Scaling and diabatic effects in quantum annealing with a D-Wave device

We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on \(L \times L\) lattices with \(L \le 32\). Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal \(L\) dependent annealing...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Weinberg, Phillip, Tylutki, Marek, Rönkkö, Jami M, Westerholm, Jan, Åström, Jan A, Manninen, Pekka, Törmä, Päivi, Sandvik, Anders W
Format: Article
Language:English
Subjects:
Annealing
Ising model
Lattices (mathematics)
Quantum phenomena
Qubits (quantum computing)
Residual energy
Two dimensional models
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Summary:We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on \(L \times L\) lattices with \(L \le 32\). 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1909.13660