Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it provide a new quantum approach which combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled-unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32-bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with minor typos corrected.

Developing Cross Section Sets for Fluorocarbon Etchants

Successful modeling of plasmas used in materials processing depends on knowledge of a variety of collision cross sections and reaction rates, both within the plasma and at the surface. Electron-molecule collision cross sections are especially important, affecting both electron transport and the generation of reactive fragments by dissociation and ionization. Because the supply of cross section data is small and measurements are difficult, computational approaches may make a valuable contribution, provided they can cope with the significant challenges posed. In particular, a computational method must deal with the full complexity of low-energy electron-molecule interactions, must treat polyatomic molecules, and must be capable of computing cross sections for electronic excitation. These requirements imply that the method will be numerically intensive and thus must exploit high-performance computers to be practical. We have developed an ab initio computational method, the Schwinger multichannel (SMC) method, that possesses the characteristics just described, and we have applied it to compute cross sections for a variety of molecules, with particular emphasis on fluorocarbon and hydrofluorocarbon etchants used in the semiconductor industry. A key aspect of this work has been an awareness that cross section sets, validated when possible against swarm data, are more useful than individual cross sections. To develop such sets, cross section calculations must be integrated within a focused collaborative effort. Here we describe electron cross section calculations carried out within the context of such a focused effort, with emphasis on fluorinated hydrocarbons including CHF3 (trifluoromethane), c-C_(4)F_(8) (octafluorocyclobutane), and C_(2)F_(4) (tetrafluoroethene)

The First Comparison Between Swarm-C Accelerometer-Derived Thermospheric Densities and Physical and Empirical Model Estimates

The first systematic comparison between Swarm-C accelerometer-derived thermospheric density and both empirical and physics-based model results using multiple model performance metrics is presented. This comparison is performed at the satellite's high temporal 10-s resolution, which provides a meaningful evaluation of the models' fidelity for orbit prediction and other space weather forecasting applications. The comparison against the physical model is influenced by the specification of the lower atmospheric forcing, the high-latitude ionospheric plasma convection, and solar activity. Some insights into the model response to thermosphere-driving mechanisms are obtained through a machine learning exercise. The results of this analysis show that the short-timescale variations observed by Swarm-C during periods of high solar and geomagnetic activity were better captured by the physics-based model than the empirical models. It is concluded that Swarm-C data agree well with the climatologies inherent within the models and are, therefore, a useful data set for further model validation and scientific research.Comment: https://goo.gl/n4QvU

Eulerian and modified Lagrangian approaches to multi-dimensional condensation and collection

Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here, an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or su- perdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow, or just gravitational acceleration without gas flow. Good agreement between the differ- ent schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. Higher moments of the size spectra are found to be a useful tool to characterize the growth of the largest drops through collection. Remarkably, the tails of the size spectra are reasonably well described by a gamma distribution in cases with gravity or turbulence. The Lagrangian schemes are generally found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results.Comment: 36 pages, 17 figure