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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analysis of buffer-IPyC separation in TRISO fuel particles

During High Temperature Gas-cooled Reactor (HTGR) operation, and due to the neutron irradiation in the reactor core, damage of the nuclear fuel coating layers occurs. The mechanism of damage formation in the TRISO fuel is explored by the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program, in which the debonding process between coating layers was also investigated. The purpose of this paper is to report simulation results for two models. Firstly, the debonding restricted model, where no gap formation between buffer and IPyC layers is permitted. Secondly, a debonding enabled model, where the gap between those layers is created. The simulations were performed with the Bison code. The inputs of the simulated models are based on data from the AGR-1 experiment. Further, the research included simulations on spherical and aspherical fuel types. The simulations match results obtained by the AGR-1 experiment, which as such shows that the Bison code is a good computational method for simulating the behavior of the gap between buffer and IPyC layers in TRISO fuel. Based on the irradiation experiments, and the Bison simulations, it was concluded that the most common scenario is a gap formation along the buffer-IPyC interface, while the least possible scenario is the situation where there is no gap formation at the buffer-IPyC junction. The computational results confirmed that the sphericity of the fuel influences the thickness of the gap that occurs at the buffer-IPyC junction, in a way that with increasing aspect ratio the gap thickness increases. In addition, the fuel sphericity does not influence the Weibull failure probability. The results obtained for spherical and aspherical fuel are nearly identical.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Material Interactions in Severe Accidents – Benchmarking the MELCOR V2.2 Eutectics Model for a BWR-3 MARK-I Station Blackout: Part I – Single Case Analysis

Here in this analysis, the two material interaction models available in the MELCOR code are benchmarked for a severe accident at a BWR under representative Fukushima Daiichi boundary conditions. This part of the benchmark investigates the impact of each material interaction model on accident progression through a detailed single case analysis. It is found that the eutectics model simulation exhibits more rapid accident progression for the duration of the accident. The slower accident progression exhibited by the interactive materials model simulation, however, allows for a greater degree of core material oxidation and hydrogen generation to occur, as well as elevated core temperatures during the ex-vessel accident phase. The eutectics model simulation exhibits more significant degradation of core components during the late in-vessel accident phase – more debris forms and relocates to the lower plenum before lower head failure. The larger debris bed observed in the eutectics model simulation also reaches higher temperatures, presenting a more significant thermal challenge to the lower head until its failure. At the end of the simulated accident scenario, however, core damage is comparable between both simulations due to significant core degradation that occurs during the ex-vessel phase in the interactive materials model simulation. A key difference between the two models’ performance is the maximum temperatures that can be reached in the core and therefore the maximum ΔT between any two components. When implementing the interactive materials model, users have the option to modify the liquefaction temperature of the ZrO 2 -interactive and UO 2 -interactive materials as a way to mimic early fuel rod failure due to material interactions. Through modification of the liquefaction of high melting point materials with significant mass, users may inadvertently limit maximum core temperatures for fuel, cladding, and debris components.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Modeling the effect of MHD activity on runaway electron generation during SPARC disruptions

Magnetohydrodynamic (MHD) instabilities and runaway electrons (REs) interact in several ways, making it important to self-consistently model these interactions for accurate predictions of RE generation and the design of mitigation strategies, such as massive gas injection (MGI). Using M3D-C1 – an extended MHD code with a RE fluid model – we investigate the effects of 3-D nonlinear MHD activity, material injection, and 2-D axisymmetric vertical displacement events (VDEs) on RE evolution during disruptions on SPARC – a high-field, high-current tokamak designed to achieve a fusion gain Q > 1. Several cases, comprising different combinations of neon (Ne) and deuterium (D 2 ) injection, are considered. Here, our results demonstrate key effects that arise from the self-consistent RE + MHD coupling, such as an initial increase in RE generation due to MHD instability growth, decreased saturation energies of the m/n = 1/1 mode driving sawteeth-like activity, RE losses in stochastic magnetic fields, and subsequent RE confinement and plateau formation due to re-healing of flux surfaces. Large RE plateaus (>5 MA) are obtained with Ne-only injection (2-5 × 10 21 atoms), while combined D 2 + Ne injection (2 × 10 21 Ne atoms; 1.8 × 10 22 D 2 molecules) produces a lower RE current (<2 MA). With D 2 + Ne injection, a post thermal quench "cold" VDE terminates the RE beam, preventing a steady plateau. These simulations couple REs, 3-D MHD instabilities, MGI, and axisymmetric VDEs for the first time in SPARC disruption simulations and represent a crucial step in understanding RE generation and mitigation in high-current devices like SPARC.

Datta, Rishabh [Massachusetts Inst. of Technology ↗
DOE OSTI2021

Metallic Fuel Performance Code Requirements for the Versatile Test Reactor Project

Metallic nuclear fuels have been proposed for use in several emerging nuclear reactor designs, and a number of codes have been developed to model these fuels and assess their performance. Qualification of these metallic nuclear fuels will ultimately require monitored irradiation of lead test assemblies, but the use of fuel performance codes can reduce the uncertainty associated with these efforts by quantifying uncertainties and estimating margins to failure ahead of time. In this work, metallic fuel performance code requirements are defined for the Versatile Test Reactor (VTR) project using input from the Experimental Breeder Reactor II functional requirements, operational requirements, and design criteria. This work focuses on the thermomechanical responses and irradiation behaviors of metallic fuel elements that are representative of the proposed VTR driver fuel design concepts. As such, many of the code requirements and physics/modeling discussions in this work are expected to be broadly applicable to metallic fuel applications outside of the VTR project.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Manufactured solutions for an electromagnetic slot model

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. Finally, we demonstrate the effectiveness of these approaches for a variety of cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Validation Assessment of Turbulent Reacting Flow Model Using The Area-Validation Metric on Medium-Scale Methanol Pool Fire Results

Accident analysis and ensuring power plant safety are pivotal in the nuclear energy sector. Significant strides have been achieved over the past few decades regarding fire protection and safety, primarily centered on design and regulatory compliance. Yet, after the Fukushima accident a decade ago, the imperative to enhance measures against fire, internal flooding, and power loss has intensified. Hence, a comprehensive, multilayered protection strategy against severe accidents is needed. Consequently, gaining a deeper insight into pool fires and their behavior through extensive validated data can greatly aid in improving these measures using advanced validation techniques. A model validation study was performed at Sandia National Laboratories in which a 30-cm diameter methanol pool fire was modeled using the SIERRA/Fuego turbulent reacting flow code. This validation study used a standard validation experiment to compare model results against, and conclusions have been published. The fire was modeled with a Large Eddy Simulation (LES) turbulence model with subgrid turbulent kinetic energy closure. Combustion was modeled using a strained laminar flamelet library approach. Radiative heat transfer was accounted for with a model utilizing the gray-gas approximation. In the present study, additional validation analysis is performed using the area validation metric (AVM). These activities are done on multiple datasets involving different variables and temporal/spatial ranges and intervals. In conclusion, the results provide insight into the use of the area validation metric on such temporally varying datasets and the importance of physics-aware use of the metric for proper analysis.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2024

Coupled Experimental/Computational Investigation of the Dynamics of Interacting Magnetized Plasmas

The interaction, or interpenetration, of magnetized plasmas of different density and/or pressure occurs in a wide variety of natural and man-made systems. Such systems include extragalactic jets propagating into the intergalactic medium, solar coronal mass ejections into background solar wind, compact toroid (CT) fueling of magnetic fusion plasmas, and jets of capsule shell impurities into DT fusion fuel, which can lead to enhanced impurity mix in inertial fusion implosions. These plasmas may take the form of jets, with open, helical magnetic structure, or plasma “bubbles” with closed magnetic fields (B-fields), such as spheromaks or CT’s. Such structures, both open and closed B-field cases, can transport heat, particles and magnetic flux or magnetic helicity into background plasma regions. For example, the origin of extragalactic magnetic fields may be due, at least in part, to transport by astrophysical jets. The goal of this proposed work was to elucidate the detailed plasma and magnetic field dynamics of high-density plasma jets (open B-field) and bubbles (closed B-field) propagating into lower density background magnetized plasma through controlled laboratory experiments and closely coupled nonlinear MHD modeling. These experiments were conducted in the HelCat (Helicon-Cathode) linear plasma device at the University of New Mexico (UNM). Plasma jets and bubbles were launched via an existing compact coaxial plasma gun, mounted on the HelCat device. This gun produced plasmas tens of cm in scale and lasting tens of microseconds, thereby allowing detailed multipoint, space- and time-resolved measurements to be made routinely. The experiments were directly modeled using the extended magnetohydrodynamic (XMHD) PERSEUS code, developed at Cornell University [23,24]. Both experimental and numerical modeling work are ongoing. The main results to date are reported here. Additional supplemental funding for one year (8/1/2019 – 7/31/2020) supported numerical investigation of photoionization processes important in many low temperature plasmas, including the HelCat device. Initial results of this modeling work is also reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

SICOPOLIS-AD v1: an open-source adjoint modeling framework for ice sheet simulation enabled by the algorithmic differentiation tool OpenAD

We present a new capability of the ice sheet model SICOPOLIS that enables flexible adjoint code generation via source transformation using the open-source algorithmic differentiation (AD) tool OpenAD.The adjoint code enables efficient calculation of the sensitivities of a scalar-valued objective function or quantity of interest (QoI) to a range of important, often spatially varying and uncertain model input variables, including initial and boundary conditions, as well as model parameters.Compared to earlier work on the adjoint code generation of SICOPOLIS, our work makes several important advances:(i) it is embedded within the up-to-date trunk of the SICOPOLIS repository – accounting for 1.5 decades of code development and improvements – and is readily available to the wider community;(ii) the AD tool used, OpenAD, is an open-source tool;(iii) the adjoint code developed is applicable to both Greenland and Antarctica, including grounded ice as well as floating ice shelves, with an extended choice of thermodynamical representations.A number of code refactorization steps were required. They are discussed in detail in an Appendix as they hold lessons for the application of AD to legacy codes at large.As an example application, we examine the sensitivity of the total Antarctic Ice Sheet volume to changes in initial ice thickness, austral summer precipitation, and basal and surface temperatures across the ice sheet.Simulations of Antarctica with floating ice shelves show that over 100 years of simulation the sensitivity of total ice sheet volume to the initial ice thickness and precipitation is almost uniformly positive, while the sensitivities to surface and basal temperature are almost uniformly negative. Sensitivity to austral summer precipitation is largest on floating ice shelves from Queen Maud to Queen Mary Land. The largest sensitivity to initial ice thickness is at outlet glaciers around Antarctica. Comparison between total ice sheet volume sensitivities to surface and basal temperature shows that surface temperature sensitivities are higher broadly across the floating ice shelves, while basal temperature sensitivities are highest at the grounding lines of floating ice shelves and outlet glaciers. A uniformly perturbed region of East Antarctica reveals that, among the four control variables tested here, total ice sheet volume is the most sensitive to variations in austral summer precipitation as formulated in SICOPOLIS.Comparison between adjoint- and finite-difference-derived sensitivities shows good agreement, lending confidence that the AD tool is producing correct adjoint code.The new modeling infrastructure is freely available at http://www.sicopolis.net (last access: 2 April 2020) under the development trunk.

58 GEOSCIENCES↗
DOE OSTI2024

Dataset for "Evaluating Deep Learning Approaches for Predictions in Unmonitored Basins with Continental-scale Stream Temperature Models" Willard et al. (2024)

This data release provides all data and code used in the paper " "Evaluating Deep Learning Approaches for Predictions in Unmonitored Basins with Continental-scale Stream Temperature Models" Willard et al. (2024)" to model stream temperature, evaluate, and assess results. The associated manuscript explores current open questions in prediction in ungauged and unmonitored basins concerning top-down versus bottom-up approaches, tradeoffs between data available and input requirements, and the appropriate representation of catchment attributes as inputs to deep learning models. Modeling was done primarily with long short-term memory (LSTM) models, and stream site coverage spans 1362 locations across the conterminous United States. The data is organized into these items items:Code repository and data for the paper " "Evaluating Deep Learning Approaches for Predictions in Unmonitored Basins with Continental-scale Stream Temperature Models" Willard et al. (2024)".Code: stream_temp_ml_regionalization.zip contains the code repositoryData to run the code: - data_dir.zip -- contains all files that should be moved to the "DATA_DIR" variable defined in the "set_env_vars.sh" script in the code repository- metadata_dir.zip -- contains all files that should be moved to the "METADATA_DIR" variable defined in the "set_env_vars.sh" script in the code repository- error_analysis_attribute_and_groundwater_dir.zip - workflows for the extended error analysis by stream attribute and groundwater influenceData produced by the code and used in the paper:- outputs_dir.zip - contains model output and results (outputs_dir/results), model weights (outputs_dir/models), and all other outputs used for the paper including feature importances.To cite this code, please use the following BibTeX or MLA entries:bibtex:@misc{willard2024streamdata, author = {Jared Willard and Fabio Ciulla and Helen Weierbach and Vipin Kumar and Charuleka Varadharajan}, title = {Dataset for "Evaluating Deep Learning Approaches for Predictions in Unmonitored Basins with Continental-scale Stream Temperature Models"}, year = {2024}, doi = {10.15485/2448016}, publisher = {ESS-DIVE Repository}, url = {https://doi.org/10.15485/2448016}}MLA: Willard, Jared, et al. Dataset for "Evaluating Deep Learning Approaches for Predictions in Unmonitored Basins with Continental-scale Stream Temperature Models". 2024. ESS-DIVE Repository, doi:10.15485/2448016.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Quasilinear modelling of collisional trapped electron modes

The simplification of collision operators is necessary for quasilinear turbulence modelling used with integrated modelling frameworks, such as the gyrokinetic code QuaLiKiz. The treatment of collisions greatly impacts the accuracy of trapped electron mode (TEM) modelling, which is necessary to predict the electron heat flux and the balance between inward and outward particle fluxes. In particular, accurate particle flux predictions are necessary to successfully model density peaking in the tokamak core. We explored two ways of improving collisional TEM model reduction for tokamak core plasmas. First, we carried out linear GENE simulations to study the complex interplay between collisions and trapped electrons. We then used these simulations to define an effective trapped fraction to characterize the collisional TEM based on two key parameters, the local inverse-aspect ratio $\epsilon$ and the collisionality $\nu ^\ast$. One aspect missing from analytical TEM research is that the collisional frequency and the bounce-transit frequency are both velocity dependent; this effective trapped fraction takes both into account. In doing so, we determined that two parameters are not enough to model the collisional TEM, as an additional third free parameter was necessary. We determined that this model, as currently formulated, is not suitable for integrated modelling purposes. Second, we directly improved QuaLiKiz's Krook operator, which relies on two free parameters. We determined that these parameters required adjustments against higher-fidelity collisional models. In order to improve density profile predictions when paired with integrated models, we refined the Krook operator by using GENE simulations as a higher-fidelity point of comparison. We then demonstrate strong improvement of density peaking predictions of QuaLiKiz within the integrated modelling framework JETTO.

fusion plasma↗
DOE OSTI2021

(U) Radiation Hydrodynamics in the Ristra Project’s Symphony code: Initial release

One of the recent focuses in the next-generation code (NGC/Ristra)project at LANL is to develop a cell-centered Lagrangian radiation-hydrodynamics code under FleCSI framework. The FleCSI frame-work provides a unified data and execution model in order to insulate production code development from the uncertainty of evolving runtimeand architectures. We have developed the code, Symphony, which in-corporates the hydrodynamics code, FleCSALE, and the radiation transport code, Puno.This memo is intended to describe the coupling of radiation and hydrodynamics within the Ristra Project’s code Symphony.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Estimating an airborne dipole source using 3-D wavefield simulations and seismic receivers on the ground

Acoustic signals can couple to the ground, providing an opportunity to use seismic stations to investigate airborne sources. The study of Bishop et al. used wavefield simulations in a fluid-solid medium to quantify the role of topography on the seismic (ground) recordings of a monopole source in the air. We build upon this study by linking wavefield forward modelling with the source estimation code MTUQ, which can accommodate point forces or moment tensors in a solid medium, as well as sources in the air (or water) if they are enabled by the forward-modelling solver. We perform a series of synthetic numerical experiments to demonstrate that a dipole airborne source can be estimated using ground-based receivers, even within the presence of realistic topography. We investigate the influence of receiver coverage, topography, and assumed source location on the estimated results. The established capabilities raise the prospects for future efforts to estimate dipole sources in 3-D models that include heterogeneity in the air and the earth in addition to topography.

58 GEOSCIENCES↗
DOE OSTI2025

Implementation of Stochastic Gradient Descent in an Automated Glow Peak Identification Software for Multiple Thermoluminescent Dosimeter Types

A glow-curve analysis code was previously developed in C++ to analyze thermoluminescent dosimeter glow curves using automated peak detection while applying a first-order kinetics model. A newer version of this code was implemented to improve the automated peak detection and curve fitting models. The Stochastic Gradient Descent Algorithm was introduced to replace the prior approach of taking first and second-order derivatives for peak detection. Additionally, early stopping mechanisms were invoked to improve the previously used Levenberg-Marquardt Algorithm employed for curve fitting. The two software versions were compared through glow curve analysis of different thermoluminescent dosimeter materials and calculation of the corresponding figures of merit. Altogether improvements were shown, namely an increase in the number of peaks detected and a reduction of the mean figure of merit by approximately 46%.

137Cs↗
DOE OSTI2024

Improving the modeling of near-wall interphase heat transfer in porous media models of Pebble Bed Reactors

Here, this work aims to improve capabilities for modeling localized effects in porous media models of Pebble Bed Reactors. The wall-channeling effect is the primary local phenomenon of interest in a PBR, where the presence of the reflector wall disrupts the pebble packing, causing the pebbles near the wall to pack less efficiently and creating large void regions. Accurate modeling of the near-wall region is important as it will affect core bypass flow and temperature predictions. Porous media models are commonly used for design scoping and plant-level simulations of PBRs. Although these models have some capabilities to model the near-wall region, the correlations that are available in porous media codes are often inaccurate when a multi-region model is used to discretize the near-wall region. This work employs a high-to-low analysis to study the accuracy of available interphase heat transfer closures. NekRS, a spectral element computational fluid dynamics code, is used to perform Large Eddy Simulations. These LES simulation results are compared to porous media model results from the Pronghorn porous media code. The friction term of the KTA drag closure is first improved, reducing the error in the prediction of the near-wall velocity from over 50% to less than 5%. This is combined with improvements to the form term from previous works to produce a drag closure that is capable of accurately modeling the wall-channeling effect across a variety of flow conditions. The Nusselt number predictions of several heat transfer correlations are compared to the high-fidelity results where it is found that the KTA heat transfer correlation is capable of accurately predicting the local Nusselt numbers that were determined in the high-fidelity simulation. Comparison of the radial solid temperature profiles, however, reveal discrepancies between NekRS and Pronghorn. It is discovered that the implementation of the interphase heat transfer coefficient that exists in many current porous media codes is not valid when local porosities are modeled. Instead, it is suggested that the interphase heat transfer coefficient should be dependent on the local porosity, the Nusselt number, and the local solid surface-to-volume ratio. Implementation of this change produces improvement in the agreement between the results obtained by NekRS and Pronghorn while using the KTA heat transfer correlation.

interphase heat transfer↗
DOE OSTI2022

Modelling the nonlinear plasma response to externally applied three-dimensional fields with the Stepped Pressure Equilibrium Code

Small-amplitude, symmetry-breaking magnetic field perturbations, including resonant magnetic perturbations (RMPs) and error fields, can profoundly impact plasma properties in both tokamaks and stellarators. In this work, we perform the first comparison between the Stepped Pressure Equilibrium Code (SPEC) (a comparatively fast and efficient equilibrium code based on energy-minimisation principles) and M3D-C 1 (a high-fidelity albeit computationally expensive initial-value extended-magnetohydro-dynamic (MHD) code) to assess the conditions under which SPEC can be used to model the nonlinear, non-ideal plasma response to an externally applied (m = 2,n = 1) RMP field in an experimentally relevant geometry. We find that SPEC is able to capture the plasma response in the weakly nonlinear regime – meaning perturbation amplitudes below the threshold for break up of the separatrix and onset of secondary magnetic island formation – when around half of the total toroidal flux is enclosed in the volume containing the q = 2 resonant surface. Further, the observed dependence of SPEC solutions on input parameters, including toroidal flux and the number of volumes into which the plasma is partitioned, indicates that additional exploration of the underlying Multi-Region Relaxed MHD physics model is needed to constrain the choice of parameters. Nonetheless, this work suggests promising applications of SPEC to optimisation and fusion plasma design.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Implementation of a Drift Flux Model into SAM with Development of a Verification and Validation Test Suite for Modeling of Noncondensable Gas Mixtures

The advanced thermal-hydraulic system code, System Analysis Module (SAM), was originally developed for the modeling of single-phase flow in advanced reactors. It has since been expanded to include a four-equation drift flux model for the modeling of two-phase flows containing a noncondensable gas. The model was expanded to support the modeling of molten salt reactor (MSR) designs in which the fuel is directly dissolved in the circulating coolant. These designs have shown that circulating gas bubbles can play an important role in the management of fission products and the operational behavior of the reactor. A drift flux model was implemented to more accurately capture the localized behavior of the void in the core and its impact on the mass transfer of fission products. A thorough assessment of the new model was performed by developing a verification and validation test suite. Verification problems were designed to test all major terms in the new governing equations. The new model converged to the correct solution at the expected order of accuracy for all verification cases. The validation cases included a wide range of flow and void conditions in different pipe geometries. Although higher void experiments show a slight underprediction of void by the drift flux model, experiments that aim to reproduce Molten Salt Reactor Experiment (MSRE) experimental conditions show good agreement with the model. The gas transport model was activated for a SAM model of the MSRE to demonstrate that it can be used in a more complex model. Finally, this gas transport model will be used along with an interfacial area transport equation being implemented in SAM for the prediction of mass transport behavior in MSR conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Effects of Hydrogen Bonding on Nuclear Data Development of Liquid Anhydrous HF

Anhydrous Hydrogen Fluoride (HF) at high temperatures and pressures is used to process and manufacture nuclear fuel. As HF is often used directly with uranium, correct neutron thermal scattering cross sections are crucial to criticality safety applications. Classical molecular dynamics (CMD) simulation of the flexible HF system was used to create the thermal scattering law (TSL) and cross sections. The initial 2-site model is used in LAMMPS, and it can not capture the H-bond. To correctly represent the H-bond effects, a second, 3-site model was constructed in GROMACS. The 3-site model handled H-bonds by connecting a massless charge to the molecule. Key model parameters were compared to experimental data to verify the approach and models. To get the normalized VACF, the model was compared using hydrogen and fluorine bond length, density, potential energy, and diffusion coefficient. The phonon DOSs for both models were derived from the normalized VACF. DOSs were used to estimate the TSL ( S ( α, β )) and neutron thermal scattering cross sections for hydrogen in HF. The TSLs were evaluated using the FLASSH code with the Schofield diffusion model. It was observed that the representation of the hydrogen bonding changes the TSL's diffusional contributions. This is represented in the low energy scattering cross section, where intermolecular binding effects shift the cross section.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Quantum error correction from complexity in Brownian SYK

We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is upper bounded by the “mutual purity” of a certain entangled state between the code subspace and environment in the isometric extension of the error channel, where the mutual purity of a density matrix ρAB is the difference $\mathcal{F}$ p ($A : B$) ≡ $\mathrm{T}$r $p^{2}_{AB}$ - $\mathrm{T}$r $p^{2}_{A}$ $\mathrm{T}$r $p^{2}_{B}$. We show that when the encoding complexity is small, the mutual purity is O(1) for the erasure of a small number of qubits (i.e., the encoding is fragile). However, this quantity decays exponentially, becoming O(1/N) for O(log N) encoding complexity. Further, at polynomial encoding complexity, the mutual purity saturates to a plateau of O(e -N ). We also find a hierarchy of complexity scales associated to a tower of subleading contributions to the mutual purity that quantitatively, but not qualitatively, adjust our error correction bound as encoding complexity increases. In the AdS/CFT context, our results suggest that any portion of the entanglement wedge of a general boundary subregion A with sufficiently high encoding complexity is robustly protected against low-rank errors acting on A with no prior access to the encoding map. From the bulk point of view, we expect such bulk degrees of freedom to be causally inaccessible from the region A despite being encoded in it.

1/N expansion↗