TY - JOUR
T1 - Mathematical aspects of quantum annealing
AU - Nishimori, Hidetoshi
AU - Morita, Satoshi
PY - 2008/1/1
Y1 - 2008/1/1
N2 - Sufficient conditions for convergence of quantum annealing are derived for optimization problems represented by the Ising model. Three different types of time evolution are considered; the real-time Schrödinger equation, the path-integral Monte Carlo method and the Green's function Monte Carlo method. It is proved that the system under each dynamics reaches the target solution in the limit of infinite time if the transverse field, representing the strength of quantum fluctuations, decreases inversely proportionally to the power of time in the asymptotic region.
AB - Sufficient conditions for convergence of quantum annealing are derived for optimization problems represented by the Ising model. Three different types of time evolution are considered; the real-time Schrödinger equation, the path-integral Monte Carlo method and the Green's function Monte Carlo method. It is proved that the system under each dynamics reaches the target solution in the limit of infinite time if the transverse field, representing the strength of quantum fluctuations, decreases inversely proportionally to the power of time in the asymptotic region.
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U2 - 10.1088/1742-6596/95/1/012021
DO - 10.1088/1742-6596/95/1/012021
M3 - Article
AN - SCOPUS:41849107557
VL - 95
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012021
ER -