Standard quantum annealing outperforms adiabatic reverse annealing with decoherence

TL;DR

This study compares standard quantum annealing and adiabatic reverse annealing in open systems, finding that decoherence diminishes the latter's advantage, making standard quantum annealing more effective in realistic noisy environments.

Contribution

It demonstrates through simulations that decoherence reduces the effectiveness of adiabatic reverse annealing, challenging its advantage over standard quantum annealing in practical scenarios.

Findings

Decoherence significantly impacts adiabatic reverse annealing performance.

Open system ARA is less sensitive to initial state choice than in closed systems.

Standard quantum annealing generally outperforms ARA under realistic noise conditions.

Abstract

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.