Confidence polytopes for quantum process tomography

In the present work, we propose a generalization of the confidence polytopes approach for quantum state tomography (QST) to the case of quantum process tomography (QPT). Our approach allows obtaining a confidence region in the polytope form for a Choi matrix of an unknown quantum channel based on the measurement results of the corresponding QPT experiment. The method uses the improved version of the expression for confidence levels for the case of several positive operator-valued measures (POVMs). We then show how confidence polytopes can be employed for calculating confidence intervals for affine functions of quantum states (Choi matrices), such as fidelities and observables mean values, which are used both in QST and QPT settings. As we discuss this problem can be efficiently solved using linear programming tools. We also demonstrate the performance and scalability of the developed approach on the basis of simulation and experimental data collected using IBM cloud quantum processor.

Transport in tight material enlightened by process tomography

The analysis of fluid transport through tight barrier materials poses two major challenges: (i) Long equilibration periods require long minimum experiment durations, and (ii) the fluid transport frequently results in complex pattern formation. Measuring times that are too short may feign transport rates that are too low; intact homogeneous samples are often missing problematic features, e.g. fractures. Both issues are detected and analyzed by using process tomography techniques, thereby providing an improved understanding of transport processes in complex materials. We thus continuously develop and apply the positron emission tomography (PET) method for geomaterials (Kulenkampff et al., 2016). This is able to trace very low concentrations of β+-emitting radionuclides during their passage through drill cores of barrier material with reasonable resolution (1 mm) and over variable periods (hours to years). The method yields time-resolved quantitative tomographic images of the tracer concentration (e.g. https://doi.org/10.5281/zenodo.166509), in contrast to input-output experiments like common permeability measurements, diffusion cells or break-through curves. Our current research includes the analysis of diffusive transport in heterogeneous shales (sandy facies of the Opalinus Clay) (BMBF and HGF iCross project), the reactive flow in fracture-filling materials of crystalline rocks (Eurad FUTURE project) and transport in engineered barriers and the contact zone (Euratom Cebama, Eurad Magic, as well as MgO and Stroefun BMWi projects). The efforts combine flow field tomography, structural imaging and reactive transport modelling to improve process understanding and to provide a bridge from the molecular to the macroscopic scale. The benefits include: Insight into temporal stability and spatial heterogeneity of the observed transport process Parameterization of local velocity distribution and effective volume as well as comparability with pore-scale model simulations Ability to quantify multiple internal transport rates without the need to register the delayed output signal Transparent and palpable visualization of processes hidden in the opaque material The method requires specific constraints of the experimental setup (size, fluid pressure, temperature). Nevertheless, it provides unique insight into reactive transport processes observed in potential materials for nuclear waste management.

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.

Supporting Visualization Analysis in Industrial Process Tomography by Using Augmented Reality—A Case Study of an Industrial Microwave Drying System

Industrial process tomography (IPT) based process control is an advisable approach in industrial heating processes for improving system efficiency and quality. When using it, appropriate dataflow pipelines and visualizations are key for domain users to implement precise data acquisition and analysis. In this article, we propose a complete data processing and visualizing workflow regarding a specific case—microwave tomography (MWT) controlled industrial microwave drying system. Furthermore, we present the up-to-date augmented reality (AR) technique to support the corresponding data visualization and on-site analysis. As a pioneering study of using AR to benefit IPT systems, the proposed AR module provides straightforward and comprehensible visualizations pertaining to the process data to the related users. Inside the dataflow of the case, a time reversal imaging algorithm, a post-imaging segmentation, and a volumetric visualization module are included. For the time reversal algorithm, we exhaustively introduce each step for MWT image reconstruction and then present the simulated results. For the post-imaging segmentation, an automatic tomographic segmentation algorithm is utilized to reveal the significant information contained in the reconstructed images. For volumetric visualization, the 3D generated information is displayed. Finally, the proposed AR system is integrated with the on-going process data, including reconstructed, segmented, and volumetric images, which are used for facilitating interactive on-site data analysis for domain users. The central part of the AR system is implemented by a mobile app that is currently supported on iOS/Android platforms.

Design and Simulation of an 8-Lead Electrical Capacitance Tomographic System for Flow Imaging

Electrical Capacitance Tomography (ECT) is a method for determining the dielectric permittivity distribution inside an object from measurements of external capacitance. The technique differs from conventional tomographic methods in which high-resolution images are formed from slices of the material. The measuring electrodes, which are metal plates, must be large enough to give a measurable change in capacitance. The main objective of this paper is the implementation and simulation of 8 external electrode ECT systems in order to increase the quality of reconstructed permittivity images while preserving the simplicity of design and fulfilling the demand for real-time process tomography. A complete sensor model was developed to improve the accuracy of the forward validation, especially the validation of measured data from neighboring electrodes. A prototype ECT sensor with high sensitivity was designed that can be applied to all materials which have low electrical conductivity. The capacitance between different electrode pairs is calculated for some typical permittivity distributions based on LabVIEW and MATLAB. The obtained capacitance data can be used to reconstruct images. The sensitivity distributions for the ECT sensors with different numbers of electrodes were analyzed. Preliminary tests were performed and the developed prototype showed good performance. The developed concept contributes to the study and comprehension of the ECT systems that can be used for the monitoring of oil-gas flow.