Quantum annealing in a degenerate two-level system

Quantum annealing is a method for avoiding the increase of the calculation cost of the combinatorial optimization problem. Since the combinatorial optimization problems are ubiquitous, quantum annealing machine with high efficiency and scalability will give an immeasurable impact on many fields. An idea for finding high success probability is one of the most important issues for quantum annealing. In this presentation, we show that a degenerate two-level system that is called quantum Wajnflasz-Pick model may provide the higher success probability than the conventional spin-1/2 model in a weak longitudinal magnetic field region. The origin of the higher success probability can be understood from the fact that the Hamiltonian in this model can be reduced into that of the spin-1/2 model. In the reduced Hamiltonian, the effective longitudinal magnetic field may open the energy gap, which suppresses the Landau–Zener tunneling providing leakage of the ground state.