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