Lower Bounds on Quantum Annealing Times

TL;DR

This paper derives fundamental lower bounds on the time required for quantum annealing, revealing the role of quantum coherence and demonstrating the optimality of certain annealing schedules in specific models.

Contribution

It provides the first rigorous lower bounds on quantum annealing times beyond the adiabatic regime, highlighting the importance of quantum coherence as a resource.

Findings

Bounds are asymptotically saturated by known models.

Fast annealing schedules are shown to be optimal.

Quantum coherence is essential for rapid annealing.

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.