One of the serious problems that quantum annealing encounters is the existence of a first-order quantum phase transition. Since the initial and final states are usually quite different, the former being trivial and the latter highly nontrivial, a sudden change of the state of the system, i.e. a first-order transition, inevitably takes place in the course of computation, which causes a difficulty because the computation time explodes exponentially as a function of the problem size at a first-order transition. We have proposed three methods that mitigate or, in some cases, remove this difficulty by the introduction of non-traditional quantum driving, (1) non-stoquastic Hamiltonian, (2) inhomogeneous field driving, and (3) reverse annealing. I will explain these methods and show how and when they are useful theoretically and practically.
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