Gate Set Tomography

Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail. The most important feature of GST, compared to older state and process tomography protocols, is that it is calibration-free. GST does not rely on pre-calibrated state preparations and measurements. Instead, it characterizes all the operations in a gate set simultaneously and self-consistently, relative to each other. Long sequence GST can estimate gates with very high precision and efficiency, achieving Heisenberg scaling in regimes of practical interest. In this paper, we cover GST's intellectual history, the techniques and experiments used to achieve its intended purpose, data analysis, gauge freedom and fixing, error bars, and the interpretation of gauge-fixed estimates of gate sets. Our focus is fundamental mathematical aspects of GST, rather than implementation details, but we touch on some of the foundational algorithmic tricks used in the pyGSTi implementation.

Summary Plots With Adjusted Error Bars: The superb Framework With an Implementation in R

Plotting the data of an experiment allows researchers to illustrate the main results of a study, show effect sizes, compare conditions, and guide interpretations. To achieve all this, it is necessary to show point estimates of the results and their precision using error bars. Often, and potentially unbeknownst to them, researchers use a type of error bars—the confidence intervals—that convey limited information. For instance, confidence intervals do not allow comparing results (a) between groups, (b) between repeated measures, (c) when participants are sampled in clusters, and (d) when the population size is finite. The use of such stand-alone error bars can lead to discrepancies between the plot’s display and the conclusions derived from statistical tests. To overcome this problem, we propose to generalize the precision of the results (the confidence intervals) by adjusting them so that they take into account the experimental design and the sampling methodology. Unfortunately, most software dedicated to statistical analyses do not offer options to adjust error bars. As a solution, we developed an open-access, open-source library for R— superb—that allows users to create summary plots with easily adjusted error bars.

Intervals

This chapter pulls together material from earlier chapters to give an introductory user’s guide to error bars and intervals. There is no ‘best’ interval that suits all needs. Several different types of intervals are compared: standard deviations, standard errors of means, standard errors of differences, confidence intervals, and least significant differences. The pros and cons of these main types of interval are reviewed. The results are presented using R graphics.

Inference for Support Vector Regression under ℓ1 Regularization

We provide large-sample distribution theory for support vector regression (SVR) with l1-norm along with error bars for the SVR regression coefficients. Although a classical Wald confidence interval obtains from our theory, its implementation inherently depends on the choice of a tuning parameter that scales the variance estimate and thus the width of the error bars. We address this shortcoming by further proposing an alternative large-sample inference method based on the inversion of a novel test statistic that displays competitive power properties and does not depend on the choice of a tuning parameter.

Basic Statistical Estimation Outperforms Machine Learning in Monthly Prediction of Seasonal Climatic Parameters

Machine learning (ML) has been utilized to predict climatic parameters, and many successes have been reported in the literature. In this paper, we scrutinize the effectiveness of five widely used ML algorithms in the monthly prediction of seasonal climatic parameters using monthly image data. Specifically, we quantify the predictive performance of these algorithms applied to five climatic parameters using various combinations of features. We compare the predictive accuracy of the resulting trained ML models to that of basic statistical estimators that are computed directly from the training data. Our results show that ML never significantly outperforms the statistical baseline, and underperforms for most feature sets. Unlike previous similar studies, we provide error bars for the relative performance of different predictors based on jackknife estimates applied to differences in predictive error magnitudes. We also show that the practice of shuffling data sequences which was employed in some previous references leads to data leakage, resulting in over-estimated performance. Ultimately, the paper demonstrates the importance of using well-grounded statistical techniques when producing and analyzing the results of ML predictive models.

Utilizing Rare-Earth-Elements Luminescence and Vibrational-Spectroscopies to Follow High Pressure Densification of Soda–Lime Glass

A new series of soda–lime glass naturally doped with Nd and doped with 0.2 wt% of Eu2O3 was densified in a multi-anvil press up to 21 GPa. The densities of the millimetric samples were precisely measured using a floatation method in a heavy liquid made with sodium polytungstate. The obtained densification curve is significantly different from the calibration previously reported, reaching a maximum densification saturation of 3.55 ± 0.14%. This difference could be due to better hydrostatic conditions realized in this new study. The densified samples were characterized using Raman and Brillouin spectroscopy, as well as the emission of both Eu3+ and Nd3+. The evolution of the spectra was evaluated using integration methods to reduce error bars. The relative precision of the calibration curves is discussed. The evolution of Nd3+ transition was found to be the most sensitive calibration. Linear dependence with the density was found for all observables, with exception for Brillouin spectroscopy showing a divergent behavior. The Brillouin shift shows an unreported minimum for a densification ~0.4%.

Seismic attenuation analysis in the central part of the Leipzig-Regensburg fault zone using the Multiple Lapse Time Window Analysis and Qopen

<p>Seismic attenuation provides valuable information about the structure of the crust. For the analysis of seismic attenuation in the central part of the Leipzig-Regensburg fault zone in Germany, where numerous areas of intracontinental earthquake swarms are located, we use 18 of the region's strongest earthquakes from the period 2008 to 2019 with a magnitude between 1.4 and 3.0 in the frequency range between 3 and 34 Hz. Two different methods were used to determine the frequency-dependent scattering and the intrinsic attenuation on one hand and to compare the two methods with respect to their results on the other hand. Both methods, the Multiple Lapse Time Windows Analysis (MLTWA) and the Qopen method use the acoustic radiative transfer theory for forward modelling to generate synthetic data and fit them to the observed data. As a by-product of Qopen, we also obtain the energy site amplifications of the stations used in the inversion, as well as the estimated moment magnitudes of the inverted earthquakes. In addition, factors that influence the inversion were investigated. Different combinations of inversion parameters were tested for the MLTWA, as well as the influence of the window length on the result of Qopen. The results from both methods provide similar results within their error bars, with intrinsic attenuation being stronger than scattering and overall, rather low attenuation values compared to other regions.</p>

High-resolution Bayesian spatial autocorrelation (SPAC) quasi-3-D Vs model of Utah FORGE site with a dense geophone array

SUMMARY We expand the application of spatial autocorrelation (SPAC) from typical 1-D Vs profiles to quasi-3-D imaging via Bayesian Monte Carlo inversion (BMCI) using a dense nodal array (49 nodes) located at the Utah Frontier Observatory for Research in Geothermal Energy (FORGE) site. Combinations of 4 and 9 geophones in subarrays provide for 36 and 25 1-D Vs profiles, respectively. Profiles with error bars are determined by calculating coherency functions that fit observations in a frequency range of 0.2–5 Hz. Thus, a high-resolution quasi-3-D Vs model from the surface to 2.0 km depth is derived and shows that surface-parallel sedimentary strata deepen to the west, consistent with a 3-D seismic reflection survey. Moreover, the resulting Vs profile is consistent with a Vs profile derived from distributed acoustic sensing (DAS) data located in a borehole at the FORGE site. The quasi-3-D velocity model shows that the base of the basin dips ∼22° to the west and topography on the basement interface coincident with the Mag Lee Wash suggests that the bedrock interface is an unconformity.

Visualizations of Topologic Entropy on SARS-CoV-2 Genomes in Multiple Regions

The outbreak of novel coronavirus (SARS-CoV-2) developed into a global pandemic in a few months. The latest study found that the virus belongs to the beta coronavirus family. SARS-CoV-2 is highly similar to Pangolin CoV and BatCoV RaTG. Advanced scientific studies help traceability and vaccine development. In addition to the subgenus classification analysis of the virus, it is interesting for further exploration to focus attention on mutations and their transmissions in different regions. New mutations may be likely to affect the symptoms of the disease and the effectiveness of vaccination. This paper is focused on the study to make error bars and scatter graphs with the support of the metagenetic analysis system MAS. Using SARS-CoV-2 genomes in different countries and regions as input datasets, topological entropy values provide global characteristic quantities based on C4 module for visualization. Sample results show that the method is powerful and useful for consistently integrating all genomes on one unique genomic index map. Various countries have confirmed their specific positions and projections under topologic entropies. Further explorations are required.