Scaling and diabatic effects in quantum annealing with a D-Wave device
Weinberg, Phillip; Tylutki, Marek; Rönkkö, Jami M.; Westerholm, Jan; Åström, Jan A.; Manninen, Pekka; Törmä, Päivi; Sandvik, Anders W.
We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on L×L lattices with L≤32. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal L dependent annealing rate v for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of v and L-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when v is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.
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