Fault testing quantum switching circuits

Test pattern generation is an electronic design automation tool that attempts to find an input (or test) sequence that, when applied to a digital circuit, enables one to distinguish between the correct circuit behavior and the faulty behavior caused by particular faults. The effectiveness of this classical method is measured by the fault coverage achieved for the fault model and the number of generated vectors, which should be directly proportional to test application time. This work address the quantum process validation problem by considering the quantum mechanical adaptation of test pattern generation methods used to test classical circuits. We found that quantum mechanics allows one to execute multiple test vectors concurrently, making each gate realized in the process act on a complete set of characteristic states in space/time complexity that breaks classical testability lower bounds.Comment: (almost) Forgotten rewrite from 200

Testing a Quantum Computer

The problem of quantum test is formally addressed. The presented method attempts the quantum role of classical test generation and test set reduction methods known from standard binary and analog circuits. QuFault, the authors software package generates test plans for arbitrary quantum circuits using the very efficient simulator QuIDDPro[1]. The quantum fault table is introduced and mathematically formalized, and the test generation method explained.Comment: 15 pages, 17 equations, 27 tables, 8 figure

Micromechanics of metal matrix composites using the Generalized Method of Cells model (GMC) user's guide

A user's guide for the program gmc.f is presented. The program is based on the generalized method of cells model (GMC) which is capable via a micromechanical analysis, of predicting the overall, inelastic behavior of unidirectional, multi-phase composites from the knowledge of the properties of the viscoplastic constituents. In particular, the program is sufficiently general to predict the response of unidirectional composites having variable fiber shapes and arrays

Characterizing maritime trade-wind convection using the HALO Microwave Package (HAMP)

This thesis explores the marine trade-wind convection and the clouds forming within by using spatial-high-resolution airborne remote sensing observations taken from the German High Altitude and LOng range research aircraft (HALO). The nadir-pointing HALO Microwave Package (HAMP) is the central tool of this thesis. HAMP comprises a cloud radar and a 26-channel microwave radiometer (MWR, 22–183 GHz), for which the atmosphere and clouds are semitransparent. The shallow cumulus clouds, like they regularly occur in the trade-wind region, are of particular interest for better understanding the climate. Several studies (e.g., Bony and Dufresne, 2005; Schneider et al., 2017) identified such clouds as a main source of model spread in climate projections. The challenge of this kind of ubiquitous clouds in the models is partly due to large spread in global observations which can be related to the small scale of shallow cumuli and the coarse-scale observations from satellites. This thesis combines three studies around HAMP from the characterization of the HAMP MWR, over the development of MWR retrievals for liquid clouds to the application by evaluating two cloud-resolving simulations. The HAMP MWR is characterized by investigating the random noise of each channel, the covariance within each of the five frequency bands, the brightness temperature (BT) offset, the offset stability, and by suggesting an offset correction. The offset and stability of the HAMP BT acquisitions are studied by comparing the measured BTs to synthetic measurements based on forward-simulated dropsondes. Offsets between −11 and +6 K show a spectral dependency, which repeatedly appears but is shifted between flights. The offsets are most likely caused by uncertainties in the calibration method and changing environmental conditions of the MWR in the belly pod during take-off and ascending. However, an offset correction based on the dropsondes can be developed for each channel as a function of the flight. To better interpret the HAMP BT observations, novel retrievals are developed based on a realistic database of synthetic measurements and corresponding atmospheric profiles. Retrievals of the liquid water path (LWP), rainwater path (RWP), and integrated water vapor (IWV) are developed to describe the clouds and their environment. The retrieved IWV using the offset-corrected BTs agrees with coincident dropsondes and water vapor lidar measurements by 1.4 kg/m² . The theoretical assessment of LWP shows that the LWP error is below 20 g/m² for LWP below 100 g/m² . The absolute LWP error increases with increasing LWP, but the relative error decreases from 20 % at 100 g/m² to 10 % at 500 g/m². The RWP retrieval, which uses the radar in addition to the MWR, can reliably detect RWP larger than 10 g/m² with a Gilbert skill score > 0.75. The retrieval results are summarized in a comparison of the clouds and their moisture environment in the two tropical seasons, which are represented by the field experiments in December 2013 (dry season) and in August 2016 (wet season). Clouds were more frequent, and their average LWP and RWP were higher in the dry season than in the wet season. However, deeper convection with the formation of large frozen particles was less frequent in the dry season. It is hypothesized, that the lower degree of cloud organization in the dry season led to smaller systems with more overall cloud cover. The higher degree of randomness in the dry season comes along with less extremes and is reflected by a narrower distribution of IWV. The variability between (especially the wet-season) flights shows, how statistics from airborne campaigns are affected by the choice of the individual flight pattern. The more homogeneous and cloudy statistics of the dry season are used to assess the representation of shallow cumulus convection and the cloud formation over the ocean in two cloud-resolving simulations generated with the ICON model. The HAMP radar and a backscatter lidar are used for detecting cloud top height (CTH), base height, and precipitation, and the MWR stratifies the cases by LWP. Forward simulators are used to derive the same measurements synthetically from the model data while applying the same instrument-specific cloud-detection thresholds. The analysis reveals a bimodal structure of the CTH. The lower mode relates to boundary layer driven clouds, while the upper mode is driven by moist shallow convection, trapped under the trade inversion at about 2.3 km above sea level. The storm-resolving model (SRM) with 1.25 km horizontal grid spacing resolves the two cloud layers to a limited extend. Most CTHs in the SRM are above the observed lower CTH mode, and top height increases with LWP. The second model with a 300 m grid (large-eddy model, LEM) represents better the observed bimodal distribution of CTH. However, the microphysical schema of neither model can produce in-cloud drizzle-sized particles that were often observed by the radar. This application study shows, how HAMP on HALO provides insightful data to help closing the uncertainty in the models, if interpreted thoroughly

Testing a Quantum Computer

We address the problem of quantum test set generation using measurement from a single basis and the single fault model. Experimental physicists currently test quantum circuits exhaustively, meaning that each n-bit permutative circuit requires ζ x 2n tests to assure functionality, and for an m stage permutative circuit proven not to function properly the current method requires ζ x 2n x m tests as the upper bound for fault localization, where zeta varies with physical implementation. Indeed, the exhaustive methods complexity grows exponentially with the number of qubits, proportionally to the number of stages in a quantum circuit and directly with zeta. This testability bound grows still exponentially with the attempted verification of quantum effects, such as the emission of a quantum source. The exhaustive method will soon not be feasible for practical application provided the number of qubits increases even a small number from the current state of the art. An algorithm is presented making fault detection feasible both now and in the foreseeable future for quantum circuits. The presented method attempts the quantum role of classical test generation and test set reduction methods known from standard binary and analog circuits. The quantum fault table is introduced, and the test generation method explained, we show that all faults can be detected that impact calculations from the computational basis. It is believed that this fundamental research will lead to the simplification of testing for commercial quantum computers

ATPG for Reversible Circuits using Technology-Related Fault Models

We address the problem of test set generation and test set reduction, to first detect, and later localize faults occurring in reversible circuits. Reversible Computation has high promise of low power consumption. Some new fault models are first presented here. An explanation of the new fault models is made based on a physical realization representing the state of the art in the reversible CMOS circuit technology. Evidence is then presented showing that the fault models presented in the current literature are not adequate for existing realizations of reversible logic such as CMOS. We designed a ATPG software package with a friendly graphical user interface to aid experimentation with various fault models. The purpose of this work is to give an overview of our findings and pave the way for a later paper fully addressing the CMOS fault models. The key experimental results are presented

Fault Models for Quantum Mechanical Switching Networks

The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered fault. Classical faults are modelled at the logical level by fault models that act on classical states. The stuck fault model, thought of as a lead connected to a power rail or to a ground, is most typically considered. A classical test set complete for the stuck fault model propagates both binary basis states, 0 and 1, through all nodes in a network and is known to detect many physical faults. A classical test set complete for the stuck fault model allows all circuit nodes to be completely tested and verifies the function of many gates. It is natural to ask if one may adapt any of the known classical methods to test quantum circuits. Of course, classical fault models do not capture all the logical failures found in quantum circuits. The first obstacle faced when using methods from classical test is developing a set of realistic quantum-logical fault models. Developing fault models to abstract the test problem away from the device level motivated our study. Several results are established. First, we describe typical modes of failure present in the physical design of quantum circuits. From this we develop fault models for quantum binary circuits that enable testing at the logical level. The application of these fault models is shown by adapting the classical test set generation technique known as constructing a fault table to generate quantum test sets. A test set developed using this method is shown to detect each of the considered faults.Comment: (almost) Forgotten rewrite from 200

Thermoelastic response of metal matrix composites with large-diameter fibers subjected to thermal gradients

A new micromechanical theory is presented for the response of heterogeneous metal matrix composites subjected to thermal gradients. In contrast to existing micromechanical theories that utilize classical homogenization schemes in the course of calculating microscopic and macroscopic field quantities, in the present approach the actual microstructural details are explicitly coupled with the macrostructure of the composite. Examples are offered that illustrate limitations of the classical homogenization approach in predicting the response of thin-walled metal matrix composites with large-diameter fibers when subjected to thermal gradients. These examples include composites with a finite number of fibers in the thickness direction that may be uniformly or nonuniformly spaced, thus admitting so-called functionally gradient composites. The results illustrate that the classical approach of decoupling micromechanical and macromechanical analyses in the presence of a finite number of large-diameter fibers, finite dimensions of the composite, and temperature gradient may produce excessively conservative estimates for macroscopic field quantities, while both underestimating and overestimating the local fluctuations of the microscopic quantities in different regions of the composite. Also demonstrated is the usefulness of the present approach in generating favorable stress distributions in the presence of thermal gradients by appropriately tailoring the internal microstructure details of the composite

Thermoelastic Theory for the Response of Materials Functionally Graded in Two Directions with Applications to the Free-Edge Problem

A recently developed micromechanical theory for the thermoelastic response of functionally graded composites with nonuniform fiber spacing in the through-thickness direction is further extended to enable analysis of material architectures characterized by arbitrarily nonuniform fiber spacing in two directions. In contrast to currently employed micromechanical approaches applied to functionally graded materials, which decouple the local and global effects by assuming the existence of a representative volume element at every point within the composite, the new theory explicitly couples the local and global effects. The analytical development is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense. Results are presented that illustrate the capability of the derived theory to capture local stress gradients at the free edge of a laminated composite plate due to the application of a uniform temperature change. It is further shown that it is possible to reduce the magnitude of these stress concentrations by a proper management of the microstructure of the composite plies near the free edge. Thus by an appropriate tailoring of the microstructure it is possible to reduce or prevent the likelihood of delamination at free edges of standard composite laminates