The Bravyi-Kitaev transformation for quantum computation of electronic structure

Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [S. B. Bravyi, A.Yu. Kitaev, Annals of Physics 298, 210-226 (2002)], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time-step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure

Mapping isoprene emissions over North America using formaldehyde column observations from space

We present a methodology for deriving emissions of volatile organic compounds (VOC) using space-based column observations of formaldehyde (HCHO) and apply it to data from the Global Ozone Monitoring Experiment (GOME) satellite instrument over North America during July 1996. The HCHO column is related to local VOC emissions, with a spatial smearing that increases with the VOC lifetime. Isoprene is the dominant HCHO precursor over North America in summer, and its lifetime (≃1 hour) is sufficiently short that the smearing can be neglected. We use the Goddard Earth Observing System global 3-D model of tropospheric chemistry (GEOS-CHEM) to derive the relationship between isoprene emissions and HCHO columns over North America and use these relationships to convert the GOME HCHO columns to isoprene emissions. We also use the GEOS-CHEM model as an intermediary to validate the GOME HCHO column measurements by comparison with in situ observations. The GEOS-CHEM model including the Global Emissions Inventory Activity (GEIA) isoprene emission inventory provides a good simulation of both the GOME data (r2 = 0.69, n = 756, bias = +11%) and the in situ summertime HCHO measurements over North America (r2 = 0.47, n = 10, bias = −3%). The GOME observations show high values over regions of known high isoprene emissions and a day-to-day variability that is consistent with the temperature dependence of isoprene emission. Isoprene emissions inferred from the GOME data are 20% less than GEIA on average over North America and twice those from the U.S. EPA Biogenic Emissions Inventory System (BEIS2) inventory. The GOME isoprene inventory when implemented in the GEOS-CHEM model provides a better simulation of the HCHO in situ measurements than either GEIA or BEIS2 (r2 = 0.71, n = 10, bias = −10%)

Sensitivity of sulfate direct climate forcing to the hysteresis of particle phase transitions

The effects of solid-aqueous phase transitions on sulfate direct climate forcing (SDCF) are investigated by using both a column model and a global chemical transport model. Aqueous particles have a larger mass extinction efficiency but a smaller backscattered fraction than their solid counterparts. The column model shows that the hysteresis of the phase transition can result in an uncertainty in the SDCF of 20%. The global chemical transport model explicitly accounts for the relative humidity processing of particles and the associated hysteresis. The model also treats the extent of sulfate neutralization by ammonia. For the anthropogenic sulfate, the base case simulation finds that solid particles contribute 41% of the global burden, 26% of the clear-sky optical thickness, 31% of the clear-sky SDCF, and 37% of the full-sky SDCF, a trend that reflects the correlation of solid particles with clear skies. A perturbation to the model, omitting hysteresis by assuming that all particles are aqueous, results in an overestimate of the SDCF by +8% compared to the base case. A converse assumption that crystallization occurs at the deliquescence relative humidity underestimates the SDCF by -8%. A case that assumes that aqueous particles occur whenever the ambient relative humidity exceeds the crystallization relative humidity biases the SDCF by +5%. A case that includes hysteresis but omits the difference in the fraction of radiation backscattered to space by aqueous compared to solid particles changes the SDCF by +15%. Seasonal and regional differences can be much larger. We recommend that the ratio of the sulfate aerosol optical thickness calculated with versus without consideration of particle hygroscopicity be reported as a standard output of SDCF models to facilitate meaningful intercomparisons among different models

Chemical NOx budget in the upper troposphere over the tropical South Pacific

The chemical NOx budget in the upper troposphere over the tropical South Pacific is analyzed using aircraft measurements made at 6-12 km altitude in September 1996 during the Global Tropospheric Experiment (GTE) Pacific Exploratory Mission (PEM) Tropics A campaign. Chemical loss and production rates of NOx along the aircraft flight tracks are calculated with a photochemical model constrained by observations. Calculations using a standard chemical mechanism show a large missing source for NOx; chemical loss exceeds chemical production by a factor of 2.4 on average. Similar or greater NOx budget imbalances have been reported in analyses of data from previous field studies. Ammonium aerosol concentrations in PEM-Tropics A generally exceeded sulfate on a charge equivalent basis, and relative humidities were low (median 25% relative to ice). This implies that the aerosol could be dry in which case N2O5 hydrolysis would be suppressed as a sink for NOx. Suppression of N2O5 hydrolysis and adoption of new measurements of the reaction rate constants for NO2 + OH + M and HNO3 + OH reduces the median chemical imbalance in the NOx budget for PEM-Tropics A from 2.4 to 1.9. The remaining imbalance cannot be easily explained from known chemistry or long-range transport of primary NOx and may imply a major gap in our understanding of the chemical cycling of NOx in the free troposphere. Copyright 2000 by the American Geophysical Union

Application and Analysis of Bounded-Impulse Trajectory Models with Analytic Gradients

In the companion paper, analytic methods were presented for computing the Jacobian entries for two-sided direct shooting trajectory models that utilize the bounded-impulse approximation. In this paper we discuss practical implementation considerations. Efficient computation of the mathematical components required to compute the partials is discussed and a guiding numerical example is provided for validation purposes. A solar electric power model suitable for preliminary mission design is presented, including a method for handling thruster cut-off events that result in non-smooth derivatives. The challenges associated with incorporating the SPICE ephemeris system into an optimization framework are discussed and an alternative is presented that results in smooth time partials. Application problems illustrate the benefits of employing analytic Jacobian calculations vs. using the method of finite differences. The importance of accurately modeling hardware and operational constraints at the preliminary design stage, and the benefits of using an analytic Jacobian in a solver that combines the monotonic basin hopping heuristic method with a local gradient search are also explored

Analytic Gradient Computation for Bounded-Impulse Trajectory Models Using Two-Sided Shooting

Many optimization methods require accurate partial derivative information in order to ensure efficient, robust, and accurate convergence. This work outlines analytic methods for computing the problem Jacobian for two different bounded-impulse spacecraft trajectory models solved using two-sided shooting. The specific two-body Keplerian propagation method used by both of these models is described. Methods for incorporating realistic operational constraints and hardware models at the preliminary stage of a trajectory design effort are also demonstrated and the analytic methods derived are tested for accuracy using automatic differentiation. A companion paper will solve several relevant problems that show the utility of employing analytic derivatives, i.e. compared to using derivatives found using finite differences

A two-step learning approach for solving full and almost full cold start problems in dyadic prediction

Dyadic prediction methods operate on pairs of objects (dyads), aiming to infer labels for out-of-sample dyads. We consider the full and almost full cold start problem in dyadic prediction, a setting that occurs when both objects in an out-of-sample dyad have not been observed during training, or if one of them has been observed, but very few times. A popular approach for addressing this problem is to train a model that makes predictions based on a pairwise feature representation of the dyads, or, in case of kernel methods, based on a tensor product pairwise kernel. As an alternative to such a kernel approach, we introduce a novel two-step learning algorithm that borrows ideas from the fields of pairwise learning and spectral filtering. We show theoretically that the two-step method is very closely related to the tensor product kernel approach, and experimentally that it yields a slightly better predictive performance. Moreover, unlike existing tensor product kernel methods, the two-step method allows closed-form solutions for training and parameter selection via cross-validation estimates both in the full and almost full cold start settings, making the approach much more efficient and straightforward to implement

Raman spectroscopy investigation of the H content of heated hard amorphous carbon layers

We revisit here how Raman spectroscopy can be used to estimate the H content in hard hydrogenated amorphous carbon layers. The H content was varied from 2 at.% to 30 at.%, using heat treatments of a a-C:H, from room temperature to 1300 K and was determined independently using ion beam analysis. We examine the correlation of various Raman parameters and the consistency of their thermal evolution with thermo-desorption results. We identify a weak band at 860 cm-1 attributed to H bonded to C(sp2). We show that the HD/HG parameter (Height ratio between the D and G bands) is quasi-linear in the full range of H content and can thus be used to estimate the H content. Conversely, we show that the m/HG parameter (ratio between the photoluminescence background, m, and the height of the G band), often used to estimate the H content, should be used with care, first because it is sensitive to various photoluminescence quenching processes and second because it is not sensitive to H bonded to C(sp2)

rTensor: An R Package for Multidimensional Array (Tensor) Unfolding, Multiplication, and Decomposition

rTensor is an R package designed to provide a common set of operations and decompositions for multidimensional arrays (tensors). We provide an S4 class that wraps around the base 'array' class and overloads familiar operations to users of 'array', and we provide additional functionality for tensor operations that are becoming more relevant in recent literature. We also provide a general unfolding operation, for which the k-mode unfolding and the matrix vectorization are special cases of. Finally, package rTensor implements common tensor decompositions such as canonical polyadic decomposition, Tucker decomposition, multilinear principal component analysis, t-singular value decomposition, as well as related matrix-based algorithms such as generalized low rank approximation of matrices and popular value decomposition

Raman micro-spectroscopy as a tool to measure the absorption coefficient and the erosion rate of hydrogenated amorphous carbon films heat-treated under hydrogen bombardment

We present a fast and simple way to determine the erosion rate and absorption coefficient of hydrogenated amorphous carbon films exposed to a hydrogen atomic source based on ex-situ Raman micro-spectroscopy. Results are compared to ellipsometry measurement. The method is applied to films eroded at different temperatures. A maximum of the erosion rate is found at ~ 450 {\degree}C in agreement with previous results. This technique is suitable for future quantitative studies on the erosion of thin carbonaceous films, especially of interest for plasma wall interactions occurring in thermonuclear fusion devices