Lower Bounds on Quantum Annealing Times

TitleLower Bounds on Quantum Annealing Times
Publication TypeJournal Article
Year of Publication2023
AuthorsGarcía-Pintos, LPedro, Brady, LT, Bringewatt, J, Liu, Y-K
JournalPhys. Rev. Lett.
Date Published4/5/2023
KeywordsFOS: Physical sciences, Quantum Physics (quant-ph)

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.