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

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

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

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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

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

A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states

We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a `more universal' dynamical element than a universal 2-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals - in effect it is only ever sensitive to the relational properties of the qubits.Comment: TR apologises for yet again finding a coauthor with a ridiculous middle name [12

Abundance Anomalies in NGC6752 - Do AGB Stars Have a Role?

We are in the process of testing a popular theory that the observed abundance anomalies in the Globular Cluster NGC 6752 are due to `internal pollution' from intermediate mass asymptotic giant branch stars. To this end we are using a chemical evolution model incorporating custom-made stellar evolution yields calculated using a detailed stellar evolution code. By tracing the chemical evolution of the intracluster gas, which is polluted by two generations of stars, we are able to test the internal pollution scenario in which the Na- and Al-enhanced ejecta from intermediate mass stars is either accreted onto the surfaces of other stars, or goes toward forming new stars. In this paper we focus mainly on the nucleosynthetic yields of the AGB stars and discuss whether these stars are the source of the observed Na-O anticorrelation. Comparing our preliminary results with observational data suggests that the qualitative theory is not supported by this quantitative study.Comment: To be published in: Nuclear Physics, Section A. 4 pages, 2 figures. Conference: "The Eighth International Symposium on Nuclei in the Cosmos", Canada, July 200

Quantum Optimization Problems

Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a quantum optimization problem using polynomial-time quantum computations and introduces the notion of an ``universal'' quantum optimization problem similar to a classical ``complete'' optimization problem. We exhibit a canonical quantum optimization problem that is universal for the class of polynomial-time quantum optimization problems. We show in a certain relativized world that all quantum optimization problems cannot be approximated closely by quantum polynomial-time computations. We also study the complexity of quantum optimization problems in connection to well-known complexity classes.Comment: date change

A stochastic evolutionary model generating a mixture of exponential distributions

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in \cite{FENN15} so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model