Statistical Assertions for Validating Patterns and Finding Bugs in Quantum Programs

In support of the growing interest in quantum computing experimentation, programmers need new tools to write quantum algorithms as program code. Compared to debugging classical programs, debugging quantum programs is difficult because programmers have limited ability to probe the internal states of quantum programs; those states are difficult to interpret even when observations exist; and programmers do not yet have guidelines for what to check for when building quantum programs. In this work, we present quantum program assertions based on statistical tests on classical observations. These allow programmers to decide if a quantum program state matches its expected value in one of classical, superposition, or entangled types of states. We extend an existing quantum programming language with the ability to specify quantum assertions, which our tool then checks in a quantum program simulator. We use these assertions to debug three benchmark quantum programs in factoring, search, and chemistry. We share what types of bugs are possible, and lay out a strategy for using quantum programming patterns to place assertions and prevent bugs.Comment: In The 46th Annual International Symposium on Computer Architecture (ISCA '19). arXiv admin note: text overlap with arXiv:1811.0544

Intermediate Mass Black Hole Induced Quenching of Mass Segregation in Star Clusters

In many theoretical scenarios it is expected that intermediate-mass black holes (IMBHs, with masses M ~ 100-10000 solar masses) reside at the centers of some globular clusters. However, observational evidence for their existence is limited. Several previous numerical investigations have focused on the impact of an IMBH on the cluster dynamics or brightness profile. Here we instead present results from a large set of direct N-body simulations including single and binary stars. These show that there is a potentially more detectable IMBH signature, namely on the variation of the average stellar mass between the center and the half-light radius. We find that the existence of an IMBH quenches mass segregation and causes the average mass to exhibit only modest radial variation in collisionally relaxed star clusters. This differs from when there is no IMBH. To measure this observationally requires high resolution imaging at the level of that already available from the Hubble Space Telescope (HST) for the cores of a large sample of galactic globular clusters. With a modest additional investment of HST time to acquire fields around the half-light radius, it will be possible to identify the best candidate clusters to harbor an IMBH. This test can be applied only to globulars with a half-light relaxation time less than or equal to 1 Gyr, which is required to guarantee efficient energy equipartition due to two-body relaxation.Comment: 15 pages, 3 figures, ApJ, in pres

Mass Segregation in NGC 2298: limits on the presence of an Intermediate Mass Black Hole

[abridged] Theoretical investigations have suggested the presence of Intermediate Mass Black Holes (IMBHs, with masses in the 100-10000 Msun range) in the cores of some Globular Clusters (GCs). In this paper we present the first application of a new technique to determine the presence or absence of a central IMBH in globular clusters that have reached energy equipartition via two-body relaxation. The method is based on the measurement of the radial profile for the average mass of stars in the system, using the fact that a quenching of mass segregation is expected when an IMBH is present. Here we measure the radial profile of mass segregation using main-sequence stars for the globular cluster NGC 2298 from resolved source photometry based on HST-ACS data. The observations are compared to expectations from direct N-body simulations of the dynamics of star clusters with and without an IMBH. The mass segregation profile for NGC 2298 is quantitatively matched to that inferred from simulations without a central massive object over all the radial range probed by the observations, that is from the center to about two half-mass radii. Profiles from simulations containing an IMBH more massive than ~ 300-500 Msun (depending on the assumed total mass of NGC 2298) are instead inconsistent with the data at about 3 sigma confidence, irrespective of the IMF and binary fraction chosen for these runs. While providing a null result in the quest of detecting a central black hole in globular clusters, the data-model comparison carried out here demonstrates the feasibility of the method which can also be applied to other globular clusters with resolved photometry in their cores.Comment: 21 pages, 3 figures, ApJ accepte

Ocean data assimilation using optimal interpolation with a quasi-geostrophic model

Optimal interpolation (OI) has been used to produce analyses of quasi-geostrophic (QG) stream function over a 59-day period in a 150-km-square domain off northern California. Hydrographic observations acquired over five surveys, each of about 6 days' duration, were assimilated into a QG open boundary ocean model. Since the true forecast error covariance function required for the OI is unknown, assimilation experiments were conducted separately for individual surveys to investigate the sensitivity of the OI analyses to parameters defining the decorrelation scale of an assumed error covariance function. The analyses were intercompared through dynamical hindcasts between surveys, since there were too few independent data for other verification of the various analyses. For the hindcasts, the QG model was initialized with an analysis for one survey and then integrated according to boundary data supplied by the corresponding analysis for the next survey. Two sets of such hindcasts were conducted, since there were only three statistically independent realizations of the stream function field for the entire observing period. For the irregular sampling strategy of the first half of the observing period, the best hindcast was obtained using the smooth analyses produced with assumed error decorrelation scales identical to those of the observed stream function (about 80 km): the root mean square difference between the hindcast stream function and the final analysis was only 23% of the observation standard deviation. The best hindcast (with a 31% error) for the second half of the observing period was obtained using an initial analysis based on an 80-km decorrelation scale and a final analysis based on a 40-km decorrelation scale. The change in decorrelation scale was apparently associated with a change in sampling strategy and the importance of the resolution of small-scale vorticity input across the open boundary. The last survey used a regular sampling scheme with good coverage (about 20-km resolution) of the entire domain so that smaller-scale features were resolved by the data. The earlier surveys used a coarser (about 75 km) sampling resolution, and smaller-scale features that were not well-resolved could not be inferred correctly even with short error covariance scales. During the hindcast integrations, the dynamical model effectively filtered the stream function fields to reduce differences between the various initial fields. Differences between the analyses near inflow boundary points ultimately dominated the differences between dynamical hindcasts. Analyses for the entire 59-day observing period of the five independent surveys were produced using continuous assimilation. A modified form of OI in which the forecast error variances were updated according to the analysis error variances and an assumed model error growth rate was also used, allowing the OI to retain information about prior assimilation. The analyses using the updated variances were spatially smoother and often in better agreement with the observations than the OI analyses using constant variances. The two sets of OI analyses were temporally smoother than the fields from statistical objective analysis (OA) and in good agreement with the only independent data available for comparison. Unfortunately, the limiting factor in the validation of the assimilation methodology remains the paucity of observations

Community characterization of heterogeneous complex systems

We introduce an analytical statistical method to characterize the communities detected in heterogeneous complex systems. By posing a suitable null hypothesis, our method makes use of the hypergeometric distribution to assess the probability that a given property is over-expressed in the elements of a community with respect to all the elements of the investigated set. We apply our method to two specific complex networks, namely a network of world movies and a network of physics preprints. The characterization of the elements and of the communities is done in terms of languages and countries for the movie network and of journals and subject categories for papers. We find that our method is able to characterize clearly the identified communities. Moreover our method works well both for large and for small communities.Comment: 8 pages, 1 figure and 2 table

A New Scintillator Tile/Fiber Preshower Detector for the CDF Central Calorimeter

A detector designed to measure early particle showers has been installed in front of the central CDF calorimeter at the Tevatron. This new preshower detector is based on scintillator tiles coupled to wavelength-shifting fibers read out by multi-anode photomultipliers and has a total of 3,072 readout channels. The replacement of the old gas detector was required due to an expected increase in instantaneous luminosity of the Tevatron collider in the next few years. Calorimeter coverage, jet energy resolution, and electron and photon identification are among the expected improvements. The final detector design, together with the R&D studies that led to the choice of scintillator and fiber, mechanical assembly, and quality control are presented. The detector was installed in the fall 2004 Tevatron shutdown and started collecting colliding beam data by the end of the same year. First measurements indicate a light yield of 12 photoelectrons/MIP, a more than two-fold increase over the design goals.Comment: 5 pages, 10 figures (changes are minor; this is the final version published in IEEE-Trans.Nucl.Sci.

Fractional and noncommutative spacetimes

We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the non-rotation-invariant but cyclicity-preserving measure of \kappa-Minkowski. At scales larger than the log-period, the fractional measure is averaged and becomes a power-law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between \kappa-Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra.Comment: 15 pages. v2: typos correcte

Statistically validated networks in bipartite complex systems

Many complex systems present an intrinsic bipartite nature and are often described and modeled in terms of networks [1-5]. Examples include movies and actors [1, 2, 4], authors and scientific papers [6-9], email accounts and emails [10], plants and animals that pollinate them [11, 12]. Bipartite networks are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set. When one constructs a projected network with nodes from only one set, the system heterogeneity makes it very difficult to identify preferential links between the elements. Here we introduce an unsupervised method to statistically validate each link of the projected network against a null hypothesis taking into account the heterogeneity of the system. We apply our method to three different systems, namely the set of clusters of orthologous genes (COG) in completely sequenced genomes [13, 14], a set of daily returns of 500 US financial stocks, and the set of world movies of the IMDb database [15]. In all these systems, both different in size and level of heterogeneity, we find that our method is able to detect network structures which are informative about the system and are not simply expression of its heterogeneity. Specifically, our method (i) identifies the preferential relationships between the elements, (ii) naturally highlights the clustered structure of investigated systems, and (iii) allows to classify links according to the type of statistically validated relationships between the connected nodes.Comment: Main text: 13 pages, 3 figures, and 1 Table. Supplementary information: 15 pages, 3 figures, and 2 Table