Rigorous convergence condition for quantum annealing

We derive a generic bound on the rate of decrease transverse field for quantum annealing to converge ground state Ising model when is formulated as an infinite-time process. Our theorem based rigorous upper excitation probability in limit and mathematically counterpart previously known result derived only from leading-order term asymptotic expansion adiabatic condition. Since our gives sufficient condition convergence transverse-field model, any specific problem may allow better, faster, control coefficient.