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DOE OSTI2025

Enhancing Unknown Waveform Detection by Learning Intra and Inter-domain Dependencies with Advanced Attention Fusion Mechanisms

Detection of unknown waveforms in mission-critical communications is a crucial area of interest for the Department of Energy (DoE). Traditional methods and recent deep learning-based approaches often assume that the training set includes all possible classes, which is impractical for detecting new waveforms. This limitation gives rise to the problem of open-set recognition (OSR), which involves correctly identifying known classes while detecting and rejecting unknown or unseen classes. To address this limitation, we propose a novel dual-domain complex-valued neural architecture that jointly processes time-domain and frequency-domain signal representations using transformer mechanisms. A transformer model is a deep learning architecture that uses self-attention mechanisms to process and learn relationships in sequential data. Our model employs a cosine similarity loss to extract domain-specific features and incorporates a transformer architecture in the latent space to weigh the importance of different features from the time and frequency domains. The transformer layer includes stacked self-attention and cross-attention modules to learn intra-domain and inter-domain dependencies, creating a more holistic signal representation. An attention-based fusion module intelligently combines the time and frequency-domain features using multi-head attention, enabling the network to learn the optimal feature for each domain in each input signal. Quantitative results demonstrate the impact of these architectural choices on overall performance, showing significant improvement after incorporating self and cross-attention modules and using complex attention fusion over simple weighted fusion. Our ongoing work will focus on addressing the limitations of threshold-based OSR methods by developing a novel generative framework that integrates a conditional diffusion probabilistic model (DPM). DPM is a generative framework that learns to synthesize complex data by reversing a gradual noising process using a neural network trained to denoise step-by-step. Our goal is to leverage the inherent strengths of DPMs for identifying unknown signals more robustly. One primary advantage of using a DPM is its ability to provide a more reliable anomaly score based on the model's reconstruction error, rather than relying solely on classifier confidence. Additionally, the iterative denoising process of DPMs makes this approach naturally resilient to low Signal-to-Noise Ratio (SNR) conditions, where traditional methods often fail. By implementing this generative framework, we aim to enhance the model's capability to accurately detect unknown waveforms and maintain performance in challenging environments.

99 - GENERAL AND MISCELLANEOUS↗

DOE OSTI2024

Probabilistic Seismic Hazard Assessment for Azerbaijan

Probabilistic Seismic Hazard Assessments (PSHA) underpin the determination of seismic loads in most contemporary seismic provisions of building codes around the world. Modern building codes are migrating towards using the entire uniform hazard spectrum at a range of vibration periods (typically up to 4 s or 10 s) rather than a single peak value such as peak ground acceleration (PGA), thus requiring a larger range of PSHA outputs. The hazard maps in the current version of the building code of Azerbaijan (2011) are in terms of intensity and peak ground acceleration. Recognizing the need for an up-to-date seismic hazard assessment in the country, Seismic Cooperation Program (SCP) under the Lawrence Livermore National Laboratory (LLNL) undertook, in coordination with the Republican Seismic Survey Center of the Azerbaijan National Academy of Sciences and the Azerbaijan Scientific Research Institute of Construction and Architecture, a PSHA study that reflects new seismic data recorded locally and recent research conducted nationally and regionally since the last update to the building code. The PSHA framework for this project was designed to help develop a new earthquake catalogue, to incorporate a novel characterization of ground motions that specifically reflects the attenuation characteristics in the eastern Caucasus, and to generate hazard information in a form that is useful for an update of the current building code or the development of a new building code for Azerbaijan. The project also aimed to provide training and support for the local seismologists and engineers related to the seismic hazard models, probabilistic seismic hazard results and their use towards changes in the building code.

58 GEOSCIENCES↗

DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗

DOE OSTI2020

Zero-Valent Iron Permeable Reactive Barrier to Remediate Volatile Organic Compounds in Groundwater - 20209

The US DOE-SRS, the US EPA, and the South Carolina Department of Health and Environmental Control determined it was appropriate to perform a non-time critical removal action at the P-Area Groundwater Operable Unit at the SRS to reduce the mass and downgradient transport of trichloroethylene in the P-Area groundwater plume. Contaminated groundwater discharges to a nearby stream, Steel Creek, within the SRS boundaries, resulting in trichloroethylene concentrations above the maximum contaminant level. Impact to surface water is limited in areal extent and supported by recently collected characterization data. The P-Area Groundwater Operable Unit encompasses the groundwater beneath an industrial area within SRS, P Area, where the P-Reactor once operated. The boundaries of the P-Area Groundwater Operable Unit extend northwest to Steel Creek, northeast toward PAR Pond, and southeast to Meyers Branch. Groundwater in the Upper Three Runs Aquifer of the P-Area Groundwater Operable Unit has been impacted by reactor and facility operations between 1954 and 1991, including tritium and volatile organic compounds. The P-Area surface units contributing to groundwater contamination were remediated as part of the P-Area Operable Unit in 2011. The P-Reactor closure is one of the first of its kind in the DOE Complex and is one of only a few full-sized production reactors in the US to undergo completion of final closure activities. The nature and extent of groundwater contamination was determined using a variety of investigative approaches such as groundwater monitoring wells, direct-push technology, and surface water samples. Groundwater contamination associated with trichloroethylene is primarily exhibited in a narrow plume that extends from the source area at P-Reactor and west to Steel Creek. Maximum contaminant level exceedances in groundwater occur over an area of ∼6.9 hectares for trichloroethylene with concentrations as high as 7.7 milligrams per liter. To the west of the P-Area facility area, the trichloroethylene groundwater plume is controlled by a buried geologic feature, assumed to be an old stream bed, that further narrows the groundwater plume in what has been designated as the 'neck area.' This narrowing of the groundwater plume provides an ideal location for a treatment barrier. The non-time critical removal action alternative chosen is to install a zero-valent iron permeable reactive barrier within the neck area of the trichloroethylene groundwater plume, perpendicular to groundwater flow direction. This technology will provide a treatment barrier that will reduce trichloroethylene groundwater concentrations by 90% and has an anticipated useful life of at least 25 years. A pre-design investigation was performed in the neck area to confirm site lithology, hydrogeology, geochemistry, and extent of trichloroethylene contamination prior to a final design. A treatability study, conducted as part of the pre-design investigation, indicated that the subsurface and groundwater in the PArea Groundwater Operable Unit is compatible with the zero-valent iron and will not lead to excessive buildup from mineralization/precipitation or biofouling. Probabilistic modeling was conducted using field and laboratory data to determine the expected performance of the zero-valent iron permeable reactive barrier. The model simulations indicated that a 3.81-centimeter thick barrier would provide greater than 90% reduction of trichloroethylene groundwater concentration. The final design of the zero-valent iron permeable reactive barrier is a barrier that will extend 80.5 linear meters in a 'zigzag' orientation to best transect the trichloroethylene plume and account for varying groundwater flow. The barrier will be installed from 13.7 meters below ground surface to 41.1 meters below ground surface for 65.8 linear meters and from 13.7 meters below ground surface to 36.6 meters below ground surface for 14.6 linear meters, the base of which is 'keyed' into a low permeability zone. The barrier is designed to a thickness of 10.2 centimeters, which was determined to reduce the trichloroethylene groundwater concentrations by greater than 90% with a safety factor of 2.67. A total of approximately 689 metric tons of zero-valent iron will be injected through 22 injection wells spaced 3.66 meters apart, using guar to suspend the zero-valent iron. Zero-valent iron permeable reactive barrier construction will be monitored through 23 installed resistivity receivers offset 7.32 meters from the zerovalent iron permeable reactive barrier. The zero-valent iron will be energized with a low-voltage 100 Hertz signal during injection and will be monitored using the resistivity receivers to ensure complete coalescence of the zero-valent iron permeable reactive barrier. The zero-valent iron was sized to have a hydraulic conductivity greater than the natural subsurface, thus promoting groundwater flow through the barrier. As contaminated groundwater contacts the zero-valent iron, volatile organic compounds, including trichloroethylene, are immediately degraded to harmless compounds such as ethylene. The performance of the zero-valent iron permeable reactive barrier will be monitored using three upgradient monitoring well clusters, six downgradient monitoring well clusters, and four in-wall monitoring wells. The in-wall monitoring wells will indicate immediate reduction of trichloroethylene mass in the groundwater and allow analyses of the zero-valent iron permeable reactive barrier health. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Hypothesis Learning in Automated Experiment: Application to Combinatorial Materials Libraries

Machine learning is rapidly becoming an integral part of experimental physical discovery via automated and high-throughput synthesis, and active experiments in scattering and electron/probe microscopy. This, in turn, necessitates the development of active learning methods capable of exploring relevant parameter spaces with the smallest number of steps. In this work, an active learning approach based on conavigation of the hypothesis and experimental spaces is introduced. This is realized by combining the structured Gaussian processes containing probabilistic models of the possible system's behaviors (hypotheses) with reinforcement learning policy refinement (discovery). This approach closely resembles classical human-driven physical discovery, when several alternative hypotheses realized via models with adjustable parameters are tested during an experiment. This approach is demonstrated for exploring concentration-induced phase transitions in combinatorial libraries of Sm-doped BiFeO 3 using piezoresponse force microscopy, but it is straightforward to extend it to higher-dimensional parameter spaces and more complex physical problems once the experimental workflow and hypothesis generation are available.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Synthesizing realistic sand assemblies with denoising diffusion in latent space

Abstract The shapes and morphological features of grains in sand assemblies have far‐reaching implications in many engineering applications, such as geotechnical engineering, computer animations, petroleum engineering, and concentrated solar power. Yet, our understanding of the influence of grain geometries on macroscopic response is often only qualitative, due to the limited availability of high‐quality 3D grain geometry data. In this paper, we introduce a denoising diffusion algorithm that uses a set of point clouds collected from the surface of individual sand grains to generate grains in the latent space. By employing a point cloud autoencoder, the three‐dimensional point cloud structures of sand grains are first encoded into a lower‐dimensional latent space. A generative denoising diffusion probabilistic model is trained to produce synthetic sand that maximizes the log‐likelihood of the generated samples belonging to the original data distribution measured by a Kullback‐Leibler divergence. Numerical experiments suggest that the proposed method is capable of generating realistic grains with morphology, shapes and sizes consistent with the training data inferred from an F50 sand database. We then use a rigid contact dynamic simulator to pour the synthetic sand in a confined volume to form granular assemblies in a static equilibrium state with targeted distribution properties. To ensure third‐party validation, 50,000 synthetic sand grains and the 1542 real synchrotron microcomputed tomography (SMT) scans of the F50 sand, as well as the granular assemblies composed of synthetic sand grains are made available in an open‐source repository.

Vlassis, Nikolaos N.↗

DOE OSTI2022

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. Additionally, a modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

42 ENGINEERING↗

DOE OSTI2023

Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties

Here we introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, we design an artificial intelligence to efficiently manipulate the topology of microstructures to generate a massive number of prototypes that exhibit constitutive responses sufficiently close to designated nonlinear constitutive behaviors. To identify the subset of microcstructures with sufficiently precise fine-tuned properties, a convolutional neural network surrogate is trained to replace high-fidelity finite element simulations to filter out prototypes outside the admissible range. Results of this study indicate that the denoising diffusion process is capable of creating microstructures of fine-tuned nonlinear material properties within the latent space of the training data. More importantly, this denoising diffusion algorithm can be easily extended to incorporate additional topological and geometric modifications by introducing high-dimensional structures embedded in the latent space. Numerical experiments are conducted on the open-source mechanical MNIST data set (Lejeune, 2020). Consequently, this algorithm is not only capable of performing inverse design of nonlinear effective media, but also learns the nonlinear structure–property map to quantitatively understand the multiscale interplay among the geometry, topology, and their effective macroscopic properties.

42 ENGINEERING↗

DOE OSTI2024

Data-driven projection pursuit adaptation of polynomial chaos expansions for dependent high-dimensional parameters

Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in the realms of UQ and inference. Among these, polynomial chaos expansions (PCE), when adapted to low-dimensional quantities of interest (QoI), provide effective yet accurate approximations for these QoI in terms of an adapted orthogonal basis. These adaptation techniques have been cast as projection pursuits in Gaussian Hilbert space in what has been referred to as a projection pursuit adaptation (PPA) by Xiaoshu Zeng and Roger Ghanem (2023). The PPA method efficiently identifies an optimal low-dimensional space for representing the QoI and simultaneously evaluates an optimal PCE within that space. The quality of this approximation clearly depends on the size of the training dataset, which is typically a function of the adapted reduced dimension. Here, the complexity of the problem is thus mediated by the complexity of the low-dimensional quantity of interest and not the complexity of the high-dimensional parameter space.

Data-driven↗

DOE OSTI2021

Post-extreme-event restoration using linear topological constraints and DER scheduling to enhance distribution system resilience

In this paper, a post-extreme-event restoration (PEER) algorithm is proposed to improve distribution system resilience. Linear topological constraints are proposed to ensure radial topology after N-k contingencies, possibly in multiple islands. The approach is made comprehensive by considering dispatchable distributed energy resources (DERs), non-dispatchable DERs, and demand responses, as well as on-load tap changers (OLTCs) and shunt capacitors. The goal is to minimize the accumulative expense caused by load reduction payment or penalty, as well as DER operation cost. As a result, the overall system will survive longer with higher resilience during an extreme event. To verify the effectiveness of the PEER algorithm, we proposed a resilience evaluation algorithm using Monte Carlo simulation (MCS) with reduced scenarios. This is based on a probabilistic model for generating random scenarios which consider the uncertainty of line faults and solar irradiance. Combined with the proposed PEER algorithm, this reduced-scenario MCS can evaluate the expected energy not served (EENS) which is an essential index for distribution system resilience. Case studies of the IEEE 33-bus and 123-bus test systems validate the proposed algorithm in reducing EENS.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Toward the application of the Risk-Based Maintenance approach to a hydrogen-fueled manufacturing plant

Safety, reliability, and maintenance of hydrogen-based equipment, including Risk-Based Maintenance (RBM), have recently gained increasing attention, as hydrogen, while key to decarbonizing hard-to-abate sectors, raises safety concerns. However, two literature gaps limit the development of risk-based strategies for hydrogen technologies. First, existing RBM methodologies do not account for hydrogen-specific components, such as electrolyzers, which differ from conventional equipment. Second, available studies on electrolyzer reliability remain largely qualitative or laboratory-scale. This study addresses these gaps by proposing an adapted RBM methodology tailored to hydrogen-fueled manufacturing facilities. Integrating qualitative tools (e.g., FMEA) with probabilistic models (e.g., Bayesian Networks) enables comprehensive hazardous scenarios identification and likelihood estimation. A conceptual layout of a glass furnace supplied by a 3 MW PEM electrolyzer is considered as a case study to demonstrate the feasibility of the adapted RBM framework in identifying high-risk components and enabling maintenance prioritization, potentially improving plant safety.

08 HYDROGEN↗

DOE OSTI2023

Floods and Heavy Precipitation at the Global Scale: 100‐Year Analysis and 180‐Year Reconstruction

Floods and heavy precipitation have disruptive impacts worldwide, but their historical variability remains only partially understood at the global scale. This article aims at reducing this knowledge gap by jointly analyzing seasonal maxima of streamflow and precipitation at more than 3,000 stations over a 100‐year period. The analysis is based on Hidden Climate Indices (HCIs). Like standard climate indices (e.g., Nino 3.4, NAO), HCIs are used as covariates explaining the temporal variability of data, but unlike them, HCIs are estimated from the data. In this work, a distinction is made between common HCIs, that affect both heavy precipitation and floods, and specific HCIs, that exclusively affect one or the other. Overall, HCIs do not show noticeable autocorrelation, but some are affected by noticeable trends. In particular, strong and wide‐ranging trends are identified in precipitation‐specific HCIs, while trends affecting flood‐specific HCIs are weaker and have more localized effects. A probabilistic model is then derived to link HCIs and large‐scale atmospheric variables (pressure, wind, temperature) and to reconstruct HCIs since 1836 using the 20CRv3 reanalysis. In turn this allows estimating the probability of occurrence of floods and heavy precipitation at the global scale. This 180‐year reconstruction highlights flood hot‐spots and hot‐moments in the distant past, well before the establishment of perennial monitoring networks. Finally, the approach presented in this study is generic and paves the way for an improved characterization of historical variability by making a better use of long but highly irregular station data sets.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

MolDiscovery: learning mass spectrometry fragmentation of small molecules

Identification of small molecules is a critical task in various areas of life science. Recent advances in mass spectrometry have enabled the collection of tandem mass spectra of small molecules from hundreds of thousands of environments. To identify which molecules are present in a sample, one can search mass spectra collected from the sample against millions of molecular structures in small molecule databases. The existing approaches are based on chemistry domain knowledge, and they fail to explain many of the peaks in mass spectra of small molecules. Here, we present molDiscovery, a mass spectral database search method that improves both efficiency and accuracy of small molecule identification by learning a probabilistic model to match small molecules with their mass spectra. A search of over 8 million spectra from the Global Natural Product Social molecular networking infrastructure shows that molDiscovery correctly identify six times more unique small molecules than previous methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Co-orchestration of multiple instruments to uncover structure–property relationships in combinatorial libraries

The rapid growth of automated and autonomous instrumentation brings forth opportunities for the co-orchestration of multimodal tools that are equipped with multiple sequential detection methods or several characterization techniques to explore identical samples. This is exemplified by combinatorial libraries that can be explored in multiple locations via multiple tools simultaneously or downstream characterization in automated synthesis systems. In co-orchestration approaches, information gained in one modality should accelerate the discovery of other modalities. Correspondingly, an orchestrating agent should select the measurement modality based on the anticipated knowledge gain and measurement cost. Herein, we propose and implement a co-orchestration approach for conducting measurements with complex observables, such as spectra or images. The method relies on combining dimensionality reduction by variational autoencoders with representation learning for control over the latent space structure and integration into an iterative workflow via multi-task Gaussian Processes (GPs). This approach further allows for the native incorporation of the system's physics via a probabilistic model as a mean function of the GPs. We illustrate this method for different modes of piezoresponse force microscopy and micro-Raman spectroscopy on a combinatorial Sm-BiFeO3 library. However, the proposed framework is general and can be extended to multiple measurement modalities and arbitrary dimensionality of the measured signals.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Probing reaction channels via reinforcement learning

Abstract Chemical reactions are dynamical processes involving the correlated reorganization of atomic configurations, driving the conversion of an initial reactant into a result product. By virtue of the metastability of both the reactants and products, chemical reactions are rare events, proceeding fleetingly. Reaction pathways can be modelled probabilistically by using the notion of reactive density in the phase space of the molecular system. Such density is related to a function known as the committor function, which describes the likelihood of a configuration evolving to one of the nearby metastable regions. In theory, the committor function can be obtained by solving the backward Kolmogorov equation (BKE), which is a partial differential equation (PDE) defined in the full dimensional phase space. However, using traditional methods to solve this problem is not practical for high dimensional systems. In this work, we propose a reinforcement learning based method to identify important configurations that connect reactant and product states along chemical reaction paths. By shooting multiple trajectories from these configurations, we can generate an ensemble of states that concentrate on the transition path ensemble. This configuration ensemble can be effectively employed in a neural network-based PDE solver to obtain an approximation solution of a restricted BKE, even when the dimension of the problem is very high. The resulting solution provides an approximation for the committor function that encodes mechanistic information for the reaction, paving a new way for understanding of complex chemical reactions and evaluation of reaction rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Wasserstein normalized autoencoder for anomaly detection

A novel anomaly detection algorithm is presented. The Wasserstein normalized autoencoder (WNAE) is a normalized probabilistic model that minimizes the Wasserstein distance between the learned probability distribution—a Boltzmann distribution where the energy is the reconstruction error of the autoencoder (AE)—and the distribution of the training data. This algorithm has been developed and applied to the identification of semivisible jets—conical sprays of visible standard model (SM) particles and invisible dark matter states—with the CMS experiment at the CERN LHC. Trained on jets of particles from simulated SM processes, the WNAE is shown to learn the probability distribution of the input data in a fully unsupervised fashion, such that it effectively identifies new physics jets as anomalies. The model exhibits stable, convergent training and recovers strong classification performance for a wide range of signals against the selected background process, for which a standard AE fails because of outlier reconstruction. In addition, the model improves upon standard normalized autoencoders while remaining fully agnostic to the signal. The WNAE directly tackles the problem of outlier reconstruction, a common failure mode of autoencoders in anomaly detection tasks.

Hayrapetyan, Aram [Yerevan Phys. Inst.]↗

DOE OSTI2023

From Optimization to Sampling Through Gradient Flows

Optimization and sampling algorithms play a central role in science and engineering as they enable finding optimal predictions, policies, and recommendations, as well as expected and equilibrium states of complex systems. The notion of “optimality” is formalized by the choice of an objective function, while the notion of an “expected” state is specified by a probabilistic model for the distribution of states. Optimizing rugged objective functions and sampling multimodal distributions is computationally challenging, especially in high-dimensional problems. Here, for this reason, many optimization and sampling methods have been developed by researchers working in disparate fields such as Bayesian statistics, molecular dynamics, genetics, quantum chemistry, machine learning, weather forecasting, econometrics, and medical imaging.

Trillos, N. García↗

DOE OSTI2020

Certified quantum measurement of Majorana fermions

Here, we propose a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We further show that observing a set of ideal measurement statistics implies anticommutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness W , which satisfies 〈 W 〉 ≤ 3 for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value 〈 W 〉 = 5 indicates the degree of confidence in the detection of Majorana fermions.

36 MATERIALS SCIENCE↗