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 $e_ressim log(N_MC)^-\zeta$, 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).
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