Faster Annealing Schedules for Quantum Annealing(General)

Morita, S

New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systems

Arnab Das, Bikas K. Chakrabarti

Satoshi Morita

New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systems

Das, Arnab, Chakrabarti, Bikas

Shu Tanaka

Luis Pedro García-Pintos, Lucas T. Brady, Jacob Bringewatt +1 more

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.