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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 1,603 records · Page 89
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Effect of the Selective Halogenation of Small Molecule Acceptors on the Blend Morphology and Voltage Loss of High-Performance Solar Cells

Herein, the impacts of the selective halogenation at two different positions of dicyanomethylene-3-indanone (IC) end groups and inner side chains of small molecular acceptors (SMAs) on the P D :SMA interfacial interactions, blend morphology, and resulting photovoltaic properties are described. In this study, four different SMAs (A1, A2, A3, and A4) with the same molecular backbone, but with different degrees of halogenation, are synthesized. The IC end groups on the backbones of the A1 and A3, and A2 and A4 SMAs are chlorinated and fluorinated, respectively; in addition, 6-phenoxyhexyl inner side chains of the A3 and A4 are chlorinated. The SMAs are paired with a chlorinated PBDT-Cl PD to construct organic solar cells (OSCs). The PBDT-Cl:A4-based OSC exhibits the highest power conversion efficiency of 17.2%, outperforming the PBDT-Cl:A1-(13.3%), PBDT-Cl:A2-(15.6%), and PBDT-Cl:A3-based OSC (16.5%). The Cl atoms on the side chains in the A3 and A4 SMAs enhance the molecular/energetic interactions at the P D :SMA interfaces and improve the blend morphology in terms of domain purity and spacing. These effects lead to the improved fill factors and reduced voltage loss of the PBDT-Cl:A3- and PBDT-Cl:A4-based OSCs. This study demonstrates the importance of appropriate halogenation of SMAs in optimizing the blend morphology, reducing voltage loss, and improving OSC performance.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Rational Design of A Chemical Bath Deposition Based Tin Oxide Electron Transport Layer for Perovskite Photovoltaics

Chemical bath deposition is widely used to deposit SnO x as an electron transport layer in perovskite solar cells (PSCs). The conventional recipe uses thioglycolic acid (TGA) to facilitate attachments of SnO x particles onto the substrate. However, nonvolatile TGA has been reported to harm the operational stability of PSCs. In this work, we introduced a volatile oxalic acid (OA) as an alternative to TGA. OA, a dicarboxylic acid, functions as a chemical linker for the nucleation and attachment of particles to the substrate in the chemical bath. Moreover, OA can be readily removed through thermal annealing followed by a mild H 2 O 2 treatment, as shown by FTIR measurements. Synergistically, the mild H 2 O 2 treatment selectively oxidizes the surface of the SnOx layer, minimizing nonradiative interface carrier recombination. EELS (electron-energy-loss-spectroscopy) confirms that the SnO x surface is dominated by Sn 4+ , while the bulk is a mixture of Sn 2+ and Sn 4+ . This rational design of a CBD SnO x layer leads to devices with T85~1,500h, a significant improvement over the TGA-based device with T80~250h. Our champion device reached a power conversion efficiency of 24.6%. This work offers a rationale for optimizing the complex parameter space of CBD SnO x to achieve efficient and stable PSCs.

14 SOLAR ENERGY↗
DOE OSTI2025

Burn parameters affect PAH emissions at conditions relevant for prescribed fires

Wildfire smoke is a health hazard as it contains carcinogenic volatile compounds and fine particulate matter. In particular, exposure to polycyclic aromatic hydrocarbons (PAHs) is a major concern, since these compounds have been recognized as important contributors to the overall carcinogenic risk. In this work, gas and particle-phase PAH emissions from combustion of Eastern White Pine (Pinus strobus) were quantified using time-of-flight mass spectrometry over a range of burn conditions representative of wildfires and prescribed fires, including fuel moisture, heat flux, and oxygen concentration. We found that changing the burn environment lead to a variability of up to 77% in phenanthrene/anthracene emissions. This could explain a large part of the variability in PAH emission factors from biomass combustion reported in the literature. Here, we found that optimal conditions for fuel moisture content of 20–30%, sample heat load of 60 - 70 kW m -2 , and oxygen concentrations of 5–15% can significantly reduce the emissions of heavy molar weight PAHs. Our analysis showed that the relative carcinogenic risk from PAH exposure can be reduced by more than 50% under optimal conditions. In light of the increasing use of prescribed fire for forest management, the relationship between emissions and burn conditions that we have established provides a guidance for assessing the expected health impact from prescription burns, and can inform strategies to reduce PAH emissions from prescribed fire activities.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2025

Phase-field modeling of diffusion bonding in 316H stainless steel: Impact of processing conditions on grain morphology and bonding quality

A novel multi-phase, multi-component phase‐field model is presented to study the diffusion bonding of 316H stainless steel. Combined with targeted experimental investigations, this model simulates the bond-growth process and predicts the bonding quality. Unlike previous models, our approach captures the simultaneous evolution of voids and grain structures, while quantifying bonding quality using defined bonding ratio. A comprehensive analysis of bond process control is performed by changing temperature, pressure and surface roughness observing the resulting bond structure, which is consistent with experimental observations and analytical predictions. Temperature is determined to be the dominant factor, with the transition from a flat to a robust bond occurring between 1000 °C and 1050 °C. At the ideal bonding temperature of 1050 °C, a surface roughness exceeding 0.6 μm or an applied stress below 4 MPa results in poor bonding quality. Beyond this, higher pressures and smoother surfaces reduce void size, accelerate void shrinkage, and lead to improved bond integrity. This diffuse-interface model can be extended to other material systems if supplied with appropriate thermodynamic and kinetic data. In conclusion, this makes it an effective modeling platform for optimizing high-temperature diffusion bonding and developing reliable bonded components such as compact heat exchangers.

Diffusion bonding↗
DOE OSTI2026

Mechanism of Vapor-Phase Infiltration of Organometallic Hf in Poly(Methyl Methacrylate) for Hybrid Resist Applications

Inorganic–organic hybrid thin films synthesized by vapor-phase infiltration (VPI) of metal oxides into organic photoresists, such as poly(methyl methacrylate) (PMMA), have recently demonstrated their utility in extreme ultraviolet lithography, critical for angstrom-era semiconductor device miniaturization. Hafnium oxide infiltration has been reported recently for this purpose, but its detailed VPI mechanism has remained largely unexplored. In this study, we investigated the VPI characteristics and mechanisms of tetrakis(dimethylamido)hafnium (TDMAHf)─the hafnium precursor predominantly used for VPI in the field─into PMMA and examined its impact on electron-beam lithography (EBL) exposure behavior. VPI was performed at temperatures ranging from 85 to 150 °C, with chemical interactions characterized using infrared reflection-absorption spectroscopy, and resist patterning performance was evaluated through EBL dose-sensitivity assessments. The results indicate that TDMAHf forms a reversible adduct with PMMA at temperatures up to 120 °C, whereas at 150 °C, covalent bond formation occurs, most likely via dealkylation that leads to acetate formation. EBL studies reveal that resist sensitivity is influenced by both infiltration temperature and developer selection, with aqueous isopropyl alcohol development demonstrating enhanced sensitivity compared to organic solvent-based development. The optimized infiltration protocol at 120 °C ensures a uniform inorganic distribution without compromising resist dissolution. These findings not only help refine hybrid resist patterning performance but also offer insights potentially applicable to the VPI of other homoleptic metal-amide organometallic VPI precursors that include TDMA ligands.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Optimization of Species-Selective Reversible Proteasome Inhibitors for the Treatment of Malaria

Abstract Malaria remains a critical global health challenge, with increasing resistance to frontline therapies necessitating novel drug targets. The proteasome has emerged as a promising target for antimalarial drug discovery. This study describes efforts to optimize a series of species-selective reversible inhibitors targeting the Plasmodium falciparum 20S proteasome. Starting from the carboxypiperidine scaffold identified through a high-throughput viability screen, we conducted iterative structure–activity relationship studies, leading to the development of highly potent and selective inhibitors with good oral bioavailability. Lead compounds demonstrated nanomolar potency against P. falciparum blood-stage parasites and selective inhibition of the parasite proteasome over the human counterpart. Cryo-EM structural studies confirmed binding at the β5 subunit, while in vivo pharmacokinetic studies identified promising candidates for further development. These findings support proteasome inhibition as a viable strategy for novel antimalarial drug development.

Gahalawat, Suraksha [UT Southwestern Medical Cente↗
DOE OSTI2021

The Effects of Temperature on the Assembly of Gold Nanoparticle by Interpolymer Complexation

Using synchrotron-based small-angle X-ray scattering techniques, we demonstrate that poly(ethylene glycol)-functionalized gold nanoparticles (PEG-AuNPs) are assembled into close-packed structures that include short-range order with face-centered cubic structure, where crystalline qualities are varied by controlling the electrolyte concentration, pH, and temperature of the suspensions. Here, we show that interpolymer complexation with poly(acrylic acid) (PAA) is induced by lowering the pH level of the PEG-AuNPs suspensions, and furthermore, increasing the temperature of the suspension strengthens interparticle attraction, leading to improved supercrystal structures. Our results indicate that this strategy creates robust nanoparticle superlattices with high thermal stability. The effects of PAA and PEG chain lengths on the assemblies are also investigated, and their optimal conditions for creating improved superlattices are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

LandScan mosaic enables high-resolution gridded population estimates with explicit uncertainty

Gridded population datasets represent high-resolution distributions of human occupancy, enabling informed decision-making across a broad range of fields. These data products are valuable for assessing environmental risk, urban development, disaster preparedness and resource allocation—areas where accurate population estimates directly enhance policy effectiveness and optimize resource distribution. Despite the importance of gridded population datasets, traditional population modeling approaches often overlook inherent uncertainties in the estimation process. This limitation can create a false sense of certainty in population estimates, potentially leading to flawed decisions by those who rely on the data. To address this methodological gap, we introduce a probabilistic machine learning modeling framework, LandScan Mosaic, that explicitly incorporates uncertainty into the population modeling process. Our approach systematically quantifies uncertainty in three key modeling parameters of the LandScan HD gridded population dataset: building use types, floor counts, and occupancy rates. By employing Monte Carlo simulations, we propagate these uncertainties through the modeling process, yielding probability distributions of population counts in place of deterministic point estimates. We demonstrate the practical application of this framework in Iloilo City, Philippines, using structured decision-making techniques and our probabilistic estimates to identify and prioritize areas most affected by projected flooding, supporting targeted interventions that address both economic and social risks. In doing so, we propose a population-specific approach for incorporating confidence into structured decision making processes. Through a comparative analysis with conventional deterministic approaches and point estimate approaches, including LandScan HD and WorldPop, we evaluate how the incorporation of machine learning and uncertainty influences decision rankings. This research advances population distribution modeling by offering a robust, quantitative approach that explicitly accounts for uncertainty in the underlying data, along with guidance for how users can apply uncertainty in their decision-making.

Environmental sciences↗
DOE OSTI2020

Training Spiking Neural Networks Using Combined Learning Approaches

Spiking neural networks (SNNs), the class of neural networks used in neuromorphic computing, are difficult to train using traditional back-propagation techniques. Spike timingdependent plasticity (STDP) is a biologically inspired learning mechanism that can be used to train SNNs. Evolutionary algorithms have also been demonstrated as a method for training SNNs. In this work, we explore the relationship between these two training methodologies. We evaluate STDP and evolutionary optimization as standalone methods for training networks, and also evaluate a combined approach where STDP weight updates are applied within an evolutionary algorithm. We also apply Bayesian hyperparameter optimization as a meta learner for each of the algorithms. We find that STDP by itself is not an ideal learning rule for randomly connected networks, while the inclusion of STDP within an evolutionary algorithm leads to similar performance, with a few interesting differences. This study suggests future work in understanding the relationship between network topology and learning rules.

Elbrecht, Daniel↗
DOE OSTI2020

UNM High Energy Physics: Task B

The High Altitude Water Cherenkov (HAWC) observatory provides a unique window into the "TeV" gamma-ray universe. HAWC provides an important 1 TeV to 1000 TeV high-mass window for indirect searches for dark matter (DM) annihilation or decay. Additional fundamental physics studies benefit from HAWC's sensitivity to variable and/or transient sources. Such transient sources include: gamma ray bursts (GRBs), temporal studies of super massive black holes (specifically Markarian (Mrk) 421 and 501), and most recently searches for gamma-ray counterparts to PeV neutrino sources (observed by IceCube) and gravitational wave sources (observed by LIGO/Virgo). The UNM (Task B) research program includes leadership of the HAWC detector and of HAWC science. During this final reporting period the UNM group includes Professor John Matthews and graduate student Zhixiang Ren with the research goal focused on the development of analysis tools to enhance the sensitivity of HAWC to <1 TeV, gamma rays. This program began in 2016 with an initial focus to work to resolve known problems with the low energy analysis bins in the HAWC data. In 2017 this evolved to the development of new analysis tools to optimize current HAWC <1 TeV sensitivity as well as how HAWC (or a future HAWC-like detector) could be modified to be significantly more sensitive to <1 TeV gamma rays. In these studies Ren lead the development and evaluation of new HAWC <1 TeV analysis tools and Matthews lead the study of possible experimental modifications to HAWC to improve the <1 TeV sensitivity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Nuclear data covariances are critical input to determine upper sub-critical limits and to design experiments to increase it [Slides]

This presentation discusses how Upper Subcritical Limits (USL) are key parameters to determine operational limits in nuclear criticality safety evaluations. It also discusses an example of plutonium casting operation using tantalum at LANL PF-4. The Whisper tool at Los Alamos relies on many inputs, including covariance data, leading the presentation to ask if an existing benchmark data be used in Whisper to adjust nuclear data and covariances to justify a higher USL. If not, Whisper can be used to help design an optimal new benchmark experiment. The presentation also seeks to determine what the possible impacts are on USL and operational limits for plutonium casting. In conclusion, nuclear data covariances are used for by Whisper for: GSSL adjustment of nuclear data and covariances, identification of most similar existing benchmark experiments to application, simulation of Upper Subcritical Limit of application, and input to optimization techniques for designing most appropriate new benchmark experiment(s) to meet requirements. This requires a complete set of nuclear data covariances, benchmarks and k-effective sensitivity profiles (for both benchmarks and applications). The presentation concludes by asking if end users should trust results that depend on current covariance data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1976

Design, economic and system considerations of large wind-driven generators

The increased search for alternative energy sources has lead to renewed interest and studies of large wind-driven generators. This paper presents the results and considerations of such an investigation. The paper emphasizes the concept selection of wind-driven generators, system optimization, control system design, safety aspects, economic viability on electric utility systems and potential electric system interfacing problems.

Jorgensen, G. E.↗
NASA NTRS1980

Multistage depressed collector with efficiency of 90 to 94 percent for operation of a dual-mode traveling wave tube in the linear region

An axisymmetric, multistage, depressed collector of fixed geometric design was evaluated in conjunction with an octave bandwidth, dual mode traveling wave tube (TWT). The TWT was operated over a wide range of conditions to simulate different applications. The collector performance was optimized (within the constraint of fixed geometric design) over the range of TWT operating conditions covered. For operation of the TWT in the linear, low distortion range, 90 percent and greater collector efficiencies were obtained leading to TWT overall efficiencies of 20 to 35 percent, as compared with 2 to 5 percent with an undepressed collector. With collectors of this efficiency and minimized beam interception losses, it becomes practical to design dual mode TWT's such that the low mode can represent operation well below saturation. Consequently, the required pulse up in beam current can be reduced or eliminated, and this mitigates beam control and dual mode TWT circuit design problems. For operation of the dual mode TWT at saturation, average collector efficiencies in excess of 85 percent were obtained for both the low and high modes across an octave bandwidth, leading to a three to fourfold increase in the TWT overall efficiency.

Ramins, P.↗
NASA NTRS2005

The Impact of Model Uncertainty on Spatial Compensation in Structural Acoustic Control

Turbulent boundary layer (TBL) noise is considered a primary contribution to the interior noise present in commercial airliners. There are numerous investigations of interior noise control devoted to aircraft panels; however, practical realization is a potential challenge since physical boundary conditions are uncertain at best. In most prior studies, pinned or clamped boundary conditions were assumed; however, realistic panels likely display a range of boundary conditions between these two limits. Uncertainty in boundary conditions is a challenge for control system designers, both in terms of the compensator implemented and the location of transducers required to achieve the desired control. The impact of model uncertainties, specifically uncertain boundaries, on the selection of transducer locations for structural acoustic control is considered herein. The final goal of this work is the design of an aircraft panel structure that can reduce TBL noise transmission through the use of a completely adaptive, single-input, single-output control system. The feasibility of this goal is demonstrated through the creation of a detailed analytical solution, followed by the implementation of a test model in a transmission loss apparatus. Successfully realizing a control system robust to variations in boundary conditions can lead to the design and implementation of practical adaptive structures that could be used to control the transmission of sound to the interior of aircraft. Results from this research effort indicate it is possible to optimize the design of actuator and sensor location and aperture, minimizing the impact of boundary conditions on the desired structural acoustic control.

Clark, Robert L.↗
DOE OSTI2026

Determining the Solubility Behavior of Kogarkoite in Simulated Nuclear Waste

Kogarkoite (Na 3 FSO 4 ) is a sparingly soluble fluoride–sulfate double salt that has been identified in high level nuclear waste sludge at the Hanford Site and, more recently, in sludge batch compilation samples at the Savannah River Site (SRS). Due to its complex dissolution behavior, which exhibits an inverse dependence on sodium ion activity, the presence of this mineral poses significant challenges to waste retrieval and processing. Incomplete dissolution during sludge washing can lead to the retention of fluoride and sulfate in the high-level waste feed, potentially causing the formation of corrosive, immiscible molten salt layers, known as "glass gall,” in vitrification melters. Current efforts to optimize flowsheet parameters and wash-water volumes are hindered by the absence of a commercially available, certified reference material, which prevents the accurate calibration of analytical methods and the verification of dissolution kinetics. To address this critical gap, this research focuses on the laboratory synthesis of pure Kogarkoite to serve as a standard for comprehensive solubility and washing performance testing. A coupled synthesis and simulant campaign was executed using an evaporative crystallization protocol designed to replicate the dynamic concentration effects observed in tank farm operations. Thirteen simulant matrices were prepared by dissolving systematically varied ratios of sodium fluoride (NaF) and sodium sulfate (Na 2 SO 4 ) in deionized water under three distinct caustic regimes: 0.0 g (control), 4.0 g (~1 M), and 12.0 g (~3 M) sodium hydroxide (NaOH). While thermodynamic equilibrium models suggest that high-caustic environments should favor the stability of the double salt7, results from this evaporative study at 25 0 C revealed a distinct kinetic divergence. Simulants with high hydroxide loading predominantly yielded large, blocky crystals of sodium sulfate decahydrate (Na 2 SO 4 .10H 2 O). Successful synthesis of pure Kogarkoite was achieved exclusively in specific NaOH-free compositional windows, where the precipitate manifested as fine, opaque granular aggregates. Ion chromatography (IC) analysis confirmed phase purity through the simultaneous stoichiometric depletion of both fluoride and sulfate from the supernatant. This successful synthesis establishes a reproducible route to generate bulk Kogarkoite, enabling the subsequent phase of quantitative dissolution testing using inhibited water to optimize sludge-batch assembly.

Sarker, Md Sharif [Florida International Univ. (FI↗
NASA NTRS2005

High Frequency QRS ECG Accurately Detects Cardiomyopathy

High frequency (HF, 150-250 Hz) analysis over the entire QRS interval of the ECG is more sensitive than conventional ECG for detecting myocardial ischemia. However, the accuracy of HF QRS ECG for detecting cardiomyopathy is unknown. We obtained simultaneous resting conventional and HF QRS 12-lead ECGs in 66 patients with cardiomyopathy (EF = 23.2 plus or minus 6.l%, mean plus or minus SD) and in 66 age- and gender-matched healthy controls using PC-based ECG software recently developed at NASA. The single most accurate ECG parameter for detecting cardiomyopathy was an HF QRS morphological score that takes into consideration the total number and severity of reduced amplitude zones (RAZs) present plus the clustering of RAZs together in contiguous leads. This RAZ score had an area under the receiver operator curve (ROC) of 0.91, and was 88% sensitive, 82% specific and 85% accurate for identifying cardiomyopathy at optimum score cut-off of 140 points. Although conventional ECG parameters such as the QRS and QTc intervals were also significantly longer in patients than controls (P less than 0.001, BBBs excluded), these conventional parameters were less accurate (area under the ROC = 0.77 and 0.77, respectively) than HF QRS morphological parameters for identifying underlying cardiomyopathy. The total amplitude of the HF QRS complexes, as measured by summed root mean square voltages (RMSVs), also differed between patients and controls (33.8 plus or minus 11.5 vs. 41.5 plus or minus 13.6 mV, respectively, P less than 0.003), but this parameter was even less accurate in distinguishing the two groups (area under ROC = 0.67) than the HF QRS morphologic and conventional ECG parameters. Diagnostic accuracy was optimal (86%) when the RAZ score from the HF QRS ECG and the QTc interval from the conventional ECG were used simultaneously with cut-offs of greater than or equal to 40 points and greater than or equal to 445 ms, respectively. In conclusion 12-lead HF QRS ECG employing RAZ scoring is a simple, accurate and inexpensive screening technique for cardiomyopathy. Although HF QRS ECG is highly sensitive for cardiomyopathy, its specificity may be compromised in patients with cardiac pathologies other than cardiomyopathy, such as uncomplicated coronary artery disease or multiple coronary disease risk factors. Further studies are required to determine whether HF QRS might be useful for monitoring cardiomyopathy severity or the efficacy of therapy in a longitudinal fashion.

Schlegel, Todd T.↗
DOE OSTI2024

Flexible Stellarator Physics Facility

We propose to build a Flexible Stellarator Physics Facility to explore promising regions of the vast parameter space of disruption-free stellarator solutions for Fusion Pilot Plants (FPPs). The FESAC Long Range Plan recognized the quasi-symmetric stellarator as “the leading US approach to developing disruption-free, low-recirculating-power fusion configurations”. To deliver the ambitious Decadal Vision for Commercial Fusion Energy, we must establish a persuasive stellarator program in parallel to the tokamak one: the stellarator will prove to be a better path to a reactor if theoretical predictions are confirmed and novel optimization techniques and strategies work as desired. Since the release of the Long Range Plan in 2020, stellarators have arguably made the most significant advances of all fusion concepts. Groundbreaking results from W7-X demonstrated low neoclassical transport and the successful operation of the island divertor. Advances in theory and modeling now allow us to minimize turbulent transport, to achieve equilibria with precise quasisymmetry, to reduce neoclassical transport and fast ion loss to levels far below what has been previously achieved, and to minimize the effect of coil manufacturing errors. If realized, these advances will lead to cost-effective stellarator designs with confinement comparable to tokamaks but without the fundamental challenges of disruptions and current drive.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2016

Computational Role of Tunneling in a Programmable Quantum Annealer

Quantum tunneling is a phenomenon in which a quantum state tunnels through energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We developed a theoretical model based on a NIBA Quantum Master Equation to describe the multi-qubit dissipative cotunneling effects under the complex noise characteristics of such quantum devices.We start by considering a computational primitive, the simplest non-convex optimization problem consisting of just one global and one local minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the critical phase during the evolution where quantum tunneling decides the right path to solution. In a later stage dissipation facilitates the multiqubit cotunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-WaveII quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specially, we provide an analysis of an optimization problem with sixteen qubits,demonstrating eight qubit cotunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

hard problems↗