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Recent theoretical and experimental studies have suggested that quantum MonteCarlo (QMC) simulation can behave similarly to quantum annealing (QA). Thetheoretical analysis was based on calculating transition rates between localminima, in the large spin limit using WentzelKramers-Brillouin (WKB)approximation, for highly symmetric systems of ferromagnetically coupledqubits. The rate of transition was observed to scale the same in QMC andincoherent quantum tunneling, implying that there might be no quantum advantageof QA compared to QMC other than a prefactor. Quantum annealing is believed toprovide quantum advantage through large scale superposition and entanglementand not just incoherent tunneling. Even for incoherent tunneling, the scalingsimilarity with QMC observed above does not hold in general. Here, we compareincoherent tunneling and QMC escape using perturbation theory, which has muchwider validity than WKB approximation. We show that the two do not scale thesame way when there are multiple homotopy-inequivalent paths for tunneling. Wedemonstrate through examples that frustration can generate an exponentialnumber of tunneling paths, which under certain conditions can lead to anexponential advantage for incoherent tunneling over classical QMC escape. Weprovide analytical and numerical evidence for such an advantage and show thatit holds beyond perturbation theory.

Can quantum Monte Carlo simulate quantum annealing?