Finding the exact counterdiabatic potential is, in principle, particularly demanding. Following recent progresses about variational strategies to approximate the counterdiabatic operator, in this paper we apply this technique to the quantum annealing of the p-spin model. In particular, for p = 3 we find a new form of the counterdiabatic potential originating from a cyclic ansatz, that allows us to have optimal fidelity even for extremely short dynamics, independently of the size of the system. We compare our results with a nested commutator ansatz, recently proposed in P. W. Claeys, M. Pandey, D. Sels, and A. Polkovnikov, Phys. Rev. Lett. 123, 090602 (2019), for p = 1 and p = 3. We also analyze generalized p-spin models to get a further insight into our ansatz. arXiv:1912.09711v1 [quant-ph]

The probability of success of quantum annealing can be improved significantly by pausing the annealer during its dynamics, exploiting thermal relaxation in a controlled fashion. In this paper, we investigate the effect of pausing the quantum annealing of the fully-connected ferromagnetic p-spin model. This analytically solvable model has a search-like behavior and is often used as a benchmark for the performances of quantum annealing. We numerically show that i) the optimal pausing point is 60 % longer than the avoided crossing time for the analyzed instance, and ii) at the optimal pausing point, we register a 45 % improvement in the probability of success with respect to a quantum annealing with no pauses of the same duration. These results are in line with those observed experimentally for less connected models with the available quantum annealers. The observed improvement for the p-spin model can be up to two orders of magnitude with respect to an isolated quantum dynamics of the same duration.Keywords: adiabatic quantum computation, quantum annealing, open quantum systems, p-spin model arXiv:1902.06788v3 [quant-ph]

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.

We investigate the quantum annealing of the ferromagnetic p-spin model in a dissipative environment (p = 5 and p = 7). This model, in the large p limit, codifies the Grover's algorithm for searching in an unsorted database. The dissipative environment is described by a phonon bath in thermal equilibrium at finite temperature. The dynamics is studied in the framework of a Lindblad master equation for the reduced density matrix describing only the spins. Exploiting the symmetries of our model Hamiltonian, we can describe many spins and extrapolate expected trends for large N , and p. While at weak system bath coupling the dissipative environment has detrimental effects on the annealing results, we show that in the intermediate coupling regime, the phonon bath seems to speed up the annealing at low temperatures. This improvement in the performance is likely not due to thermal fluctuation but rather arises from a correlated spin-bath state and persists even at zero temperature. This result may pave the way to a new scenario in which, by appropriately engineering the system-bath coupling, one may optimize quantum annealing performances below either the purely quantum or classical limit.