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At least 1,153 records · Page 64

Refinement and demonstration of a coupled BISON-Griffin workflow for designing targeted TRISO transient experiments in TREAT

The U.S. nuclear industry is expected to deploy tristructural isotropic (TRISO) particle fuel technologies for commercial reactors within the next decade. In previous work, we defined a preliminary transient design space for TRISO fuels, identified potential gaps in the available data, and began to develop multiphysics modeling tools that could be applied to design targeted Transient Reactor Test Facility (TREAT) experiments to fill these gaps. Here, this work builds on that foundation by (1) updating BISON fuel performance and Griffin reactor physics models to reflect the current TREAT experiment tube and capsule designs, (2) coupling the codes to improve the accuracy and usability of the transient design analyses, and (3) demonstrating their use over an expanded design space that includes fuel burnup. The simulated mechanical responses of the TRISO particles were complex functions of fission product accumulation, fission gas release, and irradiation-induced dimensional change in the pyrolytic carbon layers. The predicted tangential stresses in the particles' silicon carbide layers were least compressive for preheated tests involving fresh fuels but remained compressive throughout the ranges of temperature, heat rate, and burnup considered in this work. Finally, comparisons between the potential TREAT transients and historical test reactor irradiations showed that the TREAT tests would produce significantly lower average energy deposition rates, yielding less severe transients with greater relevance to near-term commercial applications. The use of these predictive capabilities has the potential to increase the value of each test, improving the overall efficiency and cost-effectiveness of transient testing for TRISO and other advanced fuels.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Demonstration of an All-Refractory Corrosion-Resistant Molten Salt Pumping and Storage Infrastructure Up to 950 degrees C

Concentrating solar power (CSP) with thermal energy storage (TES) has an estimated cost similar to solar photovoltaics (PV) with lithium-ion batteries (LIB), but CSP + TES has the potential for significantly reduced cost by operating above 700 degrees C. However, this requires a TES medium and containment infrastructure which are chemically compatible and do not degrade above 700 degrees C. MgCl2-KCl-NaCl (MKN) salt is a promising medium, but when MKN salt has small amounts of water and oxygen dissolved in it, it excessively corrodes conventional commercial alloys. Here, we consider refractory materials including graphite, carbon-carbon composite (C/C), and molybdenum because they maintain high mechanical strength at elevated temperatures and are expected to resist corrosion by MKN salt. While selection of refractory materials is often constrained by the need to remain chemically stable in air, this work uses an enclosure filled with inert gas to allow the use of materials like graphite and molybdenum. Notably, graphite components can seal against liquids unlike many brittle refractory materials. We demonstrate a centrifugal pump and mechanical seals made of refractory materials in a laboratory-scale circulation loop, which successfully operated continuously for more than 49 h at temperatures ranging from 750 degrees C to 950 degrees C with no mechanical failures or chemical degradation of the refractory materials. To the best of our knowledge, this is the highest temperature molten salt circulation loop that has been successfully developed, and this refractory infrastructure allows for operation at even much higher temperatures (<1600 degrees C) if a storage medium with a lower vapor pressure is used. The principles of this architecture are relevant to other applications with high temperature flowing metals and salts including Generation IV nuclear fission reactors for power production and molten salt electrolysis reactors for metallurgical processing.

14 SOLAR ENERGY↗

Development and demonstration of a rolling ball viscometer for molten salts with near-minimum liquidus NaCl–KCl

The thermophysical characterization of molten chloride and fluoride salts is a key interest for the development of advanced molten salt nuclear reactors. Viscosity is one thermophysical property of interest; a high-accuracy understanding of this property is necessary for modeling the thermal energy transfer and mass flow rate for a given molten salt system. Only a few methods have consistently been used to measure the viscosity of molten chloride and fluoride salt systems, and large discrepancies have been observed in the literature between independent studies of nearly identical salt systems. As such, exploration of novel measurement methods or implementations may allow for further validation, improved measurement accuracy, and overall improved understanding about optimal approaches for measuring molten salt viscosity. Here, in this study, a novel implementation of the rolling ball viscometry method was used to measure the viscosity of a 44/56 mol % mixture of NaCl–KCl within a temperature range of 714–838 °C, with the intent to demonstrate the feasibility of this technique for molten salt viscosity measurement cross-validation. The purity of this salt was confirmed through laser-induced breakdown spectroscopy. Measured viscosities were approximately 1.3–1.0 cP within this temperature range, and the overall uncertainty was 10.8%, which was determined through Gaussian error propagation. The results agree reasonably well with measured viscosities of similar NaCl–KCl mixtures in the literature (within 2%–20% depending on the temperature and study), although the experimental error in some of these comparative studies may be significant.

47 OTHER INSTRUMENTATION↗

Demonstration and characterization of insertable passive thermal switches for dynamic building envelopes

A dynamic building envelope integrated with thermal energy storage, such as phase change material (PCM), is an emerging technology that offers a promising solution to improve the energy efficiency of buildings. This study reports the development of insertable thermal switches, which modulate thermal resistance, thereby making building envelopes dynamic and enhancing the use of free ambient heating and cooling. The reported thermal switches are passive, meaning they work solely based on indoor and outdoor temperatures. A single switch when inserted into 10 × 10-in (0.064-m 2 ) XPS foam board insulation demonstrates effective thermal conductivity of 0.050 W/m-K in the resistive state and 0.285 W/m-K in the conductive state. Thermal switches exhibit an effective switching ratio of 5.7, with no noticeable degradation in performance over 770 cycles. Additionally, when integrated into a wall sample containing a PCM layer, switches significantly reduce the PCM solidification time by 43.2% during the cooling process.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Demonstration and technoeconomic analysis of dodecanol production from acetate using metabolically engineered Escherichia coli

In a circular bioeconomy, the one-way conversion of petroleum to chemicals and CO 2 is replaced with processes that reduce CO 2 to energy carriers and useful materials that are returned to CO 2 upon combustion. A circular bioeconomy that relies on photosynthesis to generate sugars as the chief energy carrier and precursor to chemical building blocks has yet to overcome many recalcitrant aspects of plant-based photosynthesis, namely, high feedstock costs, arable land scarcity, food competition, and fertilizer overuse. Acetate is a potential sustainable energy carrier because it can be produced from CO 2 either electrocatalytically or by acetogens via the Wood-Ljungdahl pathway. Here, in this work, we conducted a metabolic engineering study of Escherichia coli 's ability to convert acetate into dodecanol as a model oleochemical product. We performed techno-economic and life cycle analyses to determine break-even points with alternative fossil fuel-based strategies and identified critical process performance parameters for supporting an industrial acetate-based bioprocess. These analyses showed that oleochemical yield is the primary driver of minimum oleochemical selling price and carbon intensity. Therefore, to increase yield on acetate, we deleted the aceBAK operon, which facilitates funneling of acetate into biomass instead of product. We performed additional strain engineering to increase flux towards dodecanol and increase acetate uptake. Finally, we demonstrated increased yield in controlled bioreactors, improving from 13% of the maximum theoretical yield to 37%. Rigorous uncertainty analyses assuming a range of market conditions and future technological performances resulted in 88% and 37% of simulated scenarios having lower carbon intensities than fossil fuel-based routes and lower minimum selling prices than the market price.

Acetate↗

Integration of pH Control into Chi.Bio Reactors and Demonstration with Small-Scale Enzymatic Poly(ethylene terephthalate) Hydrolysis

Small-scale bioreactors that are affordable and accessible would be of major benefit to the research community. In previous work, an open-source, automated bioreactor system was designed to operate up to the 30 mL scale with online optical monitoring, stirring, and temperature control, and this system, dubbed Chi.Bio, is now commercially available at a cost that is typically 1–2 orders of magnitude less than commercial bioreactors. In this work, we further expand the capabilities of the Chi.Bio system by enabling continuous pH monitoring and control through hardware and software modifications. For hardware modifications, we sourced low-cost, commercial pH circuits and made straightforward modifications to the Chi.Bio head plate to enable continuous pH monitoring. For software integration, we introduced closed-loop feedback control of the pH measured inside the Chi.Bio reactors and integrated a pH-control module into the existing Chi.Bio user interface. We demonstrated the utility of pH control through the small-scale depolymerization of the synthetic polyester, poly(ethylene terephthalate) (PET), using a benchmark cutinase enzyme, and compared this to 250 mL bioreactor hydrolysis reactions. The results in terms of PET conversion and rate, measured both by base addition and product release profiles, are statistically equivalent, with the Chi.Bio system allowing for a 20-fold reduction of purified enzyme required relative to the 250 mL bioreactor setup. Through inexpensive modifications, the ability to conduct pH control in Chi.Bio reactors widens the potential slate of biochemical reactions and biological cultivations for study in this system, and may also be adapted for use in other bioreactor platforms.

09 BIOMASS FUELS↗

Exotic Carbonate Mineralization Recovered from a Deep Basalt Carbon Storage Demonstration

Mitigating climate change require transformational advances for carbon dioxide removal, including geologic carbon sequestration in reactive subsurface environments. The Wallula Basalt Carbon Storage Pilot Project demonstrated that CO 2 injected into >800 m deep Columbia River Basalt Group flow top reservoirs mineralizes on month-year timescales. Herein, we present new optical petrography, micro-computed X-ray tomography, and electron microscopy results sidewall cores collected two years after CO 2 injection. As no other anthropogenic carbonates from geologic carbon storage field studies have been recovered, this world-unique sample suite provides unparalleled insight for subsurface carbon mineralization products and paragenesis. Chemically-zoned nodules with Ca/Mn-rich cores and Fe-dominant outer rims are prominent examples of the neoformed carbonate assemblages with ankerite-siderite compositions and exotic divalent cation correlations. Further, paragenetic insights for the timing of aragonite, silica, and fibrous zeolites are clarified based on mineral texture and spatial relationships, along with time-resolved downhole fluid sampling. Collectively, these results clarify the mineralogy, chemistry, and paragenesis of carbon mineralization, providing insight into the ultimate fate and transport of CO 2 in reactive mafic-ultramafic reservoirs

54 ENVIRONMENTAL SCIENCES↗

Facile Metal Release from Pore-Lining Phases Enables Unique Carbonate Zonation in a Basalt Carbon Mineralization Demonstration

Carbon-negative strategies such as geologic carbon sequestration in continental flood basalts offers a promising route to the removal of greenhouse gases, such as CO 2 , via safe and permanent storage as stable carbonates. This potential has been successfully demonstrated at a field scale at the Wallula Basalt Carbon Storage Pilot Project where supercritical CO 2 was injected into the Columbia River Basalt Group (CRBG). Here, we analyze recovered post-injection sidewall core cross-sections containing carbonate nodules using μ-XRF chemical mapping techniques that revealed compositional zonation within the nodules. The unique nature of the subsurface anthropogenic carbonates is highlighted by the near absence of Mg in an ankerite-like composition. Furthermore, a comparison between pre- and post-injection sidewall cores along with an in-depth chemical mapping of basalt pore lining cements provides a better understanding into the source and fate of critical cationic species involved in the precipitation of carbon mineralization products. Collectively, these results provide crucial insights into carbonate growth mechanisms under a time-dependent pore fluid composition. Finally, as such, these findings will enable parameterization of predictive models for future CO 2 sequestration efforts in reactive reservoirs around the world.

54 ENVIRONMENTAL SCIENCES↗

Demonstration of MgCr 2– x Mn x O 4 Spinel Oxide Cathodes in High-Voltage Mg Batteries

Solid-solution oxide spinels with high redox voltages and facile Mg 2+ mobility have been identified as promising candidates for practical, high-voltage cathodes in Mg batteries. In this work, we discuss the development of MgCr 2-x Mn x O 4 [x = 0.5, 1, 1.2] solid-solution spinel oxides as a cathode material and their electrochemical performance paired with an Mg anode in a full cell. This work presents the first demonstration of full cells with these materials. Mg-Cr-Mn spinel oxides with varying Cr and Mn contents were synthesized using alternative synthetic routes for optimal electrochemical performance. High-resolution synchrotron powder X-ray diffraction (PXRD), solid-state nuclear magnetic resonance (NMR) spectroscopy, and electron microscopy showed that these different synthetic routes resulted in changes in structures and particle morphologies, which in turn affect the electrochemical performance. Particularly, the urea coprecipitation synthetic route resulted in high-surface-area particles that enabled lower overpotentials and increased discharge capacity. The high surface area also resulted in expedited structural degradation caused by the irreversible migration of Mg 2+ into normally vacant 16c sites in the spinel lattice. This structural degradation was lessened by using a hydrosauna-urea synthesis method, which decreased the Mg/Mn inversion ratio while retaining high-surface-area particles with good cycling performance. Furthermore, our findings highlight the necessity for high surface area or nanostructured spinel oxide cathodes with minimized Mg-Mn inversion to enable spinel oxide cathodes in Mg full cells.

Mg anode↗

Discovering and Demonstrating a Novel High-Performing 2D-Patterned Electrode for Proton-Exchange Membrane Water Electrolysis Devices

Proton-exchange membrane water electrolysis (PEMWE) produces hydrogen with high efficiency and purity but uses high-loading platinum-group metal (PGM) catalysts. Such concerns call for the development of novel electrode architectures to improve catalyst utilization and mass activity, thus promoting PEMWE cost competitiveness for large-scale implementation. In this study, we demonstrated, for the first time, a novel two-dimensional (2D)-patterned electrode with edge effects to address these challenges. The edge effect was induced by membrane properties, potential distribution, and counter electrode coverage and could be optimized by tuning the catalyst layer dimensions. To achieve identical PEMWE performance, the optimal pattern saved the 21% anode PGM catalyst compared with the conventional catalyst fully covered electrode. The PGM catalyst could be further reduced by 61% to boost mass activity with no significant performance loss. The results also indicated that the electrode uniformity in PEMWE cells might not be as critical as that in PEM fuel cells. Finally, the novel 2D-patterned electrode could effectively reduce PGM catalyst loading, accelerating affordable and large-scale production of hydrogen and other value-added chemicals via electrolysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Aircraft Measurements from a U.S. Western Wildfire Demonstrating Day and Night Differences in the Chemical Composition and Optical Properties of Biomass Burning Aerosols and Their Atmospheric Evolution

The composition and transformations of biomass burning aerosols (BBA) have been measured onboard the NOAA Twin Otter research aircraft during the Fire Influence on Regional to Global Environments and Air Quality field study. Here, we analyze real-time aerosol mass spectrometry measurements across three flights during the afternoon, late afternoon, and night of August 28, 2019, for one midsized wildfire. Analysis of several metrics showed that the aerosol composition and optical properties varied depending on the burning conditions at the fire zone and the time of day the BBA was emitted, with substantial variations in the available sunlight. The total aerosol mass loadings were dominated by organic components with a much smaller contribution from inorganic species. A gradual buildup of organic material was observed during the afternoon as the plume aged, indicating the condensation of photochemically formed low-volatility oxidized organic compounds. Highly hygroscopic ammonium nitrate was the main inorganic component, suggesting potential water content in BBA particles and the likelihood of their aqueous-phase reactivity. Depletions of particle-phase NO 3 – and Cl – relative to carbon monoxide were observed in the late afternoon and nighttime plumes, respectively, aligning with known gas-particle partitioning thermodynamics and the heterogeneous chemistry of dissolved nitrate and chloride. The wavelength-dependent light absorption by aerosol species was higher for the plume sampled at night and showed no significant changes with plume age, despite observed trends in composition and mass downwind. These differences in particle composition and optical properties demonstrate that the processes involved in BBA aging are not uniform for the same wildfire over the course of the day and depend highly on when the BBA was emitted, as well as the burning phase at the emissions source.

54 ENVIRONMENTAL SCIENCES↗

Structure Prediction of Ionic Epitaxial Interfaces with Ogre Demonstrated for Colloidal Heterostructures of Lead Halide Perovskites

Colloidal epitaxial heterostructures are nanoparticles composed of two different materials connected at an interface, which can exhibit properties different from those of their individual components. Combining dissimilar materials offers exciting opportunities to create a wide variety of functional heterostructures. However, assessing structural compatibility–the main prerequisite for epitaxial growth–is challenging when pairing complex materials with different lattice parameters and crystal structures. This complicates both the selection of target heterostructures for synthesis and the assignment of interface models when new heterostructures are obtained. Here, we demonstrate Ogre as a powerful tool to accelerate the design and characterization of colloidal heterostructures. To this end, we implemented developments tailored for the high-efficiency prediction of epitaxial interfaces between ionic/polar materials, which encompass most colloidal semiconductors. These include the use of pre-screening candidate models based on charge balance at the interface and the use of a classical potential for fast energy evaluations, with parameters automatically calculated based on the input bulk structures. These developments are validated for perovskite-based CsPbBr 3 /Pb 4 S 3 Br 2 heterostructures, where Ogre produces interface models in excellent agreement with density functional theory and experiments. Furthermore, we use Ogre to rationalize the templating effect of CsPbCl 3 on the growth of lead sulfochlorides, where perovskite seeds induce the formation of Pb 4 S 3 Cl 2 rather than Pb 3 S 2 Cl 2 due to better epitaxial compatibility. Finally, combining Ogre simulations with experimental data enables us to unravel the structure and composition of the hitherto unsolved CsPbBr 3 /Bi x Pb y S z interface, and to assign a structure to several other reported metal halide- and oxide-based interfaces. The Ogre package is available on GitHub or via the OgreInterface desktop application, available for Windows, Linux, and Mac.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct Demonstration of Topological Stability of Magnetic Skyrmions via Topology Manipulation

Topological protection precludes a continuous deformation between topologically inequivalent configurations in a continuum. Motivated by this concept, magnetic skyrmions, topologically nontrivial spin textures, are expected to exhibit topological stability, thereby offering a prospect as a nanometer-scale nonvolatile information carrier. In real materials, however, atomic spins are configured as not continuous but discrete distributions, which raises a fundamental question if the topological stability is indeed preserved for real magnetic skyrmions. Answering this question necessitates a direct comparison between topologically nontrivial and trivial spin textures, but the direct comparison in one sample under the same magnetic fields has been challenging. Here we report how to selectively achieve either a skyrmion state or a topologically trivial bubble state in a single specimen and thereby experimentally show how robust the skyrmion structure is in comparison with the bubbles. We demonstrate that topologically nontrivial magnetic skyrmions show longer lifetimes than trivial bubble structures, evidencing the topological stability in a real discrete system. Our work corroborates the physical importance of the topology in the magnetic materials, which has hitherto been suggested by mathematical arguments, providing an important step toward ever-dense and more-stable magnetic devices.

36 MATERIALS SCIENCE↗

Energetic Basis and Design of Enzyme Function Demonstrated Using GFP, an Excited-State Enzyme

We report the past decades have witnessed an explosion of de novo protein designs with a remarkable range of scaffolds. It remains challenging, however, to design catalytic functions that are competitive with naturally occurring counterparts as well as biomimetic or nonbiological catalysts. Although directed evolution often offers efficient solutions, the fitness landscape remains opaque. Green fluorescent protein (GFP), which has revolutionized biological imaging and assays, is one of the most redesigned proteins. While not an enzyme in the conventional sense, GFPs feature competing excited-state decay pathways with the same steric and electrostatic origins as conventional ground-state catalysts, and they exert exquisite control over multiple reaction outcomes through the same principles. Thus, GFP is an “excited-state enzyme”. Herein we show that rationally designed mutants and hybrids that contain environmental mutations and substituted chromophores provide the basis for a quantitative model and prediction that describes the influence of sterics and electrostatics on excited-state catalysis of GFPs. As both perturbations can selectively bias photoisomerization pathways, GFPs with fluorescence quantum yields (FQYs) and photoswitching characteristics tailored for specific applications could be predicted and then demonstrated. The underlying energetic landscape, readily accessible via spectroscopy for GFPs, offers an important missing link in the design of protein function that is generalizable to catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Description and Demonstration of the Coupled Community Earth System Model v2 – Community Ice Sheet Model v2 (CESM2‐CISM2)

Abstract Earth system/ice‐sheet coupling is an area of recent, major Earth System Model (ESM) development. This work occurs at the intersection of glaciology and climate science and is motivated by a need for robust projections of sea‐level rise. The Community Ice Sheet Model version 2 (CISM2) is the newest component model of the Community Earth System Model version 2 (CESM2). This study describes the coupling and novel capabilities of the model, including: (1) an advanced energy‐balance‐based surface mass balance calculation in the land component with downscaling via elevation classes; (2) a closed freshwater budget from ice sheet to the ocean from surface runoff, basal melting, and ice discharge; (3) dynamic land surface types; and (4) dynamic atmospheric topography. The Earth system/ice‐sheet coupling is demonstrated in a simulation with an evolving Greenland Ice Sheet (GrIS) under an idealized high CO 2 scenario. The model simulates a large expansion of ablation areas (where surface ablation exceeds snow accumulation) and a large increase in surface runoff. This results in an elevated freshwater flux to the ocean, as well as thinning of the ice sheet and area retreat. These GrIS changes result in reduced Greenland surface albedo, changes in the sign and magnitude of sensible and latent heat fluxes, and modified surface roughness and overall ice sheet topography. Representation of these couplings between climate and ice sheets is key for the simulation of ice and climate interactions.

Muntjewerf, Laura↗

Predictive Inverse Model for Advective Heat Transfer in a Short–Circuited Fracture: Dimensional Analysis, Machine Learning, and Field Demonstration

Identifying fluid flow maldistribution in planar geometries is a well–established problem in subsurface science/engineering. Of particular importance to the thermal performance of enhanced (or “engineered”) geothermal systems is identifying the existence of nonuniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a genetic algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two–dimensional Hele–Shaw geometry (i.e., parallel plates). The inverse problem is solved by minimizing the L2 norm between simulated residence time distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C–Dot nanoparticle). Principal component analysis (PCA) of spatially correlated permeability fields enabled reduction of the parameter space by more than a factor of 10 and restricted the inverse search to reservoir–scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding–plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. Here, the results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.

42 ENGINEERING↗

Demonstration of non-destructive and isotope-sensitive material analysis using a short-pulsed laser-driven epi-thermal neutron source

Neutrons are a valuable tool for non-destructive material investigation as their interaction cross sections with matter are isotope sensitive and can be used complementary to x-rays. So far, most neutron applications have been limited to large-scale facilities such as nuclear research reactors, spallation sources, and accelerator-driven neutron sources. Here we show the design and optimization of a laser-driven neutron source in the epi-thermal and thermal energy range, which is used for non-invasive material analysis. Neutron resonance spectroscopy, neutron radiography, and neutron resonance imaging with moderated neutrons are demonstrated for investigating samples in terms of isotope composition and thickness. The experimental results encourage applications in non-destructive and isotope-sensitive material analysis and pave the way for compact laser-driven neutron sources with high application potential.

36 MATERIALS SCIENCE↗

Experimental demonstration of continuous quantum error correction

The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, the protocol increases the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗