Quantum Annealing — Transverse-Field Ising

Simulated quantum tunneling finds the ground state of a random Ising problem

Transverse field Γ: 1.000 Energy: —
Quantum annealing solves optimization problems by starting with a large transverse field Γ (quantum fluctuations) and slowly reducing it, allowing quantum tunneling to escape local minima. H = -ΣJ_ijσ^z_iσ^z_j - ΓΣσ^x_i. The simulation uses path-integral Monte Carlo (imaginary-time replicas) to represent quantum superposition classically.