Recent Publications

Lorenzo Stella

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  1. Title: Optimization through quantum annealing: theory and some applications

    Author(s): Battaglia D.A., Stella L.,

    Contemporary Physics, 47, No. 4, pp. 195-208 (July-August 2006)

    doi: 10.1080/00107510600861454

    Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional ( classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing - highlighting the crucial differences between these two methods - by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems ( namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.

  2. Title: Monte Carlo studies of quantum and classical annealing on a double well

    Author(s): Stella L., Santoro G.E., Tosatti E.,

    Physical Review B, 73, No. 14, Art. No. 144302 (April 2006)

    doi: 10.1103/PhysRevB.73.144302

    We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double well. In classical (thermal) annealing, the dependence upon the move chosen in a Metropolis scheme is studied and correlated with the spectrum of the associated Markov transition matrix. In quantum annealing, the path integral Monte Carlo approach is found to yield nontrivial sampling difficulties associated with the tunneling between the two wells. The choice of fictitious quantum kinetic energy is also addressed. We find that a "relativistic" kinetic energy form, leading to a higher probability of long real-space jumps, can be considerably more effective than the standard nonrelativistic one.