Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient classical means. More specifically we introduce the class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection, and prove first that post-IQP equals the classical class PP. Using this result we show that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, even up to 41% multiplicative error in the probabilities, then the infinite tower of classical complexity classes known as the polynomial hierarchy, would collapse to its third level. We mention some further results on the classical simulation properties of IQP circuit families, in particular showing that if the output distribution results from measurements on only O(log n) lines then it may in fact be classically efficiently sampled.Comment: 13 page

Knot Graphs

We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of the intersection of the cycle and cocycle spaces is an effective numerical invariant of these classes

A multifrequency evaluation of active and passive microwave sensors for oil spill detection and assessment

An evaluation is given of how active and passive microwave sensors can best be used in oil spill detection and assessment. Radar backscatter curves taken over oil spills are presented and their effect on synthetic aperture radar (SAR) imagery are discussed. Plots of microwave radiometric brightness variations over oil spills are presented and discussed. Recommendations as to how to select the best combination of frequency, viewing angle, and sensor type for evaluation of various aspects of oil spills are also discussed

A Parametric Study of Tillage Effects on Radar Backscatter

Radar backscatter data for different field configurations and modulation function curves for angular and frequency variations are presented. A simplistic approach to modeling this effect is presented. It is concluded that: (1) row direction is a significant contributor to radar backscatter from cropland and must be considered when making radar measurements over bare or sparsely vegetated fields; (2) while the effect decrease with increasing frequency, it is still large (5 dB) at 13.3 GHz; (3) row effects are independent of linear polarization; (4) there is a strong aspect angle sensitivity which is a function of the scene and radar system parameters

An unconventional approach to imaging radar calibration

An unconventional approach to imaging radar calibration was considered for the entire system, including the imaging processing as a measurement instrument. The technique made use of a calibrated aircraft scatterometer as a secondary standard to measure the backscatter (sigma zero) of large units of constant roughness. These measured roughness units when viewed by an imaging radar system can be used to provide gray scale level, corresponding to known degrees of roughness. To obtain a calibrated aircraft scatterometer, a homogeneous smooth surface was measured by both the aircraft scatterometer and a sphere calibrated ground system. This provided a measure of the precision and accuracy of the aircraft system. The aircraft system was then used to measure large roughness units in the Death Valley, California area. Transfer of the measured roughness units to radar imagery was demonstrated

Case of Ununited Fracture of the Humerus. Failure of Brainardʼs Operation, and of the Scton:

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Characterization of Alkali Metal Dispensers and Non-Evaporable Getter Pumps in Ultra-High Vacuum Systems for Cold Atomic Sensors

A glass ultrahigh vacuum chamber with rubidium alkali metal dispensers and non-evaporable getter pumps has been developed and used to create a cold atomic sample in a chamber that operates with only passive vacuum pumps. The ion-mass spectrum of evaporated gases from the alkali metal dispenser has been recorded as a function of dispenser current. The efficacy of the non-evaporable getter pumps in promoting and maintaining vacuum has been characterized by observation of the Rb vapor optical absorption on the D2 transition at 780 nm and vacuum chamber pressure rate of rise tests. We have demonstrated a sample of laser-cooled Rb atoms in this chamber when isolated and operating without active vacuum pumps

Effects of Climate Change on Peatland Reservoirs: A DOC Perspective

Peatland reservoirs are global hotspots for drinking water provision and are likely to become more important as demand per capita rises and the climate changes. Dissolved organic carbon (DOC) is associated with harmful disinfection byproducts and reduced aesthetic quality, and its removal is the major treatment cost. Littoral zones are known to be disproportionately important for DOC production through macrophyte inputs, and such communities are predicted to expand with warming in northern regions. However, little is known about autochthonous DOC contributions and their response to climatic change. Here we exposed mesocosms to elevated CO2 (eCO2), warming and a combined treatment across a trophic gradient. Regression analysis indicated that while sediments, macrophytes, and phytoplankton are important DOC sources (P < 0.05), benthic algal biomass showed the strongest relationship with DOC (P < 0.05), suggesting it is an underestimated source. DOC removal indicators, namely phenol oxidase (depolymerization) and respiration (mineralization) were inversely related to DOC concentration in oligohumic (P < 0.05) and oligotrophic (P < 0.1) systems, suggesting heterotrophic processes are important in DOC removal. DOC concentrations increased across all systems (P < 0.05), irrespective of trophic status, due to increased photoautotrophic inputs (macrophyte, pelagic, and benthic algae) under eCO2, warming, and combined scenarios, with inhibited depolymerization and mineralization under eCO2, even when combined with warming (P < 0.05 and P < 0.05 excepting the oligo-mesotrophic reservoir P < 0.1 respectively). Increased DOC loads of all fractions, regardless of provenance, are predicted in a future climate and, thus, investment in techniques to remove a greater range of DOC fractions is proposed to help “future proof” drinking water supplies

The Chemical Evolution of Helium in Globular Clusters: Implications for the Self-Pollution Scenario

We investigate the suggestion that there are stellar populations in some globular clusters with enhanced helium (Y from 0.28 to 0.40) compared to the primordial value. We assume that a previous generation of massive Asymptotic Giant Branch (AGB) stars have polluted the cluster. Two independent sets of AGB yields are used to follow the evolution of helium and CNO using a Salpeter initial mass function (IMF) and two top-heavy IMFs. In no case are we able to produce the postulated large Y ~ 0.35 without violating the observational constraint that the CNO content is nearly constant.Comment: accepted for publication in Ap

Two-Color/Two-Dye Planar Laser-Induced Fluorescence Thermography for Temperature Measurements at an Evaporating Meniscus

In the present work the applicability of 2c/2d PLIF-Thermography to evaporation processes is investigated. To analyze the applicability of 2c/2d PLIF-Thermography to evaporation processes a stationary evaporating liquid meniscus was chosen as test scenario. A stationary evaporating liquid meniscus was chosen because it is considered the simplest representation of the evaporation process which includes most of the physical phenomena. An experimental setup was designed and implemented which allowed the investigation of the applicability of the 2c/2d PLIF-Thermography to a stationary evaporating liquid meniscus. The setup enabled the investigations at a stationary evaporating liquid meniscus in a closed, single species system in a temperature range of 21 °C to 31 °C. A channel-based imaging spectrometer with two spectral channels was designed and implemented for the 2c/2d PLIF-Thermography. As detectors for the fluorescence signal sCMOS cameras were used. The channel-based imaging spectrometer had a spatial resolution of 14 μm per pixel. For the excitation of the fluorescent dyes a laser light sheet was generated by a high repetition rate pulsed frequency doubled Nd:YAG laser system which was synchronized with the detectors of the channel-based imaging spectrometer. Two dye combinations suitable for 2c/2d PLIF-Thermography in ethanol were investigated in detail regarding the influence of temperature, laser fluence, dye concentration, photobleaching, pressure and dissolved air/oxygen. The two dye combinations investigated were Rhodamine 6G combined with DCM and Rhodamine 6G combined with Pyridine 1. Based on the investigations the dye combination Rhodamine 6G and Pyridine 1 dissolved in ethanol was chosen for the investigations regarding the applicability of 2c/2d PLIF-Thermography to evaporation processes, because of its superior dependence on temperature. Experimental and data evaluation procedures for the calibration and the evaluation 2c/2d PLIF-Thermography measurement data were developed and implemented. An exponential and a second order polynomial approach for the calibration and evaluation of the 2c/2d PLIF-Thermography measurement data were implemented and compared with each other regarding the representation of the calibration data. The second order polynomial model showed a superior performance and therefore was chosen to be used for this work. With the settings used for the measurements in this work a confidence interval of 0.2 °C at a confidence level of 95 % could be reached for the 2c/2d PLIF-Thermography. The investigations at the stationary evaporating liquid meniscus revealed that a reliable application of the 2c/2d PLIF-Thermography to evaporation processes is not possible. Only for very low evaporation rates temperature measurements seemed to be possible. For higher evaporation rates the measured temperatures significantly deviated locally to higher temperatures which exceeded the applied evaporator temperature and therefore can be regarded as erroneous. The deviations were observed in and close to the region where the liquid-vapor interface meets the evaporator wall. In this region an increase of the fluorescence signal could be observed. This was most likely caused by the accumulation of fluorescent dyes induced by the evaporation process. An analysis regarding the origin of this deviations leads to the conclusion that they are most likely caused by a local violation of the assumption of a constant concentration ratio of the two dyes. The local dye concentration ratio is assumed to be shifted by the different diffusion rates of the two fluorescent dyes caused by the different diffusion coefficients of the two dyes used. Therefore any 2c/2d PLIF-Thermography application to evaporation processes would be compromised by the drawback that it cannot be guaranteed that the concentration ratio is locally constant