Reverse quantum annealing of the p -spin model with relaxation

Abstract

In reverse quantum annealing, the initial state is an eigenstate of the final problem Hamiltonian and the transverse field is cycled rather than strictly decreased as in standard (forward) quantum annealing. We present a numerical study of the reverse quantum annealing protocol applied to the p-spin model (p = 3), including pausing, in an open system setting accounting for dephasing in the energy eigenbasis, which results in thermal relaxation. We consider both independent and collective dephasing and demonstrate that in both cases the open system dynamics substantially enhances the performance of reverse annealing. Namely, including dephasing overcomes the failure of purely closed system reverse annealing to converge to the ground state of the p-spin model. We demonstrate that pausing further improves the success probability. The collective dephasing model leads to somewhat better performance than independent dephasing. The protocol we consider corresponds closely to the one implemented in the current generation of commercial quantum annealers, and our results help to explain why recent experiments demonstrated enhanced success probabilities under reverse annealing and pausing.

Breakdown of the weak coupling limit in quantum annealing

“…That the empirical total success probability is 1 in this case shows that the p = 2 problem is easy also for forward annealing, in contrast to the p = 3 case studied in Ref. [46], which numerically found very small values of success probability near s inv = 0. This may be explained by the very fast forward annealing in this parameter region in Ref.…”

“…This may be explained by the very fast forward annealing in this parameter region in Ref. [46], which keeps the system almost unchanged from the quantum-disordered state at s = s inv . Aside from this subtlety, our experimental data are consistent with the numerical results of Ref.…”

“…We remark that the p-spin model has been studied before in the context of reverse annealing, for p = 3 [46]. The choice of p = 3 was motivated by the fact that this model has a first order phase transition in the thermodynamic limit [22][23][24] (gap closing exponentially in the system size) and thus is a hard problem for conventional (forward) quantum annealing.…”

“…While gadgets can be used to embed such a model in physical hardware supporting only two-body interactions, this comes at the cost of using up qubits and also introduces various errors [47]. Hence the study [46] was purely numerical. The p-spin model with p = 2, which undergoes a second-order phase transition (polynomially closing gap), can be directly represented in the hardware graph of the D-Wave devices, and we do this here.…”

An Application of Quantum Annealing Computing to Seismic Inversion

“…The annealing is performed backward from the known classical state to a state of quantum superposition, then proceeding forward it is possible to reach a new classical state that is a better solution than the initial one. Recently, it has been shown that it is possible to refine local solutions with recursive applications of reverse annealing [65][66][67][68]. We believe that the development of hybrid quantum-classical methods, such as mentioned above, will be essential to solve complex seismic problems on quantum annealers in the near future.…”