For many optimization algorithms the time to solution depends not only on the problem size but also on the specific problem instance and may vary by many orders of magnitude. It is then necessary to investigate the full distribution and especially its tail. Here, we analyze the distributions of annealing times for simulated annealing and simulated quantum annealing (by path integral quantum Mon...

Population annealing is a Monte Carlo algorithm that marries features from simulated-annealing and parallel-tempering Monte Carlo. As such, it is ideal to overcome large energy barriers in the free-energy landscape while minimizing a Hamiltonian. Thus, population-annealing Monte Carlo can be used as a heuristic to solve combinatorial optimization problems. We illustrate the capabilities of popu...

We study the performance of quantum annealing for systems with ground-state degeneracy by directly solving the Schrödinger equation for small systems and quantum Monte Carlo simulations for larger systems. The results indicate that naive quantum annealing using a transverse field may not be well suited to identify all degenerate ground-state configurations, although the value of the ground-stat...

Researchers successfully use an array of quantum dots to create and study a Heisenberg spin chain.

A Simulated Annealing method is presented for the solution of nonlinear time series estimation problems, by maximization of the a Posteriori Likelihood function. Homogeneous temperature annealing is proposed for smoothing problems and inhomogeneous temperature annealing for filtering problems. Both methods of annealing guarantee convergence to the Maximum A Posteriori Likelihood (MAP) estimate....