes and the corresponding hamiltonians plague operators 7=ⅡIze e∈p ertex operators qubits on links e∈ 01 0-1 10 IX H=-(∑S+∑S
A: Toric codes and the corresponding Hamiltonians qubits on links plaque operators: vertex operators:
Hamiltonian and ground states: plaque operators H ∑Sp+∑S Sp=llZe e∈p Sv)=spv)sp∈{-1,+1 vertex operators X Sy)=slv)S∈{-1,+1 e∈0 ground state has all Sp= Sv=+l 仁亡L II Sp=I I Su=I every energy level is 4-fold degenerate
Hamiltonian and ground states: ground state has all plaque operators: vertex operators: every energy level is 4-fold degenerate!!