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.

11 pages, 7 figures

References in corpus (9)

• Bounds for the adiabatic approximation with applications to quantum computation
• Decoherence in adiabatic quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• On quantum mean-field models and their quantum annealing
• Accuracy vs run time in adiabatic quantum search
• Improving quantum annealing of the ferromagnetic $p$-spin model through pausing
• Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet

Cited by in corpus (1)

• Why and when is pausing beneficial in quantum annealing?