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DOE OSTI2024

Application of Partial Least Squares Approaches to Pyroprocessing ER Data

Multivariate approaches show promise for application to process monitoring for safeguards of pyroprocessing. Past MPACT work explored the application of Principal Component Analysis (PCA) to detect off-normal conditions in pyroprocessing electrorefiner (ER) data from in the Hot Fuel Examination Facility (HFEF) at Idaho National Laboratory (INL) known as the Scalable Pyrochemical Recycling testbed (SPyRe) ER. PCA, however, does not consider the output variables. In FY24, multivariate analysis was extended from PCA to Partial Least Squares (PLS) analysis. PLS maximizes the variance between both the input signals and output variables. In the case of this work, PLS was applied in two different manners: Predictive PLS and Discriminant PLS. Predictive PLS maximizes the covariance between the process variables of the ER and the measured U concentration from in-situ voltammetry. Discriminant PLS maximizes the covariance between the process variables and a set of training process “states” such as known off-normal conditions. By projecting into the latent variable space in PLS, the process variables can be regressed onto the outputs and predictions can be made for new data sets. In this work, by applying predictive PLS, a penalized non-linear PLS approach was able to make predictions of concentration based on test and training data and detect when operations were off-normal. However, the predictive PLS does not classify the signals to which off-normal operations are attributable. Discriminant PLS can be used to classify off-normal operations but is inadequate to properly classify specific off-normal classes like power supply faults when the Discriminant PLS model is only specifically trained to detect that off-normal class. When all faults are trained against the observation data, all three operational classes are accurately classified and distinguished. Thus, future application of latent variable techniques should not select any given method, but should use a mixture of PCA, Predictive PLS, and Discriminant PLS.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Evaluating the Durability of Balance of Systems Components Using Combined-Accelerated Stress Testing

The degradation of photovoltaic (PV) balance of systems (BoS) components is not well-studied, but the consequences include: offline-modules, -strings, -inverters; system shutdown; arc-faults; and fires. A utility provider experienced a ~30% failure rate in their power transfer chain, attributed to branch connectors. Field-failed specimen assemblies were therefore examined, consisting of cable connector, branch connector and discrete fuse components. Unused field-vintage specimens are presently being examined using combined-accelerated stress testing (C-AST) to clarify the most influential environmental stressors as well as the effect of external mechanical perturbation. A benchtop prototype fixture was used to develop the perturbation capability for C-AST. The benchtop experiments were also used to develop the in-situ data acquisition of specimen: current, voltage, and temperature. A significant increase in operating temperature, ~100 deg C from ~40 deg C, and a different failure mode was observed immediately once periodic mechanical perturbation was applied. The current at failure was decreased from 35 A (with failure occurring in the fuses) to 15 A (failure at the male/female metal pin connection). After initial examination using X-ray computed tomography, the external plastic was machined away from failed specimens to allow failure analysis, including the extraction of the internal convolute springs for morphological examination (optical- and electron-microscopy). Chemical composition analysis included: energy-dispersive X-ray spectroscopy, differential scanning calorimetry, and Fourier transform infrared spectroscopy.

balance of systems↗

DOE OSTI2022

Evaluating the Durability of Balance of Systems Components Using Combined-Accelerated Stress Testing: Preprint

The degradation of photovoltaic (PV) balance of systems (BoS) components is not well-studied, but the consequences include: offline-modules, -strings, -inverters; system shutdown; arc-faults; and fires. A utility provider experienced a ~30% failure rate in their power transfer chain, originally attributed to branch connectors. Field-failed specimen assemblies were therefore examined, consisting of cable connector, branch connector, and discrete fuse components. Unused field-vintage specimens are presently being examined using combined-accelerated stress testing (C-AST) to clarify the most influential environmental stressors as well as the effect of external mechanical perturbation. A benchtop prototype fixture was used to develop the perturbation capability for the C-AST chamber. The benchtop experiments were also used to develop the in-situ data acquisition of specimen: current, voltage, and temperature. A significant increase in operating temperature, ~100 deg C from ~40 deg C, and a different failure mode was observed promptly once periodic mechanical perturbation was applied. The current at failure was decreased from 35 A (with failure in the fuses) to 15 A (failure at the male/female metal pin connection). After initial examination using X-ray computed tomography, the external plastic was machined away from failed specimens to allow failure analysis, including the extraction of the internal convolute springs for morphological examination (optical- and electron-microscopy).

balance of systems↗

DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗

DOE OSTI2021

Desert Peak Geodatabase for Geothermal Exploration Artificial Intelligence

These files contain the geodatabases related to the Desert Peak Geothermal Field. It includes all input and output files used in the project. The files include data categories of raw data, pre-processed data, and analysis (post-processed data). In each of these categories there are six additional types of raster catalogs including Radar, SWIR, Thermal, Geophysics, Geology, and Wells. The files for the Desert Peak Geothermal Site are used with the Geothermal Exploration Artificial Intelligence to identify indicators of blind geothermal systems. The included zip file is a geodatabase to be used with ArcGIS and the tar file is an inclusive database that encompasses the inputs and outputs for the Desert Peak Geothermal Field.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

Subsurface Characterization and Machine Learning Predictions at Brady Hot Springs Results

Geothermal power plants typically show decreasing heat and power production rates over time. Mitigation strategies include optimizing the management of existing wells - increasing or decreasing the fluid flow rates across the wells - and drilling new wells at appropriate locations. The latter is expensive, time-consuming, and subject to many engineering constraints, but the former is a viable mechanism for periodic adjustment of the available fluid allocations. Data and supporting literature from a study describing a new approach combining reservoir modeling and machine learning to produce models that enable strategies for the mitigation of decreased heat and power production rates over time for geothermal power plants. The computational approach used enables translation of sets of potential flow rates for the active wells into reservoir-wide estimates of produced energy and discovery of optimal flow allocations among the studied sets. In our computational experiments, we utilize collections of simulations for a specific reservoir (which capture subsurface characterization and realize history matching) along with machine learning models that predict temperature and pressure timeseries for production wells. We evaluate this approach using an "open-source" reservoir we have constructed that captures many of the characteristics of Brady Hot Springs, a commercially operational geothermal field in Nevada, USA. Selected results from a reservoir model of Brady Hot Springs itself are presented to show successful application to an existing system. In both cases, energy predictions prove to be highly accurate: all observed prediction errors do not exceed 3.68% for temperatures and 4.75% for pressures. In a cumulative energy estimation, we observe prediction errors that are less than 4.04%. A typical reservoir simulation for Brady Hot Springs completes in approximately 4 hours, whereas our machine learning models yield accurate 20-year predictions for temperatures, pressures, and produced energy in 0.9 seconds. This paper aims to demonstrate how the models and techniques from our study can be applied to achieve rapid exploration of controlled parameters and optimization of other geothermal reservoirs. Includes a synthetic, yet realistic, model of a geothermal reservoir, referred to as open-source reservoir (OSR). OSR is a 10-well (4 injection wells and 6 production wells) system that resembles Brady Hot Springs (a commercially operational geothermal field in Nevada, USA) at a high level but has a number of sufficiently modified characteristics (which renders any possible similarity between specific characteristics like temperatures and pressures as purely random). We study OSR through CMG simulations with a wide range of flow allocation scenarios. Includes a dataset with 101 simulated scenarios that cover the period of time between 2020 and 2040 and a link to the published paper about this project, where we focus on the Machine Learning work for predicting OSR's energy production based on the simulation data, as well as a link to the GitHub repository where we have published the code we have developed (please refer to the repository's readme file to see instructions on how to run the code). Additional links are included to associated work led by the USGS to identify geologic factors associated with well productivity in geothermal fields. Below are the high-level steps for applying the same modeling + ML process to other geothermal reservoirs: 1. Develop a geologic model of the geothermal field. The location of faults, upflow zones, aquifers, etc. need to be accounted for as accurately as possible 2. The geologic model needs to be converted to a reservoir model that can be used in a reservoir simulator, such as, for instance, CMG STARS, TETRAD, or FALCON 3. Using native state modeling, the initial temperature and pressure distributions are evaluated, and they become the initial conditions for dynamic reservoir simulations 4....

15 GEOTHERMAL ENERGY↗

DOE OSTI2022

Evaluating the Durability of Balance of Systems Components Using Combined-Accelerated Stress Testing

The degradation of photovoltaic (PV) balance of systems (BoS) components is not well-studied, but the consequences include offline modules, strings, and inverters; system shutdown; arc faults; and fires. A utility provider experienced a ~30% failure rate in their power transfer chain, originally attributed to branch connectors. Field-failed specimen assemblies were therefore examined, consisting of cable connector, branch connector, and discrete fuse components. In this study, unused field-vintage specimens are examined using combined-accelerated stress testing (C-AST) to clarify the most influential environmental stressors as well as the effect of external mechanical perturbation. A benchtop prototype fixture was used to develop the perturbation capability for the C-AST chamber. The benchtop experiments were also used to develop the in-situ data acquisition of specimen current, voltage, and temperature. A significant increase in operating temperature (~100 degrees C from ~40 degrees C) and a different failure mode were observed promptly once periodic mechanical perturbation was applied. The current at failure was decreased from 35 A (with failure in the fuses) to 15 A (failure at the male/female metal pin connection). After initial examination using X-ray computed tomography, the external plastic was machined away from failed specimens to allow for failure analysis, including the extraction of the internal convolute springs for morphological examination (optical and electron microscopy).

balance of systems↗

DOE OSTI2021

Reconfigurable Framework for Resilient Semantic Segmentation for Space Applications

Deep learning (DL) presents new opportunities for enabling spacecraft autonomy, onboard analysis, and intelligent applications for space missions. However, DL applications are computationally intensive and often infeasible to deploy on radiation-hardened (rad-hard) processors, which traditionally harness a fraction of the computational capability of their commercial-off-the-shelf counterparts. Commercial FPGAs and system-on-chips present numerous architectural advantages and provide the computation capabilities to enable onboard DL applications; however, these devices are highly susceptible to radiation-induced single-event effects (SEEs) that can degrade the dependability of DL applications. In this article, we propose Reconfigurable ConvNet (RECON), a reconfigurable acceleration framework for dependable, high-performance semantic segmentation for space applications. In RECON, we propose both selective and adaptive approaches to enable efficient SEE mitigation. In our selective approach, control-flow parts are selectively protected by triple-modular redundancy to minimize SEE-induced hangs, and in our adaptive approach, partial reconfiguration is used to adapt the mitigation of dataflow parts in response to a dynamic radiation environment. Combined, both approaches enable RECON to maximize system performability subject to mission availability constraints. We perform fault injection and neutron irradiation to observe the susceptibility of RECON and use dependability modeling to evaluate RECON in various orbital case studies to demonstrate a 1.5–3.0× performability improvement in both performance and energy efficiency compared to static approaches.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Validation of Play Fairway Analysis of the geothermal potential of Camas Prairie, south-central Idaho, by an exploration well

Abstract Play Fairway Analysis (PFA) methodology was adapted for geothermal exploration at Camas Prairie, Idaho. Geophysical data, structural and geologic mapping, volcanic rock ages and vent locations, and the distribution of thermal springs and wells all indicated a relatively high geothermal potential along the southern margin of the Prairie. An exploration well (USU Camas-1) was drilled to a depth of 618.3 m to validate the PFA. A permeable zone was encountered at ~ 357.5 m with a maximum measured temperature of ~ 80 °C, which was suppressed following the injection of cold water. A moderate transmissivity of ~ 0.25–1 cm 2 /s estimated from an injection test as well a seasonal artesian flow at ~ 0.7 L/s corroborate the presence of a permeable zone. The existence of a lacustrine clay seal was confirmed near the bottom of the basin-fill sediment occupying the upper 314 m of the well. Geothermometers suggest the USU Camas-1 well water equilibrated at a reservoir temperature of ~ 120 °C. Based on the locations of both thermal and cold wells, geothermal fluids appear to be flowing upward along one or both of two fault systems. The presence of young basalts and elevated helium isotope ratios suggest that the heat source of Camas Prairie is magmatic. However, the faults may be acting as a conduit for geothermal fluids to rise from great depth without a shallow magmatic source being present. Camas Prairie is a promising area for geothermal development, but the relatively low reservoir temperatures indicate this resource may not be suitable for electric generation. Perhaps the best use would be for heating.

Lachmar, Thomas E. (ORCID:0000000249640119)↗

NASA NTRS1991

Control system failure monitoring using generalized parity relations

Many applications require that a control system must be tolerant to the failure of its components. This is especially true for large space-based systems that must work unattended and with long periods between maintenance. Fault tolerance can be obtained by detecting the failure of the control system component, determining which component has failed, and reconfiguring the system so that the failed component is isolated from the controller. Component failure detection experiments that were conducted on an experimental space structure, the NASA Langley Mini-Mast are presented. Two methodologies for failure detection and isolation (FDI) exist that do not require the specification of failure modes and are applicable to both actuators and sensors. These methods are known as the Failure Detection Filter and the method of Generalized Parity Relations. The latter method was applied to three different sensor types on the Mini-Mast. Failures were simulated in input-output data that were recorded during operation of the Mini-Mast. Both single and double sensor parity relations were tested and the effect of several design parameters on the performance of these relations is discussed. The detection of actuator failures is also treated. It is shown that in all the cases it is possible to identify the parity relations directly from input-output data. Frequency domain analysis is used to explain the behavior of the parity relations.

Vanschalkwyk, Christiaan Mauritz↗

NASA NTRS2010

Predicting Ares I Reaction Control System Performance by Utilizing Analysis Anchored with Development Test Data

The Ares I launch vehicle is an integral part of NASA s Constellation Program, providing a foundation for a new era of space access. The Ares I is designed to lift the Orion Crew Module and will enable humans to return to the Moon as well as explore Mars.1 The Ares I is comprised of two inline stages: a Space Shuttle-derived five-segment Solid Rocket Booster (SRB) First Stage (FS) and an Upper Stage (US) powered by a Saturn V-derived J-2X engine. A dedicated Roll Control System (RoCS) located on the connecting interstage provides roll control prior to FS separation. Induced yaw and pitch moments are handled by the SRB nozzle vectoring. The FS SRB operates for approximately two minutes after which the US separates from the vehicle and the US Reaction Control System (ReCS) continues to provide reaction control for the remainder of the mission. A representation of the Ares I launch vehicle in the stacked configuration and including the Orion Crew Exploration Vehicle (CEV) is shown in Figure 1. Each Reaction Control System (RCS) design incorporates a Gaseous Helium (GHe) pressurization system combined with a monopropellant Hydrazine (N2H4) propulsion system. Both systems have two diametrically opposed thruster modules. This architecture provides one failure tolerance for function and prevention of catastrophic hazards such as inadvertent thruster firing, bulk propellant leakage, and over-pressurization. The pressurization system on the RoCS includes two ambient pressure-referenced regulators on parallel strings in order to attain the required system level single Fault Tolerant (FT) design for function while the ReCS utilizes a blow-down approach. A single burst disk and relief valve assembly is also included on the RoCS to ensure single failure tolerance for must-not-occur catastrophic hazards. The Reaction Control Systems are designed to support simultaneously firing multiple thrusters as required

Stein, William B.↗

NASA NTRS2008

Direct Adaptive Control of Systems with Actuator Failures: State of the Art and Continuing Challenges

In this paper, the problem of controlling systems with failures and faults is introduced, and an overview of recent work on direct adaptive control for compensation of uncertain actuator failures is presented. Actuator failures may be characterized by some unknown system inputs being stuck at some unknown (fixed or varying) values at unknown time instants, that cannot be influenced by the control signals. The key task of adaptive compensation is to design the control signals in such a manner that the remaining actuators can automatically and seamlessly take over for the failed ones, and achieve desired stability and asymptotic tracking. A certain degree of redundancy is necessary to accomplish failure compensation. The objective of adaptive control design is to effectively use the available actuation redundancy to handle failures without the knowledge of the failure patterns, parameters, and time of occurrence. This is a challenging problem because failures introduce large uncertainties in the dynamic structure of the system, in addition to parametric uncertainties and unknown disturbances. The paper addresses some theoretical issues in adaptive actuator failure compensation: actuator failure modeling, redundant actuation requirements, plant-model matching, error system dynamics, adaptation laws, and stability, tracking, and performance analysis. Adaptive control designs can be shown to effectively handle uncertain actuator failures without explicit failure detection. Some open technical challenges and research problems in this important research area are discussed.

Tao, Gang↗

NASA NTRS1990

Photoclinometric analysis of wrinkle ridges on Lunae Planum, Mars

Wrinkle ridges are common morphologic features on Mars. Both volcanic and tectonic mechanisms were suggested to explain their origin; recent work has focused on a compressional origin. Analysis of terrestrial analogs has greatly influenced and aided the understanding of wrinkle ridge formation. An important aspect necessary to intrepret structure is topography. Topographic profiles across ridges can provide important constraints for models of internal structure and analyzing deformation associated with ridges. Topographic maps of Mars are too coarse to resolve the topography of individual ridges; therefore, monoscopic photoclinometry was used to derive topographic profiles for the ridges. Profiles spaced a few kilometers apart were obtained for each ridge, the number depended on ridge length, morphology, and albedo variation. Photoclinometry relies on pixel brightness variations which results from topography, albedo, or both. Because of the albedo variations, photoclimometric profiles can not be extended across large distances, such as between adjacent ridges (about 20 to 80 km). However, the technique is applicable to shorter distances, such as the distance across typical ridges. Profiles were measured across the ridge and extended a few kilometers on either side, including all visible components of the ridge. The results of these measurements and the use of internal structure and topographic profile models for estimating the shortening due to folding and faulting are discussed.

Plescia, J. B.↗

DOE OSTI2023

Multiscale spatial analysis of fracture nodes in two dimensions

Spatial arrangement of fractures as a function of scale is an important component of fracture quantification for inferential and predictive modeling. Available methods that analyze fracture spatial arrangement are based on one-dimensional spacing data; therefore, they are limited to semi-parallel fractures. Such methods cannot be applied to fracture networks in higher dimensions, particularly when fractures have different orientations. Here to characterize fracture arrangements in two dimensions, we propose using Ripley’s K-function, as a method of point pattern analysis, to quantify spatial arrangement of fracture nodes. Fracture nodes, such as barycenters, intersection points, and tips, are point-based representations of fracture locations and connectivity within the fracture network. We introduce formulations for isotropic as well as directional analyses of spatial arrangement. In addition, we derive formulations for edge correction in circular and rectangular study domains. Finally, we demonstrate applications of Ripley’s K-function on two natural fracture datasets. Our proposed method supports quantification and characterization of fracture spatial arrangements that allow practitioners to build representative models of fractures in the subsurface.

02 PETROLEUM↗

DOE OSTI2026

A Cryogenic Muon Tagging System Integrated with a Superconducting Qubit Device for Radiation-Induced Error Mitigation

Superconducting qubits are highly sensitive to ionizing radiation, which can induce correlated errors and limit scalable fault-tolerant quantum computing. In particular, cosmic-ray muons can deposit energy in the substrate, generating phonon bursts that break Cooper pairs and produce quasiparticles, leading to correlated decoherence events across multiple qubits. We present the development of a cryogenic muon tagging system based on Kinetic Inductance Detectors (KIDs) and its integration with superconducting quantum hardware. Originally developed within the ACE-SuperQ project and validated as a standalone detector, the system demonstrated a muon tagging efficiency of approximately 90% and excellent agreement with Monte Carlo simulations. Building on this validation, the tagging system has been integrated with a multi-qubit superconducting chip operated in a dilution refrigerator. The detector configuration consists of a multi-layer KID stack arranged above and below the quantum device, enabling time-coincident identification of muon-induced events within the same cryogenic environment. The integrated setup has been successfully commissioned, enabling simultaneous operation of the qubit chip and the muon tagging system. A first measurement campaign has been carried out, and preliminary data show time-correlated events between the muon tagging detectors and the qubit readout. A quantitative analysis of radiation-induced effects on qubit performance is currently ongoing. This work represents a step toward the implementation of event-level radiation tagging as a tool for characterizing and potentially mitigating correlated errors in superconducting quantum processors, while establishing a modular platform for future studies at the interface between particle physics and quantum information science.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗

NASA NTRSDate not supplied

Design for Reliability (DfR) in Space Life Support

The engineering process of Design for Reliability (DfR) is well established in the automotive and aerospace industries. DfR should be useful in the future development of space life support systems. DfR is a sequence of tasks that develop system requirements and plan reliability analysis and testing. First and fundamentally, the reliability requirement is defined. Next the system reliability model is developed, often using a reliability block diagram. The overall system reliability requirement is allocated to the subsystems and an estimate of the attainable reliability is made. This expected reliability can be improved by simplifying the design by removing components or by replacing less reliable components. Improving reliability can require difficult compromises, such as reducing performance requirements, increasing budget, or extending testing. The actual system reliability can be determined only by testing, which should continue long enough to provide the required confidence in the measured value. New systems often have unexpected design errors that cause failures in early testing. The usual reliability improvement process of testing, finding the failure modes, and redesigning to remove them reduces the failure rate and is referred to as “reliability growth.” After redesign has been completed, the system should be further tested to determine the actual achieved reliability more accurately. If the final system failure rate is too high, redundant systems can be used to improve overall operational reliability. Adding redundancy simply to increase the one- or two-fault tolerance metric may sometimes reduce reliability. Reliability can be improved in three ways: redesigning the system to include more reliable subsystems and components, reliability growth testing and failure mode removal, and by using parallel redundant systems. DfR should combine these approaches to achieve the required reliability while managing performance, cost, and schedule.

Reliability↗

NASA NTRSDate not supplied

Design for Reliability (DfR) in Space Life Support

Reliability↗

DOE OSTI2026

Fault-tolerant resource comparison of qudit and qubit encodings for diagonal quadratic operators

Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings, but their fault-tolerant advantage over qubit encodings remains unclear. We compare the non-Clifford cost of implementing quadratic diagonal evolutions, exemplified by 𝑈 = 𝑒$^{−𝑖⁢𝑡⁢𝜙^2_𝑥}$ in a uniform field-amplitude discretization of a real scalar field, using either one logical 𝑑-level qudit or 𝑛 𝑏 = ⌈log 2⁡ 𝑑⌉ logical qubits. We analyze two standard settings: product-formula simulation and linear combination of unitaries (LCU) per block encoding, taking the resource metric to be the number of non-Clifford gates after synthesis into a discrete logical gate set. Because tight synthesis bounds for general single-qudit rotations are not known, we express the qudit constructions in terms of embedded two-level SU⁡(2) rotations and derive explicit finite-𝑑 break-even conditions for their synthesis cost; these serve as compiler targets for when qudit encodings can outperform the qubit baseline. Within the constructive models studied here, product-formula implementations would require an exponentially stronger per-primitive synthesis advantage for qudits to win asymptotically, while in the LCU setting the qubit encoding is asymptotically cheaper in 𝑑. Nevertheless, the finite-𝑑 threshold analysis identifies low-dimensional regions in which qudits can yield meaningful constant-factor savings, particularly for LCU-based implementations. As a secondary analysis of the LCU construction, we use an idealized negligible-overhead qubit-qudit code-switching model to give an absolute 𝑇-count comparison and reinterpret the savings as an allowable per-switch overhead budget.

Godwood, Samuel [Univ. of Liverpool (United Kingdo↗