Quantum Annealing and Analog Quantum Computation

We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of such computationally hard problems to the classical spin glass problems. The quantum spin glass problems arise with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a general framework for realizing analog quantum computation.Comment: 22 pages, 7 figs (color online); new References Added. Reviews of Modern Physics (in press

Divide-and-Conquer Method for Instanton Rate Theory

Ring-polymer instanton theory has been developed to simulate the quantum dynamics of molecular systems at low temperatures. Chemical reaction rates can be obtained by locating the dominant tunneling pathway and analyzing fluctuations around it. In the standard method, calculating the fluctuation terms involves the diagonalization of a large matrix, which can be unfeasible for large systems with a high number of ring-polymer beads. Here we present a method for computing the instanton fluctuations with a large reduction in computational scaling. This method is applied to three reactions described by fitted, analytic and on-the-fly ab initio potential-energy surfaces and is shown to be numerically stable for the calculation of thermal reaction rates even at very low temperature

Optimal parametrizations of adiabatic paths

The parametrization of adiabatic paths is optimal when tunneling is minimized. Hamiltonian evolutions do not have unique optimizers. However, dephasing Lindblad evolutions do. The optimizers are simply characterized by an Euler-Lagrange equation and have a constant tunneling rate along the path irrespective of the gap. Application to quantum search algorithms recovers the Grover result for appropriate scaling of the dephasing. Dephasing rates that beat Grover imply hidden resources in Lindblad operators.Comment: 4 pages, 2 figures; To prevent from misunderstanding, we clarified the discussion of an apparent speedup in the Grover algorithm; figures improved + minor change

Multicast Mobility in Mobile IP Version 6 (MIPv6) : Problem Statement and Brief Survey

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