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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Benchmarking noise extrapolation with the OpenPulse control framework

Distilling precise estimates from noisy intermediate scale quantum (NISQ) data has recently attracted considerable attention Kandala et al., Nature (London) 567, 491 (2019). In order to augment digital qubit metrics, such as gate fidelity, we discuss analog error mitigability, i.e., the ability to accurately distill precise observable estimates, as a hybrid quantum classical computing benchmarking task. Specifically, using Rabi oscillations as a test program, we characterize single qubit error rates on IBM's Poughkeepsie superconducting quantum hardware, incorporate control-mediated noise dependence into a generalized rescaling protocol, and analyze how noise characteristics influence Richardson extrapolation-based error mitigation. Finally, our results identify regions in the space of Hamiltonian control fields and circuit depth which are most amenable to reliable noise extrapolation, as well as shed light on how low-level hardware characterization can be used as a predictive tool for uncertainty quantification in error-mitigated NISQ computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Automated Controller Hardware-In-The-Loop Testbed for EV Charger Resilience Analysis

This paper focuses on the development of a tool that includes an automated testbed with controls, protection, and communications integrated into a real-time system to provide a platform to generate data sets for failure modes and effects analysis. This tool establishes a value for automation of data generation for different scenarios and addresses the gap of nonexistent field data for different applications and use cases. The features of this tool can further be expanded to include multiple power electronics models, communication protocols, and scaled system architectures. This general framework was evaluated for a DC fast charger system use case to provide quantitative solution for resiliency.

Starke, Michael↗
DOE OSTI2024

Interlaced Characterization and Calibration (ICC) for Improved Computational Simulation Credibility

Accurate material characterization and model calibration are pivotal for simulations used for high-consequence engineering decisions. Current characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data is collected for a specific model of interest, (3) provide only mean parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work developed a new paradigm—coined Interlaced Characterization and Calibration (ICC)—which drives forward the state-of-the-art in model calibration by bringing together recent advancements into one improved workflow. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) provides uncertainty metrics on the calibrated model parameters, and (4) incorporates these advances into a quasi real-time feedback loop. The ICC framework was validated synthetically with both low-fidelity and high-fidelity simulations paired with several different elastoplastic material models, and was also demonstrated experimentally with an aluminum 6061 cruciform exemplar specimen. Results showed that the ICC framework—in which Bayesian optimal experimental design actively guided the experiment— resulted in calibrations with similar or better accuracy than predetermined experiments based on subject matter expertise. Moreover, the ICC framework produced a complete model calibration— with quantified uncertainties on model parameters—in 1 week, a 5 - 10× increase in efficiency over traditional approaches. Thus, the ICC paradigm improves both the calibration process and quality, by (1) improving efficiency, which increases agility of solid mechanics modeling and enables utilization of computational simulation (CompSim) at earlier stages of the design cycle and (2) providing quantified, and in some cases reduced, parameter uncertainties, which increases confidence in model predictions and supports credible decision making.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Performance Evaluation of Intelligent Solar Control Software Through Hardware-in-the-Loop (CRADA Final Report)

Recent research has highlighted the potential for solar to act as a zero-marginal-cost and zero-emission flexibility resource on the bulk power system when operated with advanced control systems. To increase the performance of these systems, leading technologies, including machine learning (ML) and hierarchical inverter set point allocation, have been developed by Latimer Controls, Inc. to estimate the headroom of large PV plants for grid operation and control; however, these technologies lack comprehensive validation under real-world application scenarios. Latimer Controls, Inc. received two voucher awards for research at a national laboratory from the Department of Energy American Made Solar Prize Round 6. The National Renewable Energy Laboratory (NREL) was selected to collaborate with Latimer staff to conduct a performance evaluation of Latimer PV control software. The NREL team will develop a hardware-in-the-loop (HIL) testbed to perform testing and validation of the Latimer PV control technology in a de-risked yet realistic testbed environment. Latimer and NREL worked together to analyze the test data, draw conclusions from the results, and disseminate the resulting scientific findings. In this CRADA work, we propose to test and validate the real-world application of the Latimer Control solution in an HIL environment. We evaluate the performance of different flexible solar technologies in responding to automatic generation control signals in a closed-loop fashion. In particular, a data-driven potential high limit (PHL) estimation is developed for large solar plants to accurately estimate their headroom so that they have fast and short-time regulation and control capability to participate in grid services and respond to grid signals in real time (e.g., AGC). This PHL estimation algorithm is embedded in a hardware power plant controller (PPC) and tested with an IEEE-39 bus system model developed in RTDS. To account for the varying cloud conditions and diverse inverter dispatches, we developed a 135-MW PV plant with detailed modeling of 27 individual PV modules and inverters using RTDS. The real-world communications used in such big plants, such as ModBus TCP/IP for inverter level and DNP3 for plant level, were developed to emulate the real-world applications in big PV plants. The ML-based PHL estimation method is tested under nine separate weather scenarios against the ‘reference-control’ solution, hereafter referred to as the baseline solution. The baseline method reserves a subset of inverters (reference group) to operate at their PHL at all times and dispatches only the remaining inverters (control group) at curtailed levels to fulfill the flexibility need. Despite being successfully piloted by NREL in California in 2017 and Chile in 2020, there exist two gaps in the state of the art to fully unlock the flexibility of PV plants: a. There is a trade-off between the PHL estimation accuracy and the flexibility range. b. There lacks granularity in the PHL estimation to capture the variation across inverters. The Latimer solution seeks to address these gaps by applying machine learning methods to improve PHL estimation accuracy while accounting for variability at every inverter. Performance metrics were taken from the 2023 Georgia Power CARES utility-scale RFP. The results demonstrate that the ML-based approach outperforms the traditional baseline method in PHL estimation accuracy for 7 of 9 scenarios. The average PHL error across the nine scenarios was 7.40% for the ML-based method, 2.06% less than the 9.46% PHL error average across scenarios that was exhibited by the baseline method. Additionally, the PHL error was below 5% for at least 95% of the testing interval for 3 of 9 tested intervals with the ML approach, whereas it did not achieve this metric for any of the baseline tests. Overall, simulation results indicate the superior performance of an ML-based approach compared to the conventional baseline reference-control approach, showcasing its potential to support grid stability and operational efficiency. This laboratory HIL testing using real PPC, representative power system simulation models in real-time with detailed PV plant and inverter models, and real-world communication protocols gives us confidence that this machine learning based PHL estimation algorithm works well in the hardware PPC and therefore de-risks future field commissioning. The end goal of this project is to advance grid technology to address the grid operation challenges brought by solar plant’s variability and uncertainties in power generation.

14 SOLAR ENERGY↗
DOE OSTI2025

Optimizing Material Selection and Operational Conditions for XHV Systems: Lessons from AISI 1020 and 316L Comparative Studies

In this study, AISI 1020 low-carbon steel is investigated as a cost-effective alternative to SS316 stainless steel for reaching extreme high vacuum (XHV) conditions. After being baked at 400°C, a vacuum chamber made of the low-carbon steel material exhibited an outgassing rate approximately 2000 times smaller than a similar chamber made of stainless steel. Its activation energy for hydrogen diffusion (27 kJ/mol) is less than half that of stainless steel (60.3 kJ/mol), indicating more efficient hydrogen removal during bakeout. MolFlow+ simulations supported the experimental data and demonstrated the importance of system geometry optimization and minimizing stainless steel content for achieving optimal vacuum performance. AISI 1020's magnetic properties, typically considered disadvantageous for accelerator applications, could benefit spin-polarized electron sources by shielding photocathodes from stray fields while simultaneously providing improved vacuum through reduced outgassing. To optimize AISI 1020's performance in XHV systems, practical considerations include pre-baking protocols and careful system design to minimize stainless steel components.

Al-Allaq, Aiman H.↗
DOE OSTI2022

Leafweb: Dataset in Support of Coupled Modeling of Photophysics, Photochemistry, and Biochemistry of Photosynthesis, December 2022 Release

This data set contains measurements of leaf gas exchange and Pulse-Amplitude Modulated (PAM) fluorometry of light, carbon dioxide (CO2), oxygen (O2), and temperature responses from 26 C3 photosynthetic and four C4 photosynthetic species measured by independent researchers in Canada, China, Finland, Netherlands, and United States in the field, garden, or greenhouse. Data were collected between 1987 and 2021, however data for individual species only provide coverage over a few hours to one year. Species include three lianas, three shrubs, two boreal deciduous trees, two boreal evergreen needle-leaf tree, three temperate deciduous trees, four tropical deciduous trees, three tropical evergreen trees, one C3 grass, three C4 grasses, and six crop varieties. These measurements are conducted according to standard protocols in gas exchange (Long and Bernacchi 2003) and PAM fluorometry (Baker 2008). The Scots pine (Pinus sylvestris) dataset contains one-year continuous fluorometry observations made at intervals of 10 or 30 minutes in the field under natural environments using Walz monitoring PAM. Measurements from all other 29 species include simultaneous PAM fluorometry and gas exchange observations. Among these 29 species, seven species were measured with light response curves only (i.e., light intensity varied systematically with ambient CO2 concentration controlled at a constant level, e.g., 400 ppm). All the other 22 species were measured with both the light response and CO2 response (i.e., ambient CO2 concentration varied systematically with light intensity controlled at a constant level, e.g., 1200 µmolm-2s-1). For most species, measurements were made with temperature controlled at ~ 25 degrees Celsius (C) with the exceptions of Scots pine (natural diurnal and seasonal variations), tomato cultivar Basket Vee (~ 21 degrees C), and cotton which contained temperature stress experiments (9 to 40 degrees C). All measurements were made at ambient O2 concentration except for the tomato cultivar Basket Vee and cotton which used two O2 levels (2 and 21%) and rice and tomato cultivar Growdena which used five O2 levels (2, 10, 21, 35, and 50%). This dataset supports the complete modeling of photosynthesis at the leaf scale, including photophysical, photochemical, and biochemical reactions. It will support research in the applications of remotely sensed solar induced chlorophyll fluorescence and the responses of energy dissipation pathways to environmental variations across species and climates. This dataset contains 260 data files in comma separate (.csv) format contained inside 11 compressed (*.zip) files. Additional metadata are provided: one data dictionary, a species information table, and a file-level metadata file in comma separate (.csv) format and a user guide in PDF (*.pdf) format.

air temperature↗
DOE OSTI2022

Application of wideband pulsed high-frequency EPR to molecular quantum spin science

This presentation provides an overview of a range of new applications in the area of molecular quantum spin science that are now possible at the US National High Magnetic Field Laboratory as a result of the development of a wideband, high-power 94 GHz pulsed EPR spectrometer. Here, this instrument allows true Fourier-transform detected experiments spanning a 1 GHz instantaneous bandwidth, akin to what has been possible in NMR for several decades. The presentation will begin by describing experiments on a nitroxide radical using chirped pulses, enabling acquisition of the full spectrum in a single sequence, thus providing a very efficient and convenient means to measure the field orientation dependence of the spin-lattice relaxation time, T 1 . This will be followed by a discussion of a coherent population transfer protocol involving the 2S + 1 = 8 Zeeman levels associated with the spin S = 7/2 Gd 3+ ion, potentially paving the way towards implementation of well-known quantum search algorithms. It will also be shown how the use of chirped pulses provides a route to achieving highly non-thermal spin populations, suggesting novel initialization schemes.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Revealing topology in metals using experimental protocols inspired by K-theory

Topological metals are conducting materials with gapless band structures and nontrivial edge-localized resonances. Their discovery has proven elusive because traditional topological classification methods require band gaps to define topological robustness. Inspired by recent theoretical developments that leverage techniques from the field of C*-algebras to identify topological metals, here, we directly observe topological phenomena in gapless acoustic crystals and realize a general experimental technique to demonstrate their topology. Specifically, we not only observe robust boundary-localized states in a topological acoustic metal, but also re-interpret a composite operator—mathematically derived from the K-theory of the problem—as a new Hamiltonian whose physical implementation allows us to directly observe a topological spectral flow and measure the topological invariants. Our observations and experimental protocols may offer insights for discovering topological behaviour across a wide array of artificial and natural materials that lack bulk band gaps.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Microwave-Free Dynamic Nuclear Polarization via Sudden Thermal Jumps

Dynamic nuclear polarization (DNP) presently stands as the preferred strategy to enhance the sensitivity of nuclear magnetic resonance measurements, but its application relies on the use of high-frequency microwave to manipulate electron spins, an increasingly demanding task as the applied magnetic field grows. Here we investigate the dynamics of a system hosting a polarizing agent formed by two distinct paramagnetic centers near a level anticrossing. We theoretically show that nuclear spins polarize efficiently under a cyclic protocol that combines alternating thermal jumps and radio-frequency pulses connecting hybrid states with opposite nuclear and electronic spin alignment. Central to this process is the difference between the spin-lattice relaxation times of either electron spin species, transiently driving the electronic spin bath out of equilibrium after each thermal jump. Without the need for microwave excitation, this route to enhanced nuclear polarization may prove convenient, particularly if the polarizing agent is designed to feature electronic level anticrossings at high magnetic fields.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Quantifying and Controlling Entanglement in the Quantum Magnet Cs 2 CoCl 4

The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs 2 CoCl 4 , a close realization of the S = 1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. Overall, we find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.

1-dimensional spin chains↗
DOE OSTI2026

Data & Code from Phoenix CPPP Phase 2 Analysis

This data and code package supports the analysis presented in “Beyond Surface Cooling: Comprehensive Field Assessment of Reflective Pavement Thermal Performance in Phoenix, Arizona” and provides fully reproducible workflows for evaluating the thermal performance of cool pavement treatments in a hot urban environment. The dataset integrates multi-modal field measurements collected across residential and nonresidential settings, including mobile air temperature traverses, stationary air temperature monitoring, residential mean radiant temperature (MRT) measurements, subsurface temperature profiles, and controlled testbed observations. The data package contains raw and processed datasets in comma-separated value (CSV) format, accompanying metadata files describing site characteristics and measurement protocols, and R scripts (.R files) used for data cleaning, time synchronization, spatial and temporal matching, quality control filtering, statistical comparison, and figure generation. All analyses were conducted using R (version ≥ 4.2.0) with commonly available packages (e.g., tidyverse, lubridate, data.table, ggplot2). No proprietary software is required to reproduce results. Field campaigns were designed to quantify the effects of high-reflectance pavement coatings on surface temperature, near-surface air temperature, subsurface heat propagation, and radiative heat exposure. Temporal alignment procedures include standardized timestamp conversion and nearest-neighbor matching of high-frequency sensor measurements to stop-based metadata within defined tolerance windows to ensure comparability across instruments. The workflows generate summary statistics, treatment–control contrasts, depth-dependent thermal gradients, and time-series visualizations used in the associated publication. By integrating mobile, stationary, radiative, and subsurface measurements within a unified and transparent processing framework, this package enables comprehensive evaluation of cool pavement performance across multiple thermal exposure pathways and supports reuse in future urban heat mitigation and climate resilience studies.

AIR TEMPERATURE↗
DOE OSTI2022

Transmission estimation at the quantum Cramér-Rao bound with macroscopic quantum light

The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical resources. Theoretically, the fundamental minimum uncertainty in the estimation of a parameter for a given probing state is bounded by the quantum Cramér-Rao bound. From a practical perspective, it is necessary to find physical measurements that can saturate this fundamental limit and to show experimentally that it is possible to perform measurements with the required precision to do so. Here we perform experiments that saturate the quantum Cramér-Rao bound for transmission estimation over a wide range of transmissions when probing the system under study with a continuous wave bright two-mode squeezed state. To properly take into account the imperfections in the generation of the quantum state, we extend our previous theoretical results to incorporate the measured properties of the generated quantum state. For our largest transmission level of 84%, we show a 62% reduction over the optimal classical protocol in the variance in transmission estimation when probing with a bright two-mode squeezed state with -8 dB of intensity-difference squeezing. Given that transmission estimation is an integral part of many sensing protocols, such as plasmonic sensing, spectroscopy, calibration of the quantum efficiency of detectors, etc., the results presented promise to have a significant impact on a number of applications in various fields of research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Monte Carlo Simulations of Polarized Radiative Transfer in Neutron Star Atmospheres

Soft X-ray emission from neutron stars affords powerful diagnostic tools for uncovering their surface and interior properties, as well as their geometric configurations. In the atmospheres of neutron stars, the presence of magnetic fields alters the photon-electron scattering cross sections, resulting in nontrivial angular dependence of intensity and polarization of the emergent signals. This paper presents recent developments of our Monte Carlo simulation, MAGTHOMSCATT, which tracks the complex electric field vector for each photon during its transport. Our analysis encompasses the anisotropy and polarization characteristics of X-ray emission for field strengths ranging from nonmagnetic to extremely magnetized regimes that are germane to magnetars. In the very low field domain, we reproduced the numerical solution to the radiative transfer equation for nonmagnetic Thomson scattering, and provided analytical fits for the angular dependence of the intensity and the polarization degree. These fits can be useful for studies of millisecond pulsars and magnetic white dwarfs. By implementing a refined injection protocol, we show that, in the magnetar regime, the simulated intensity and polarization pulse profiles of emission from extended surface regions becomes invariant with respect to the ratio of photon (ω) and electron cyclotron (ω B ) frequencies once ω/ω B ≲ 0.01. This circumvents the need for simulations pertinent to really high magnetic field strengths, which are inherently slower. Our approach will be employed elsewhere to model observational data to constrain neutron star geometric parameters and properties of emitting hot spots on their surfaces.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Multi-qubit nanoscale sensing with entanglement as a resource

Nitrogen vacancy (NV) centres in diamond are widely deployed as local magnetic sensors, using single-qubit control to measure both time-averaged fields and noise with nanoscale spatial resolution. Moving beyond single qubits to multi-qubit control enables new sensing modalities such as measuring nonlocal spatiotemporal correlators or using entangled states to enhance measurement sensitivity. Here, in this work, we describe protocols for using optically unresolved NV centre pairs and nuclear spins as multi-qubit sensors for measuring correlated noise at nanometre length scales. For noninteracting NV centres, we implement a phase-cycling protocol that disambiguates magnetic correlations from variance fluctuations, leveraging the presence of a third qubit, a 13 C nucleus, to effect coherent single-NV spin flips and enable phase cycling even for co-aligned NV centres that are spectrally unresolved. For length scales around 10 nm, we create maximally entangled Bell states through dipole–dipole coupling between two NV centres and use these entangled states to directly read out the magnetic field correlation, rather than reconstructing it from independent measurements of unentangled NV centres. Importantly, this changes the scaling of sensitivity with readout noise from quadratic to linear. For conventional off-resonant readout of the NV centre spin state (for which the readout noise is roughly 30 times the quantum projection limit), this results in more than an order of magnitude improvement in sensitivity. Finally, we demonstrate methods for detecting high spatial- and temporal-resolution correlators with pairs of strongly interacting NV centres.

condensed-matter physics↗
DOE OSTI2025

Continuum-electron interferometry for enhancement of photoelectron circular dichroism and measurement of bound, free, and mixed contributions to chiral response

We develop photoelectron interferometry based on laser-assisted extreme ultraviolet ionization for flexible and robust control of photoelectron circular dichroism in randomly oriented chiral molecules. A comb of XUV photons ionizes a sample of chiral molecules in the presence of a time-delayed infrared or visible laser pulse promoting interferences between components of the XUV-ionized photoelectron wave packet. In striking contrast to multicolor phase control schemes relying on pulse shaping techniques, the magnitude of the resulting chiral signal is here controlled by the time delay between the XUV and laser pulses. Furthermore, we show that the relative polarization configurations of the XUV and IR fields allow for disentangling the contributions of bound and continuum states to the chiral response. Our proposal provides a simple, robust, and versatile tool for the control of photoelectron circular dichroism and experimentally feasible protocol for probing the individual contributions of bound and continuum states to the photoelectron circular dichroism in a time-resolved manner.

atomic and molecular processes in external fields↗
DOE OSTI2020

IEEE 1547-2018 Based Interoperable PV Inverter with Advanced Grid-Support Functions

Grid integration of photovoltaic (PV) inverters has been increasing in the past decade. As a result of the uncertainties introduced with high penetrations of PV, better monitoring and control of the PV inverters becomes crucial for improving overall system stability. This paper focuses on the communications capability of the inverter controller and on enabling interoperability. Multiple standards are available to enable interoperability in PV inverters. In this paper, an interoperable controller, enabled by Distributed Network Protocol 3 (DNP3) communications protocols, is developed for a grid-connected, three-phase PV inverter. The DNP3 server for the PV inverter is programmed on the real-time layer of the field-programmable gate array (FPGA)-based inverter controller. Set points for advanced inverter control functions, such as volt/VAr curves, ride-through curves, are sent from a DNP3 client, a simulated distribution management system application, to the PV inverter through DNP3. This communications capability of the inverter controller is validated using a controller-hardware-in-the-loop experimental setup. The code developed to achieve the interoperability is available in the public domain through open-source software licensing. This interoperability will enable smoother grid integration of smart PV inverters with advanced grid-support functions as well as allow better monitoring and control of PV inverters for grid stability.

14 SOLAR ENERGY↗
DOE OSTI2023

Machine learning assisted derivation of minimal low-energy models for metallic magnets

Abstract We consider the problem of extracting a low-energy spin Hamiltonian from a triangular Kondo Lattice Model (KLM). The non-analytic dependence of the effective spin-spin interactions on the Kondo exchange excludes the use of perturbation theory beyond the second order. We then introduce a Machine Learning (ML) assisted protocol to extract effective two- and four-spin interactions. The resulting spin model reproduces the phase diagram of the original KLM as a function of magnetic field and single-ion anisotropy and reveals the effective four-spin interactions that stabilize the field-induced skyrmion crystal phase. Moreover, this model enables the computation of static and dynamical properties with a much lower numerical cost relative to the original KLM. A comparison of the dynamical spin structure factor in the fully polarized phase computed with both models reveals a good agreement for the magnon dispersion even though this information was not included in the training data set.

Sharma, Vikram (ORCID:0000000189105519)↗
DOE OSTI2025

Solving the Bernstein-Vazirani problem using Majorana-based topological quantum algorithms

Executing quantum algorithms using Majorana zero modes—a major milestone for the field of topological quantum computing—requires a platform that can be scaled to large quantum registers, can be controlled in real time and space, and a braiding protocol that uses the unique properties of these exotic particles. Here, we demonstrate the first successful simulation of a Majorana-based, fault-tolerant quantum algorithm to solve the Bernstein-Vazirani problem in two-dimensional magnet-superconductor hybrid structures from initialization to read-out of the final many-body state. Utilizing the Majorana zero modes’ topological properties, we introduce an optimized braiding protocol for the algorithm and a scalable architecture for its implementation with an arbitrary number of qubits. We visualize the algorithm protocol in real time and space by computing the non-equilibrium density of states, which is proportional to the time-dependent differential conductance, and the non-equilibrium charge density, which assigns a unique signature to each final state of the algorithm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗