Abstract
We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic -spin model, for which the conventional quantum annealing has been shown to have difficulties in finding the ground state efficiently due to a first-order transition. We study the phase diagram of this system both analytically and numerically. Using the static approximation, we find that there exists a quantum path to reach the final ground state from the trivial initial state that avoids first-order transitions for intermediate values of . We also study numerically the energy gap between the ground state and the first excited state and find evidence for intermediate values of for which the time complexity scales polynomially with the system size at a second-order transition point along the quantum path that avoids first-order transitions. These results suggest that quantum annealing would be able to solve this problem with intermediate values of efficiently, in contrast to the case with only simple transverse-field fluctuations.
1 More- Received 8 March 2012
DOI:https://doi.org/10.1103/PhysRevE.85.051112
©2012 American Physical Society