Theory of Quantum Annealing of an Ising Spin Glass

Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. Comparing classical and quantum Monte Carlo annealing protocols on the random two-dimensional Ising model we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing, based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the residual energy after annealing is inversely proportional to a power of the logarithm of the annealing time, but the quantum case has a larger power which makes it fasterComment: RevTex, 8 pages, 3 figure

Faster annealing schedules for quantum annealing

New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systemsComment: 10 pages, 5 figures, minor correction

Variable Annealing Length and Parallelism in Simulated Annealing

In this paper, we propose: (a) a restart schedule for an adaptive simulated annealer, and (b) parallel simulated annealing, with an adaptive and parameter-free annealing schedule. The foundation of our approach is the Modified Lam annealing schedule, which adaptively controls the temperature parameter to track a theoretically ideal rate of acceptance of neighboring states. A sequential implementation of Modified Lam simulated annealing is almost parameter-free. However, it requires prior knowledge of the annealing length. We eliminate this parameter using restarts, with an exponentially increasing schedule of annealing lengths. We then extend this restart schedule to parallel implementation, executing several Modified Lam simulated annealers in parallel, with varying initial annealing lengths, and our proposed parallel annealing length schedule. To validate our approach, we conduct experiments on an NP-Hard scheduling problem with sequence-dependent setup constraints. We compare our approach to fixed length restarts, both sequentially and in parallel. Our results show that our approach can achieve substantial performance gains, throughout the course of the run, demonstrating our approach to be an effective anytime algorithm.Comment: Tenth International Symposium on Combinatorial Search, pages 2-10. June 201

Influence of chemical and magnetic interface properties of Co-Fe-B / MgO / Co-Fe-B tunnel junctions on the annealing temperature dependence of the magnetoresistance

The knowledge of chemical and magnetic conditions at the Co40Fe40B20 / MgO interface is important to interpret the strong annealing temperature dependence of tunnel magnetoresistance of Co-Fe-B / MgO / Co-Fe-B magnetic tunnel junctions, which increases with annealing temperature from 20% after annealing at 200C up to a maximum value of 112% after annealing at 350C. While the well defined nearest neighbor ordering indicating crystallinity of the MgO barrier does not change by the annealing, a small amount of interfacial Fe-O at the lower Co-Fe-B / MgO interface is found in the as grown samples, which is completely reduced after annealing at 275C. This is accompanied by a simultaneous increase of the Fe magnetic moment and the tunnel magnetoresistance. However, the TMR of the MgO based junctions increases further for higher annealing temperature which can not be caused by Fe-O reduction. The occurrence of an x-ray absorption near-edge structure above the Fe and Co L-edges after annealing at 350C indicates the recrystallization of the Co-Fe-B electrode. This is prerequisite for coherent tunneling and has been suggested to be responsible for the further increase of the TMR above 275C. Simultaneously, the B concentration in the Co-Fe-B decreases with increasing annealing temperature, at least some of the B diffuses towards or into the MgO barrier and forms a B2O3 oxide