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A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part II: Idealized Markov Chain Monte Carlo Experiments

Observationally informed development of a new framework for bulk rain microphysics, the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS; described in Part I of this study), is demonstrated. This scheme’s development is motivated by large uncertainties in cloud and weather simulations associated with approximations and assumptions in existing microphysics schemes. Here, a proof-of-concept study is introduced using a Markov chain Monte Carlo sampling algorithm with BOSS to probabilistically estimate microphysical process rates and parameters directly from a set of synthetically generated rain observations. The framework utilized is an idealized steady-state one-dimensional column rainshaft model with specified column-top rain properties and a fixed thermodynamical profile. Different configurations of BOSS—flexibility being a key feature of this approach—are constrained via synthetic observations generated from a traditional three-moment bulk microphysics scheme. The ability to retrieve correct parameter values when the true parameter values are known is illustrated. For cases when there is no set of true parameter values, the accuracy of configurations of BOSS that have different levels of complexity is compared. It is found that addition of the sixth moment as a prognostic variable improves prediction of the third moment (proportional to bulk rain mass) and rain rate. In contrast, increasing process rate formulation complexity by adding more power terms has little benefit—a result that is explained using further-idealized experiments. BOSS rainshaft simulations are shown to well estimate the true process rates from constraint by bulk rain observations, with the further benefit of rigorously quantified uncertainty of these estimates.

58 GEOSCIENCES↗

Statistical uncertainty of fission matrix eigenvalues using perturbation theory

Eigenvalue search of high dominance ratio systems may be slow to converge. The fission matrix element is defined by its element (FM){sub ij}, which are the probability for a neutron born in cell i to create a fission in cell j for a spatial mesh of n{sub i}*n{sub j} elements. Fission matrices are used in Monte Carlo criticality simulations to enhance computing speed, but also to find higher order eigenvalues. However, few studies have been made on the link between statistical uncertainties of fission matrix elements and eigenvalues uncertainties. Thus, dominance ratio statistical uncertainties remain unknown. This paper uses a new generalized perturbation theory (GPT) method to estimate sensitivities of eigenvalues to fission matrix elements and then to calculate dominance ratio uncertainties.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Machine Learning Reduced Order Model for Cost and Emission Assessment of a Pyrolysis System

Biomass pyrolysis is a promising approach for producing economic and environmentally-friendly fuels and bioproducts. Biomass pyrolysis experiments show that feedstock properties have a significant impact on product yields and composition. Scientists are developing detailed chemical reaction mechanisms to capture the relationships between biomass composition and pyrolysis yields. These mechanisms can be computationally intensive. In this study, we investigate the use of a machine learning reduced order model (ROM) for assessing the costs and emissions of a pyrolysis biorefinery. Here, we developed a Kriging-based ROM to predict pyrolysis yields of 314 feedstock samples based on the results of a detailed chemical kinetic pyrolysis mechanism. The ROM is integrated into a chemical process model for calculating mass and energy yields in a commercial-scale (2000 tonne/day) biorefinery. The ROM estimated biofuel yields of 65 to 130 gallons per ton of dry biomass. This results in biofuel minimum fuel-selling prices of $2.62 to $5.43 per gallon and emissions of -13.62 to 145 kg of CO 2 per MJ. The ROM achieved an average mean square error of 1.8e-20 and a mean absolute error of 0.53%. These results suggest that ROMs can facilitate rapid feedstock screening for biorefinery systems.

09 BIOMASS FUELS↗

Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Restricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter (β) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

97 MATHEMATICS AND COMPUTING↗

Novel application of neutrinos to evaluate U.S. nuclear weapons performance

There is a growing realization that neutrinos can be used as a diagnostic tool to better understand the inner workings of a nuclear weapon. Robust estimates demonstrate that an Inverse Beta Decay (IBD) neutrino scintillation detector built at the Nevada Test Site with a 1000-ton active target mass at a standoff distance of 500 m would detect thousands of antineutrino events per nuclear test. This would provide less than 4% statistical error on the measured antineutrino rate and 5% error on antineutrino energy. Extrapolating this to an error on the test device explosive yield requires knowledge from evaluated nuclear databases, non-equilibrium fission rates, and assumptions on internal neutron fluxes. Initial calculations demonstrate that the total number of neutrinos emitted per fission in the first 10 3 s after a short pulse of 239 Pu fission is about a factor of two less than that from Pu fissioning under steady state conditions. Furthermore, there are significant energy spectral differences as a function of time after the pulse that must be considered. These and other model dependencies will be discussed in the paper. In the absence of nuclear weapons testing, many of the technical and theoretical challenges of a full nuclear test could be mitigated with a low cost smaller scale 20 ton fiducial mass IBD demonstration detector placed near a pulsed reactor. Potential reactors include the Texas A&M University TRIGA 1 GW–10 ms pulsed facility or the Sandia Annular Core Research Reactor. The short duty cycle and repeatability of pulses would provide critical real environment testing and measurements, which would be valuable for planning a possible real test shot in the future. Furthermore, the antineutrino rate as a function of time data would provide unique constraints on fission databases and model assumptions. Finally, there are impactful science drivers such as sensitive searches for ∼1 eV 2 sterile neutrinos and ∼MeV scale axions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Rodeo Algorithm for Quantum Computing

We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $\ [E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by a suppression factor δ, the required computational effort scales as $\ O[|\log \delta|/(p \epsilon)]$, where p s the squared overlap of the initial state with the target eigenvector. The method, which we call the rodeo algorithm, uses auxiliary qubits to control the time evolution of the Hamiltonian minus some tunable parameter E . In this manner, we converge to the target eigenvector with exponential accuracy in the number of measurements. In addition to preparing eigenvectors, the method can also compute the full spectrum of the Hamiltonian. We illustrate the performance with several examples. For energy eigenvalue determination with error $\epsilon$, the computational scaling is $\ O[(\log \epsilon)^2/(p \epsilon)]$. For eigenstate preparation, the computational scaling is $\ O(\log \Delta/p)$, where $\Delta$ is the magnitude of the orthogonal component of the residual vector. The speed for eigenstate preparation is exponentially faster than that for phase estimation or adiabatic evolution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Assessment of Flow-Enhanced Electrochemical Sensor Testing and Deployments for MSRs

This report serves as the deliverable for Milestone M3RS-23AN0401061 that is part of Work Package RS-23AN040106 (Flow Enhanced Sensors for MSRs – ANL). The goal of this milestone was to determine performance of the flow enhanced electrochemical sensor (FEES) and modular flow instrumentation testbed (MFIT) in safeguards relevant scenarios. Flow enhanced electrochemical sensors are a type of electroanalytical sensor that has been developed at Argonne National Laboratory to be installed directly into MSR flow conduits to make measurements of the salt composition. These sensors represent a significant improvement in capabilities compared to earlier electroanalytical sensors that instead can only be operated in quiescent conditions. Previous work has focused on testing of the FEES in flowing conditions provided by the MFIT to assess the accuracy and precision of the sensor measurements. To further improve this capability, in FY23 we undertook a campaign of safeguards relevant scenarios in molten salt containing a range of uranium chloride concentrations (0 to 3 wt%). All the testing carried out in FY23 was aided by a control system designed to automatically actuate flow conditions and collect data. This new automation system is estimated to have increased experimental throughput by a factor of four and enabled testing in a variety of complex conditions. The advancements in throughput and repeatability led to improved quantification of actinide concentrations using the in-flow sensors, with a reduction of the mean absolute relative error from 5.6% in FY22 to 3.1% in FY23. In addition to safeguards scenarios run in the MFIT, FY23 work included deployment of a FEES at a partner institution where it will be tested in a flowing salt loop. The FEES was successfully integrated into that loop and is being tested prior to loop startup. In FY23, work also continued on the smaller flow system that we have named the mini-MFIT. This smaller system is capable of rapid prototyping of new sensor designs prior to installation in the larger MFIT radiological flow system. Work was carried out to test this new system in non-radiological molten salts in a separate glovebox. This work is helping us to enhance the accuracy of our salt monitoring capabilities through the integration of multiple types of sensors. The high degree of accuracy required by 10 CFR 74 represents a significant challenge, and further design evolution and integration of the sensors into multimodal sensing frameworks will be needed to further push the measurement accuracy to the needed level.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Satellite Embedding-Based Population Imputation for Areas with Missing Building Footprint Data: A Computer Vision-Based Approach

High-resolution population modeling is important for supporting effective decision-making across diverse sectors. LandScan Mosaic generates population estimates at the level of individual buildings and aggregates them to 3 arc-second grids, and this approach performs well in regions where building footprint data are comprehensive and reliable. However, large portions of the globe still suffer from incomplete, sparse, or entirely missing building stock datasets, creating a structural limitation for strictly building-based population models. To address this research gap, this study proposes a computer vision-based framework that employs Google Earth Engine satellite embeddings and UNet, which allows us to directly impute grid-level population estimates in building-data-deficient areas. Applied to Taiwan as a case study, the framework achieved strong predictive performance with R$^{2}$ of 0.89, RMSE of 18.70, and MAE of 8.41, outperforming traditional machine learning approaches. Notably, the proposed framework effectively addressed building false-positive errors inherent in Global Human Settlement Layer (GHSL) data, correctly identifying uninhabited areas that were erroneously classified as populated. The framework also offers significant advantages for global population mapping, particularly in terms of scalability and temporal consistency, thereby extending the coverage and accuracy of high-resolution population products in data-scarce regions worldwide. Urban planners, decision makers, and related stakeholders can obtain granular population distributions to support more accurate and targeted infrastructure investment, service delivery, resource allocation, and risk assessment decisions.

97 MATHEMATICS AND COMPUTING↗

Using AI for Wave-front Estimation with the Rubin Observatory Active Optics System

Abstract The Vera C. Rubin Observatory will, over a period of 10 yr, repeatedly survey the southern sky. To ensure that images generated by Rubin meet the quality requirements for precision science, the observatory will use an active-optics system (AOS) to correct for alignment and mirror surface perturbations introduced by gravity and temperature gradients in the optical system. To accomplish this, Rubin will use out-of-focus images from sensors located at the edge of the focal plane to learn and correct for perturbations to the wave front. We have designed and integrated a deep-learning (DL) model for wave-front estimation into the AOS pipeline. In this paper, we compare the performance of this DL approach to Rubin’s baseline algorithm when applied to images from two different simulations of the Rubin optical system. We show the DL approach is faster and more accurate, achieving the atmospheric error floor both for high-quality images and low-quality images with heavy blending and vignetting. Compared to the baseline algorithm, the DL model is 40× faster, the median error 2× better under ideal conditions, 5× better in the presence of vignetting by the Rubin camera, and 14× better in the presence of blending in crowded fields. In addition, the DL model surpasses the required optical quality in simulations of the AOS closed loop. This system promises to increase the survey area useful for precision science by up to 8%. We discuss how this system might be deployed when commissioning and operating Rubin.

79 ASTRONOMY AND ASTROPHYSICS↗

Risk Analysis of Various Design Architectures for High Safety-significant Safety-related Digital Instrumentation and Control Systems of Nuclear Power Plants during Accident Scenarios

This report documents the plus-up activities performed by Idaho National Laboratory (INL) during Fiscal Year (FY) 2022 for the U.S. Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) Program, Risk Informed Systems Analysis (RISA) Pathway, digital instrumentation and control (DI&C) risk assessment project. In FY 2019, the RISA Pathway initiated a project to develop a risk assessment strategy for delivering a strong technical basis to support effective, licensable, and secure DI&C technologies for digital upgrades/designs. An integrated risk assessment technology for the DI&C systems was proposed for this strategy, which aims to (1) provide a best-estimate, risk-informed capability to quantitatively and accurately estimate the safety margin obtained from plant modernization, especially for the high safety-significant safety-related (HSSSR) DI&C systems, (2) support and supplement existing advanced risk-informed DI&C design guides by providing quantitative risk information and evidence, (3) offer a capability of design architecture evaluation of various DI&C systems to support system design decisions and diversity and redundancy applications, (4) assure the long-term safety and reliability of HSSSR DI&C systems, and (5) reduce uncertainty in costs and support integration of DI&C systems in the plant. To achieve these technical goals and deal with the expensive licensing justifications from regulatory insights, the LWRS-developed framework instructs nuclear vendors and utilities on how to effectively lower the costs associated with digital compliance and speed industry advances by: (1) defining an integrated risk-informed analysis process for DI&C upgrade, including hazard analysis, reliability analysis, and consequence analysis, (2) applying systematic and risk-informed tools to address common cause failures (CCFs) and quantify corresponding failure probabilities for DI&C technologies, particularly software CCFs, (3) evaluating the impact of digital failures at the component level, system level, and plant level, and (4) providing insights and suggestions on designs to manage the risks, thus to support the development, licensing, and deployment of advanced DI&C technologies on nuclear power plant (NPPs). Adding diversity within system or components is the main means to eliminate and mitigate CCFs, but diversity also increases plant complexity and errors and may not address all sources of systematic failures. How to optimize the diversity and redundancy applications for the safety-critical DI&C systems remains a challenge. To deal with the technical issues in addressing potential software CCFs in HSSSR DI&C systems of NPPs and supporting relevant design optimization, the framework provides: ? An integrated best-estimate, risk-informed capability to address new technical digital issues quantitatively, accurately, and efficiently in plan modernization progress, such as software CCFs in HSSSR DI&C systems of NPPs ? A common and a modularized platform for DI&C designers, software developers, cybersecurity analysts, and plant engineers to efficiently predict and prevent risk in the early design stage of DI&C systems ? Technical bases and risk-informed insights to assist U.S. Nuclear Regulatory Commission (NRC) and industry to address and fulfill the risk-informed alternatives for evaluation of CCFs in HSSSR DI&C systems of NPPs ? An integrated risk-informed tool that offers a capability of design architecture evaluation of various DI&C systems to support system design decisions in diversity and redundancy applications. The plus-up research and development efforts of this project in FY 2022 are focused on methodology improvement of software CCF modeling and estimation, prevention analysis, importance analysis and risk analysis of various design architectures of HSSSR DI&C systems. This work greatly enhances the capability of the LWRS-developed framework for the risk assessment and design optimization of safety-critical DI&C systems. It should be noted that all the analyses are performed for the demonstration of the LWRS-developed framework, not for the evaluation of relevant systems. Results are obtained based on very limited design information and testing data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

Here, in this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

early-time solution↗

Bayesian model-data comparison incorporating theoretical uncertainties

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of properly accounting for theoretical uncertainties. In this Letter, we present a Bayesian framework that explicitly quantifies these uncertainties by statistically modeling theory errors, guided by qualitative knowledge of a theory’s varying reliability across the input domain. We demonstrate the effectiveness of this approach using two systems: a simple ball drop experiment and multi-stage heavy-ion simulations. In both cases incorporating model discrepancy leads to improved parameter estimates, with systematic improvements observed as additional experimental observables are integrated.

Bayesian methods↗

Combining Computational Modeling with Reaction Kinetics Experiments for Elucidating the In Situ Nature of the Active Site in Catalysis

Microkinetic modeling based on density functional theory (DFT) derived energetics is important for addressing fundamental questions in catalysis. The quantitative fidelity of microkinetic models (MKMs), however, is often insufficient to conclusively infer the mechanistic details of a specific catalytic system. Here, this can be attributed to a number of factors such as an incorrect model of the active site for which DFT calculations are performed, deficiencies in the hypothesized reaction mechanism, inadequate consideration of the surface environment under reaction conditions, and intrinsic errors in the DFT exchange-correlation functional. Despite these limitations, we aim at developing a rigorous understanding of the reaction mechanism and of the nature of the active site for heterogeneous catalytic chemistries under reaction conditions. By achieving parity between experimental and modeling outcomes through robust parameter estimation and by ensuring coverage-consistency between DFT calculations and MKM predictions, it is possible to systematically refine the mechanistic model and, thereby, our understanding of the catalytic active site in situ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Forces from Stochastic Density Functional Theory under Nonorthogonal Atom-Centered Basis Sets

We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atom-centered basis set representation (Fabian et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2019, 9, e1412, 10.1002/wcms.1412) and apply it to the Tryptophan Zipper 2 (Trp-zip2) peptide solvated in water. We use an embedded-fragment approach to reduce the statistical errors (fluctuation and systematic bias), where the entire peptide is the main fragment and the remaining 425 water molecules are grouped into small fragments. We analyze the magnitude of the statistical errors in the forces and find that the systematic bias is of the order of 0.065 eV/Å (~1.2 × 10 -3 E h / a 0 ) when 120 stochastic orbitals are used, independently of system size. This magnitude of bias is sufficiently small to ensure that the bond lengths estimated by stochastic DFT (within a Langevin molecular dynamics simulation) will deviate by less than 1% from those predicted by a deterministic calculation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dimensional Interpolation for Random Walk

In this work, we employ a simple and accurate dimensional interpolation formula for the shapes of random walks at D = 3 and D = 2 based on the analytically known solutions at both limits D = ∞ and D = 1. The results obtained for the radius of gyration of an arbitrary shaped object have about 2% error compared with accurate numerical results at D = 3 and D = 2. We also calculated the asphericity for a three-dimensional random walk using the dimensional interpolation formula. The results agree very well with the numerically simulated results. The method is general and can be used to estimate other properties of random walks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Muon capture on the deuteron in chiral effective field theory

Here, we consider the capture of a muon on a deuteron. An uncertainty analysis of the dominant channels is important for a careful analysis of forthcoming experimental data. We quantify the theoretical uncertainties of chiral effective-field-theory predictions of the muon-deuteron capture rate from the relevant neutron-neutron partial wave channels in the final state. We study the dependence on the cutoff used to regularize the interactions, low-energy constants calibrated using different fitting data and strategies, and truncation of the effective-field-theory expansion of the currents. Combining these approaches gives as an estimate of $Γ^{1/2}_{μd}$ = 399.1 ± 7.6 ± 4.4 s –1 for capture from the atomic doublet state, and $Γ^{3/2}_{μd}$= 12.31 ± 0.47 ± 0.04 s –1 for capture from the quartet state and the first and second uncertainties given here are due to the effective field theory truncation error and the uncertainty in the axial radius, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dark energy survey year 3 results: High-precision measurement and modeling of galaxy-galaxy lensing

We present and characterize the galaxy-galaxy lensing signal measured using the first three years of data from the Dark Energy Survey (DES Y3) covering 4132 deg 2 . These galaxy-galaxy measurements are used in the DES Y3 3 × 2 pt cosmological analysis, which combines weak lensing and galaxy clustering information. We use two lens samples: a magnitude-limited sample and the redmagic sample, which span the redshift range ∼ 0.2 – 1 with 10.7 and 2.6 M galaxies, respectively. For the source catalog, we use the metacalibration shape sample, consisting of ≃ 100 M galaxies separated into four tomographic bins. Our galaxy-galaxy lensing estimator is the mean tangential shear, for which we obtain a total SNR of ∼ 148 for maglim ( ∼ 120 for redmagic), and ∼ 67 ( ∼ 55 ) after applying the scale cuts of 6 Mpc / h . Thus we reach percent-level statistical precision, which requires that our modeling and systematic-error control be of comparable accuracy. The tangential shear model used in the 3 × 2 pt cosmological analysis includes lens magnification, a five-parameter intrinsic alignment model, marginalization over a point mass to remove information from small scales and a linear galaxy bias model validated with higher-order terms. We explore the impact of these choices on the tangential shear observable and study the significance of effects not included in our model, such as reduced shear, source magnification, and source clustering. We also test the robustness of our measurements to various observational and systematics effects, such as the impact of observing conditions, lens-source clustering, random-point subtraction, scale-dependent metacalibration responses, point spread function residuals, and B modes.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing Quantum Telecloning on Superconducting Quantum Processors

Quantum information cannot be perfectly cloned, but approximate copies of quantum information can be generated. Quantum telecloning combines approximate quantum cloning, more typically referred to as quantum cloning, and quantum teleportation. Quantum telecloning allows approximate copies of quantum information to be constructed by separate parties, using the classical results of a Bell measurement made on a prepared quantum telecloning state. Quantum telecloning can be implemented as a circuit on quantum computers using a classical coprocessor to compute classical feedforward instructions using if statements based on the results of a midcircuit Bell measurement in real time. We present universal symmetric optimal 1 → M telecloning circuits and experimentally demonstrate these quantum telecloning circuits for M = 2 up to M = 10, natively executed with real-time classical control systems on IBM Quantum superconducting processors, known as dynamic circuits. We perform the cloning procedure on many different message states across the Bloch sphere, on seven IBM Quantum processors, optionally using the error suppression technique X–X sequence digital dynamical decoupling. Two circuit optimizations are utilized: one that removes ancilla qubits for M = 2,3 , and one that reduces the total number of gates in the circuit but still uses ancilla qubits. Parallel single-qubit tomography with maximum likelihood estimation density matrix reconstruction is used in order to compute the mixed-state density matrices of the clone qubits, and clone quality is measured using quantum fidelity. These results present one of the largest and most comprehensive noisy intermediate-scale quantum computer experimental analyses on (single qubit) quantum telecloning to date. The clone fidelity sharply decreases to 0.5 for M > 5 , but for M = 2 , we are able to achieve a mean clone fidelity of up to 0.79 using dynamical decoupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗