Standard quantum annealing outperforms adiabatic reverse annealing with decoherence

We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this protocol allows avoidance of first-order quantum phase transitions selected models, resulting exponential speedup compared with standard annealing, provided that initial state algorithm is close Hamming distance to target one. Here, we show decoherence can significantly modify conclusion: by resorting master equation approach, simulate dynamics ferromagnetic $p$-spin model $p=3$ under independent and collective dephasing. For both models decoherence, performance ARA far less sensitive choice than its unitary counterpart, and, most significantly, large loses time solution advantage annealing. These results suggest as a stand-alone strategy unlikely experimentally outperform ``forward'' error mitigation strategies will likely be required order realize benefits realistic, noisy settings.