Quantum Annealing: Transverse-Field Ising Model

Quantum tunneling finds ground states by slowly quenching a transverse magnetic field

Controls

Annealing Schedule

3.00
1.00
0.02

Grid

16

State

Energy
Magnetization
Γ / J
Phase

Physics

The TFIM Hamiltonian has a quantum phase transition at Γ/J = 1 (1D). Above: paramagnetic (quantum). Below: ferromagnetic (ordered).
H = -J Σ σᵢᶻσⱼᶻ - Γ Σ σᵢˣ
QA: Γ(t) → 0 adiabatically
Spin color: blue = ↑, red = ↓. Quantum coherence shown by mixed-color flickering near Γ/J ≈ 1.