@incollection{statphys23_0800,
	title = {Quantum annealing in the random field Ising model},
	address = {Genova, Italy},
	author = {M. Sarjala and V. Petäjä and M. Alava},
	booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
	editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
	month = {9-13 July},
	url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=800},
	year = {2007},
	biburl = {http://www.bibsonomy.org/bibtex/2f184fbed130e386e05c861608adc5ef3/statphys23},
	abstract = {We have investigated the performance of quantum annealing (QA) applied to the random field Ising model (RFIM) [1]. The RFIM presents an interesting test problem, being exactly solvable in polynomial time with combinatorial optimization graph algorithms, but yet it has a highly non-trivial energy landscape at zero temperature. QA is based on searching for the ground-state of a classical Hamiltonian by adiabatically switching off an appropriate source of quantum fluctuations [2].

Our main focus is on the decay rate of the residual energy, defined as the energy excess from the ground state,. This is found to be $e_{res}sim log(N_{MC})^{-\zeta}$, with the $\zeta$ in the range $2...6$, depending on the 
strength of the random field and the dimension of the problem [1]. In particular, the fastest decay rates are close to those predicted by theoretical arguments for the maximum value of $\zeta$ [1,2]. Such results are only obtained 
by optimizing the details of the quantum-to-classical mapping of the system, and by choosing carefully the QA schedule. 

1) Sarjala M, Petäjä V and Alava M, J. Stat. Mech., P01008 (2006). \\
2) Santoro G E, Martonak R, Tossatti E and Car R, Science, 295, 2427 (2002).},
	keywords = {annealing field ising model quantum random statphys23 topic-9 }
}