53 research outputs found
Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian
We study the relation between quantum fluctuations and the significant
enhancement of the performance of quantum annealing in a mean-field
Hamiltonian. First-order quantum phase transitions were shown to be reduced to
second order by antiferromagnetic transverse interactions in a mean-field-type
many-body-interacting Ising spin system in a transverse field, which means an
exponential speedup of quantum annealing by adiabatic quantum computation. We
investigate if and how quantum effects manifest themselves around these first-
and second-order phase transitions to understand if the antiferromagnetic
transverse interactions appended to the conventional transverse-field Ising
model induce notable quantum effects. By measuring the proximity of the
semiclassical spin-coherent state to the true ground state as well as the
magnitude of the concurrence representing entanglement, we conclude that
significant quantum fluctuations exist around second-order transitions, whereas
quantum effects are much less prominent at first-order transitions. Although
the location of the transition point can be predicted by the classical picture,
system properties near the transition need quantum-mechanical descriptions for
a second-order transition but not necessarily for first order. It is also found
that quantum fluctuations are large within the ferromagnetic phase after a
second-order transition from the paramagnetic phase. These results suggest that
the antiferromagnetic transverse interactions induce marked quantum effects,
and this fact would be related to closely to the significant enhancement of the
performance of quantum annealing.Comment: 9 pages, 8 figure
イギリスの初等シティズンシップ教育に関する資料 ―Don Rowe著 『シティズンシップ教育の導入 小学校のためのハンドブック』― (A & C Black社, London, 2001年)
- …