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Quantum annealing (QA) is a promising method for solving combinatorialoptimization problems whose solutions are embedded into a ground state of theIsing Hamiltonian. This method employs two types of Hamiltonians: a driverHamiltonian and a problem Hamiltonian. After a sufficiently slow change fromthe driver Hamiltonian to the problem Hamiltonian, we can obtain the targetground state that corresponds to the solution. The inclusion of non-stoquasticterms in the driver Hamiltonian is believed to enhance the efficiency of theQA. Meanwhile, decoherence is regarded as of the main obstacles for QA. Here,we present examples showing that non-stoaquastic Hamiltonians can lead tocatastrophic failure of QA, whereas a certain decoherence process can be usedto avoid such failure. More specifically, when we include anti-ferromagneticinteractions (i.e., typical non-stoquastic terms) in the Hamiltonian, we areunable to prepare the target ground state even with an infinitely longannealing time for some specific cases. In our example, owing to a symmetry,the Hamiltonian is block-diagonalized, and a crossing occurs during the QA,which leads to a complete failure of the ground-state search. Moreover, we showthat, when we add a certain type of decoherence, we can obtain the ground stateafter QA for these cases. This is because, even when symmetry exists inisolated quantum systems, the environment breaks the symmetry. Our counterintuitive results provide a deep insight into the fundamental mechanism of QA.

Catastrophic failure of quantum annealing owing to non-stoquastic Hamiltonian and its avoidance by decoherence