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arXiv · 2210.15687

Lower Bounds on Quantum Annealing Times

Luis Pedro García-Pintos·Lucas T. Brady·Jacob Bringewatt·Yi-Kai Liu
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Abstract

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.

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Luis Pedro García-Pintos, Lucas T. Brady, Jacob Bringewatt, Yi-Kai Liu. 2022-10-27. Lower Bounds on Quantum Annealing Times. https://doi.org/10.1103/physrevlett.130.140601

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