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Lower Bounds on Quantum Annealing Times



Luis Pedro Garcia-Pintos, Lucas Brady, Jacob Bringewatt, Yi-Kai Liu


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.
Physical Review Letters


Quantum mechanics, adiabatic theorem, quantum annealing


Garcia-Pintos, L. , Brady, L. , Bringewatt, J. and Liu, Y. (2023), Lower Bounds on Quantum Annealing Times, Physical Review Letters, [online],, (Accessed March 3, 2024)
Created April 5, 2023, Updated April 7, 2023