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It is rigorously shown that an appropriate quantum annealing for anyfinite-dimensional spin system has no quantum first-order transition intransverse magnetization. This result can be applied to finite-dimensionalspin-glass systems, where the ground state search problem is known to be hardto solve. Consequently, it is strongly suggested that the quantum first-ordertransition in transverse magnetization is not fatal to the difficulty ofcombinatorial optimization problems in quantum annealing.

Proof of avoidability of the quantum first-order transition in transverse magnetization in quantum annealing of finite-dimensional spin glasses