Quantum annealing is originally proposed as a heuristic technique to solve hard optimization problems. It exploits quantum tunneling effect, as opposed to thermal fluctuation in the case of simulated annealing, to explore the energy landscape efficiently. In this talk, I will introduce the basic idea of quantum annealing, the available hardware implementations up to now, and various applications in the context of solving combinatorial optimization problems, probabilistic sampling, machine learning, and simulation of frustrated quantum spin systems. Some important questions in this field, such as the real performance advantage of quantum annealing over classical algorithms, are largely controversial and open.

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