Quantum Optimization: Spin Glasses and Wavefunction Annealing

The density matrix renormalization group (DMRG) has been extended in order to analyse the quantum spin glass transition (QSGT) for a random Ising model in a transverse field --$\Gamma$-- on a random graph with fixed connectivity $K=3$. The system is solved easily for a high value of $\Gamma$, and the wavefunction is {\em annealed} decreasing it slowly until the transition is reached. This way, the QSGT has been characterized in detail. A further decrease of $\Gamma$, down to $\Gamma=0$, allows to obtain the solution of the classical minimization problem associated, thus providing a possible alternative route to quantum annealing methods. Reference: J. Rodriguez-Laguna, G.E. Santoro, {\em Quantum Spin Glass Transition: the Ising model on random graphs}, submitted to Phys. Rev. B. ArXiv: {\tt cond-mat/0610661} (2006).