Quantum Annealing: Ising Diabatic Transitions

Simulate time-dependent Schrödinger equation for a transverse-field Ising model. Observe Landau-Zener diabatic transitions as annealing speed varies.

20
1.0
2
Press "Run Annealing" to start.
Hamiltonian:
H(t) = −A(t)Σᵢσˣᵢ − B(t)JΣᵢⱼσᶻᵢσᶻⱼ

A(t)=1−t/T, B(t)=t/T

Landau-Zener: excitation probability
P_ex ≈ exp(−πΔ²T/2)
where Δ = minimum gap at critical point.

Slow annealing → stays in ground state (adiabatic). Fast → diabatic excitation.