Abstract
Quantum annealing is an innovative idea and 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. However, the conventional quantum annealing machine may not have a high success probability for finding the solution because the energy gap closes exponentially as a function of the system size. To propose an idea for finding high success probability is one of the most important issues. Here we show that a degenerate two-level system provides the higher success probability than the conventional spin-1/2 model in a weak longitudinal magnetic field region. The physics behind this is that the quantum annealing in this model can be reduced into that in the spin-1/2 model, where the effective longitudinal magnetic field may open the energy gap, which suppresses the Landau–Zener tunneling providing leakage of the ground state. We also present the success probability of the Λ-type system, which may show the higher success probability than the conventional spin-1/2 model.
Highlights
Quantum annealing is an innovative idea and method for avoiding the increase of the calculation cost of the combinatorial optimization problem
We find that the quantum Wajnflasz–Pick model is more efficient than the conventional spin-1/2 model in the weak longitudinal magnetic field region as well as in the strong coupling region between degenerate states
We have analytically shown that the quantum Wajnflasz–Pick model can be reduced into the spin-1/2 model, where effect of the transverse magnetic field in the original Hamiltonian emerges as the effective additional longitudinal magnetic field in the reduced Hamiltonian, which possibly opens the energy gap between the ground state and the first excited state in the reduced Hamiltonian
Summary
Quantum annealing is an innovative idea and method for avoiding the increase of the calculation cost of the combinatorial optimization problem. We employ the common sets of parameters in both quantum Wajnflasz–Pick model and the conventional spin-1/2 model, including the coupling strength Jij, the magnetic fields hiz,x, and the annealing time T .
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