%0 Book Section %1 statphys23_0800 %A Sarjala, M. %A Petäjä, V. %A Alava, M. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K annealing field ising model quantum random statphys23 topic-9 %T Quantum annealing in the random field Ising model %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=800 %X 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 $e_ressim log(N_MC)^-\zeta$, 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).

@incollection{statphys23_0800, 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).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Sarjala, M. and Petäjä, V. and Alava, M.}, biburl = {https://www.bibsonomy.org/bibtex/2f184fbed130e386e05c861608adc5ef3/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {42066de446eb73b4a7f3534521bc9888}, intrahash = {f184fbed130e386e05c861608adc5ef3}, keywords = {annealing field ising model quantum random statphys23 topic-9}, month = {9-13 July}, timestamp = {2007-06-20T10:16:29.000+0200}, title = {Quantum annealing in the random field Ising model}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=800}, year = 2007 }