Multiphoton resonances for all-optical quantum logic with multiple cavities

We develop a theory for the interaction of multilevel atoms with multimode cavities yielding cavity-enhanced multiphoton resonances. The locations of the resonances are predicted from the use of effective two- and three-level Hamiltonians. As an application we show that quantum gates can be realized when photonic qubits are encoded on the cavity modes in arrangements where ancilla atoms transit the cavity. The fidelity of operations is increased by conditional measurements on the atom and by the use of a selected, dual-rail, Hilbert space. A universal set of gates is proposed, including the Fredkin gate and iSWAP operation; the system seems promising for scalability

Delayed acceptance ABC-SMC

Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a~model that is specified in the form of a~simulator, and approximates the likelihood at a~parameter value $\theta$ by simulating auxiliary data sets $x$ and evaluating the distance of $x$ from the true data $y$. However, ABC is not computationally feasible in cases where using the simulator for each $\theta$ is very expensive. This paper investigates this situation in cases where a~cheap, but approximate, simulator is available. The approach is to employ delayed acceptance Markov chain Monte Carlo (MCMC) within an ABC sequential Monte Carlo (SMC) sampler in order to, in a~first stage of the kernel, use the cheap simulator to rule out parts of the parameter space that are not worth exploring, so that the ``true'' simulator is only run (in the second stage of the kernel) where there is a~reasonable chance of accepting proposed values of $\theta$. We show that this approach can be used quite automatically, with few tuning parameters. Applications to stochastic differential equation models and latent doubly intractable distributions are presented

On open quantum systems, effective Hamiltonians and device characterization

High fidelity models, which support accurate device characterization and correctly account for environmental effects, are crucial to the engineering of scalable quantum technologies. As it ensures positivity of the density matrix, one preferred model for open systems describes the dynamics with a master equation in Lindblad form. The Linblad operators are rarely derived from first principles, resulting in dynamical models which miss those additional terms that must generally be added to bring the master equation into Lindblad form, together with concomitant other terms that must be assimilated into an effective Hamiltonian. In first principles derivations such additional terms are often cancelled (countered), frequently in an ad hoc manner. In the case of a Superconducting Quantum Interference Device (SQUID) coupled to an Ohmic bath, the resulting master equation implies the environment has a significant impact on the system's energy. We discuss the prospect of keeping or cancelling this impact; and note that, for the SQUID, measuring the magnetic susceptibility under control of the capacitive coupling strength and the externally applied flux, results in experimentally measurable differences between models. If this is not done correctly, device characterization will be prone to systemic errors.Comment: 5 pages, 3 figure

Estimating total standing herbaceous biomass production with LANDSAT MSS digital data

Rangeland biomass data were correlated with spectral vegetation indices, derived from LANDSAT MSS data. LANDSAT data from five range and three other land use sites in Willacv and Cameron Counties were collected on October 17 and December 10, 1975, and on July 31 and September 23, 1976. The overall linear correlation of total standing herbaceous biomass with the LANDSAT derived perpendicular vegetation index was highly significant (r = 0.90**) for these four dates. The standard error of estimate was 722 kg/ha. Biomass data were recorded for two of these range sites for 8 months (March through October) during the 1976 growing season. Standing green biomass accounted for most of the increase in herbage, starting in June and ending about September and October. These results indicate that satellite data may be useful for the estimation of total standing herbaceous biomass production that could aid range managers in assessing range condition and animal carrying capacities of large and inaccessible range holdings

Reflectance of litter accumulation levels at five wavelengths within the 0.5- to 2.5 micron waveband

Reflectance was measured for 1-m2 range grass plots with two canopy treatments (standing and clipped) and four levels of litter accumulation and for grain sorghum with two canopy treatments. Reflectance was significantly higher at the 0.65- to 1.65-, and 2.20-micrometer. Wavelengths for both grass and grain sorghum canopies when the canopies were clipped and the resulting litter was removed. The natural accumulation of litter under the grass canopy did not significantly affect reflectance. The 1.65- and 2.20-micrometer wavelength reflectances of the live grass and the intact litter were 21.8% and 16.2%, respectively, and those of grain sorghum were 21.8% and 16.5%, respectively

Boundary value problems for elliptic partial differential operators on bounded domains

For a symmetric operator or relation A with infinite deficiency indices in a Hilbert space we develop an abstract framework for the description of symmetric and self-adjoint extensions A_Θ of A as restrictions of an operator or relation T which is a core of the adjoint A^*. This concept is applied to second order elliptic partial differential operators on smooth bounded domains, and a class of elliptic problems with eigenvalue dependent boundary conditions is investigated

Structure and Response in the World Trade Network

We examine how the structure of the world trade network has been shaped by globalization and recessions over the last 40 years. We show that by treating the world trade network as an evolving system, theory predicts the trade network is more sensitive to evolutionary shocks and recovers more slowly from them now than it did 40 years ago, due to structural changes in the world trade network induced by globalization. We also show that recession-induced change to the world trade network leads to an \emph{increased} hierarchical structure of the global trade network for a few years after the recession.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let