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At least 91 records · Page 5

Diabatic error and propagation of Majorana zero modes in interacting quantum dots systems

Motivated by recent experimental progress in realizing Majorana zero modes (MZMs) using quantum dot systems, we investigate the diabatic errors associated with the movement of those MZMs. The movement is achieved by tuning time-dependent gate potentials applied to individual quantum dots, effectively creating a moving potential wall. To probe the optimized movement of MZMs, we calculate the experimentally accessible time-dependent fidelity and local density-of-states using many-body time-dependent numerical methods. Furthermore, our analysis reveals that an optimal potential wall height is crucial to preserve the well-localized nature of the MZM during its movement. Moreover, we analyze diabatic errors in realistic quantum-dot systems, incorporating the effects of repulsive Coulomb interactions and disorder in both hopping and pairing terms. Additionally, we provide a comparative study of diabatic errors arising from the simultaneous versus sequential tuning of multiple gates during the MZMs movement. Finally, we estimate the timescale required for MZM transfer in a six-quantum-dot system, demonstrating that MZM movement is feasible and can be completed well within the qubit's operational lifetime in practical quantum-dot setups.

Density of states

A General Framework for Error-controlled Unstructured Scientific Data Compression

Data compression plays a key role in reducing storage and I/O costs. Traditional lossy methods primarily target data on rectilinear grids and cannot leverage the spatial coherence in unstructured mesh data, leading to suboptimal compression ratios. We present a multi-component, error-bounded compression framework designed to enhance the compression of floating-point unstructured mesh data, which is common in scientific applications. Our approach involves interpolating mesh data onto a rectilinear grid and then separately compressing the grid interpolation and the interpolation residuals. This method is general, independent of mesh types and typologies, and can be seamlessly integrated with existing lossy compressors for improved performance. We evaluated our framework across twelve variables from two synthetic datasets and two real-world simulation datasets. The results indicate that the multi-component framework consistently outperforms state-of-the-art lossy compressors on unstructured data, achieving, on average, a 2.3 − 3.5× improvement in compression ratios, with error bounds ranging from 1 × 10 the −6 to 1×10−2. We further investigate impact of hyperparameters, such as grid spacing and error allocation, to deliver optimal compression ratios in diverse datasets.

Gong, Qian

Implementation and (Inverse Modified) Error Analysis for Implicitly Templated ODE-Nets

We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform inverse modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. It is shown that training an ODE-net using an unrolled implicit scheme returns a close approximation of an inverse modified differential equation (IMDE). In addition, we establish a theoretical basis for hyperparameter selection when training such ODE-nets, whereas current strategies usually treat numerical integration of ODE-nets as a black box. We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss. This helps accelerate training while maintaining accuracy. Several numerical experiments are performed to demonstrate the advantages of the proposed algorithm compared to nonadaptive unrollings and validate the theoretical analysis. Here, we also note that this approach naturally allows for incorporating partially known physical terms in the equations, giving rise to what is termed “gray box” identification.

ODE-nets

QProR: An Efficient Framework for Quantity-of-Interest Based Progressive Retrieval with Guaranteed Error Control

Scientific applications generate an unprecedented volume of data, overwhelming the network and file systems’ bandwidth and posing challenges for efficient and scalable data retrieval and analysis. Progressive data compression offers a promising solution by enabling on-demand retrieval at reduced size. However, existing progressive methods either fail to bound the errors in essential quantities of interest (QoIs) derived from raw data or suffer from suboptimal retrieval efficiency. In this work, we propose QProR, an efficient QoI-based progressive framework that optimizes progressive retrieval for target QoIs. Our key contributions include: (1) a systematic framework that integrates error-controlled lossy compressors with bitplane encoding while decoupling the two processes for high flexibility and adaptability; (2) a novel weighted bitplane encoding method which incorperates QoI knowledge into data refactoring to enhance retrieval efficiency; (3) an optimized retrieval strategy that accounts for the varying impacts of different variables on multivariate QoIs; (4) comprehensive evaluations using six real-world datasets from multiple scientific applications and thorough comparisons against state of the arts. Experimental results demonstrate that QProR achieves up to 80.38% reduction in the retrieval size under the same requested QoI error tolerance, when compared with the best-performing existing methods. When transferring 384 GB of scientific data to remote sites, QProR delivers up to 1.68 × speedup in the end-to-end data transfer performance.

Li, Wenbo [University of Kentucky]

Improving the efficiency of learning-based error mitigation

Error mitigation will play an important role in practical applications of near-term noisy quantum computers. Current error mitigation methods typically concentrate on correction quality at the expense of frugality (as measured by the number of additional calls to quantum hardware). To fill the need for highly accurate, yet inexpensive techniques, we introduce an error mitigation scheme that builds on Clifford data regression (CDR). The scheme improves the frugality by carefully choosing the training data and exploiting the symmetries of the problem. We test our approach by correcting long range correlators of the ground state of XY Hamiltonian on IBM Toronto quantum computer. We find that our method is an order of magnitude cheaper while maintaining the same accuracy as the original CDR approach. The efficiency gain enables us to obtain a factor of 10 improvement on the unmitigated results with the total budget as small as 2 ⋅ 10 5 shots. Furthermore, we demonstrate orders of magnitude improvements in frugality for mitigation of energy of the LiH ground state simulated with IBM's Ourense-derived noise model.

97 MATHEMATICS AND COMPUTING

CV4Quantum: Reducing the Sampling Overhead in Probabilistic Error Cancellation Using Control Variates

Quasiprobabilistic decompositions (QPDs) play a key role in maximizing the utility of near-term quantum hardware. For example, Probabilistic Error Cancellation (PEC) (an error mitigation technique) and circuit cutting (which enables large quantum computations to be performed on quantum hardware with a limited number of qubits) both involve QPDs. Computations based on QPDs typically incur large sampling overheads that grow exponentially with the number of error-terms mitigated or number of circuit-cuts employed, limiting their practical feasibility. In this work, we adapt the control variates variance reduction technique from the statistics literature in order to reduce the sampling overhead in QPD-based computations. We demonstrate our method using simulation experiments that mimic a realistic PEC scenario. In our experiments, we observed a more than 50% reduction in the number of samples needed to achieve a given precision, in more than 50% of the PEC-based estimations performed in the study when using our approach. We discuss how future research on constructing good control variates can lead to even stronger sampling overhead reduction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

Error field predictability and consequences for ITER

Abstract ITER coil tolerances are re-evaluated using the modern understanding of coupling to least-stable plasma modes and an updated center-line-traced model of ITER’s coil windings. This reassessment finds the tolerances to be conservative through a statistical, linear study of n = 1 error fields (EFs) due to tilted, shifted misplacements and nominal windings of central solenoid and poloidal field coils within tolerance. We also show that a model-based correction scheme remains effective even when metrology quality is sub-optimal, and compare this to projected empirical correction schemes. We begin with an analysis of the necessity of error field correction (EFC) for daily operation in ITER using scalign laws for the EF penetration threshold. We then consider the predictability of EF dominant mode overlap across early planned ITER scenarios and, as measuring EFs in high power scenarios can pose risks to the device, the potential for extrapolation to the ITER Baseline Scenario (IBS). We find that carefully designing a scenario matching currents proportionally to those of the IBS is far more important than plasma shape or profiles in accurately measuring an optimal correction current set.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Quantum simulation of boson-related Hamiltonians: techniques, effective Hamiltonian construction, and error analysis

Elementary quantum mechanics proposes that a closed physical system consistently evolves in a reversible manner. However, control and readout necessitate the coupling of the quantum system to the external environment, subjecting it to relaxation and decoherence. Consequently, system-environment interactions are indispensable for simulating physically significant theories. A broad spectrum of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into optimized fermion algorithms for near-future quantum simulations. In particular, when a quantum system is surrounded by an external environment, its basic physics can usually be simplified to a spin or fermionic system interacting with bosonic modes. Nevertheless, troublesome factors such as the magnitude of the bosonic degrees of freedom typically complicate the direct quantum simulation of these interacting models, necessitating the consideration of a comprehensive plan. This strategy should specifically include a suitable fermion/boson-to-qubit mapping scheme to encode sufficiently large yet manageable bosonic modes, and a method for truncating and/or downfolding the Hamiltonian to the defined subspace for performing an approximate but highly accurate simulation, guided by rigorous error analysis. In this pedagogical tutorial review, we aim to provide such an exhaustive strategy, focusing on encoding and simulating certain bosonic-related model Hamiltonians, inclusive of their static properties and time evolutions. Specifically, we emphasize two aspects: (1) the discussion of recently developed quantum algorithms for these interacting models and the construction of effective Hamiltonians, and (2) a detailed analysis regarding a tightened error bound for truncating the bosonic modes for a class of fermion-boson interacting Hamiltonians.

bosonic Hamiltonian

FedCSpc: A Cross-Silo Federated Learning System With Error-Bounded Lossy Parameter Compression

Cross-Silo federated learning is widely used for scaling deep neural network (DNN) training over data silos from different locations worldwide while guaranteeing data privacy. Communication has been identified as the main bottleneck when training large-scale models due to large-volume model parameters and gradient transmission across public networks with limited bandwidth. Most previous works focus on gradient compression, while limited work tries to compress parameters that can not be ignored and extremely affect communication performance during the training. Here, to bridge this gap, we propose FedCSpc: an efficient cross-silo federated learning system with an XAI-driven adaptive parameter compression strategy for large-scale model training. Our work substantially differs from existing gradient compression techniques due to the distinct data features of gradient and parameter. The key contributions of this paper are fourfold. (1) Our designed FedCSpc proposes to compress the parameter during the training using the state-of-the-art error-bounded lossy compressor – SZ3. (2) We develop an adaptive compression error bound adjustment algorithm to guarantee the model accuracy effectively. (3) We exploit an efficient approach to utilize the idle CPU resources of clients to compress the parameters. (4) We perform a comprehensive evaluation with a wide range of models and benchmarks on a GPU cluster with 65 GPUs. Results show that FedCSpc can achieve the same model accuracy as FedAvg while reducing the data volume of parameters and gradients in communication by up to 7.39× and 288×, respectively. With 32 clients on a 4 Gb size model, FedCSpc significantly outperforms FedAvg in wall-clock time in the emulated WAN environment (at the bandwidth of 1 Gbps or lower without loss of generality).

SZ3

FedEFsz: Fair Cross-Silo Federated Learning System With Error-Bounded Lossy Compression

Cross-Silo federated learning systems have been identified as an efficient approach to scaling DNN training across geographically-distributed data silos to preserve the privacy of the training data. Communication efficiency and fairness are two major issues that need to be both satisfied when federated learning systems are deployed in practice. Simultaneously guaranteeing both of them, however, is exceptionally difficult because simply combining communication reduction and fairness optimization approaches often causes non-converged training or drastic accuracy degradation. Here, to bridge this gap, we propose FedEFsz. On the one hand, it integrates the state-of-the-art error-bounded lossy compressor SZ3 into cross-silo federated learning systems to significantly reduce communication traffic during the training. On the other hand, it achieves a high fairness (i.e., rather consistent model accuracy and performance across different clients) through a carefully designed heuristic algorithm that can tune the error-bound of SZ3 for different clients during the training. Extensive experimental results based on a GPU cluster with 65 GPU cards show that FedEFsz improves the fairness across different benchmarks by up to 60.88% and meanwhile reduces the communication traffic by up to 315×.

Cross-Silo Federated Learning Systems

Model Form Error Correction for a Black-Box Thermal Battery Heat Transfer Simulation

Thermal batteries are crucial for supplying power to high-consequence engineering applications such as rockets. Computational simulations have been developed to predict thermal battery behavior, but these simulations often suffer from modeling errors, including model form uncertainty. Addressing this uncertainty can be achieved by quantifying either the model discrepancy in the output or the model form error (MFE) in the governing equation. MFE is particularly valuable as it can be better extrapolated beyond observed outputs, which is essential for predictions involving changes in external system loading, system configuration and geometry, or output quantities. This paper employs a state estimation approach to estimate MFE using experimental data and then utilizes machine learning (ML) to model its relationship with state variables. A nonintrusive technique is used to estimate MFE in a black-box thermal battery heat transfer simulation. The trained machine learning model for MFE is then applied to correct simulation predictions under extrapolated initial conditions and battery configurations. In conclusion, the methodology's performance is evaluated using additional experimental data, demonstrating its effectiveness in improving prediction accuracy.

Batteries

Tough Errors are no Match (TEAM): Optimizing the Quantum Compiler for Noise Resilience

This project builds toward a comprehensive error-mitigating toolkit that makes quantum programming more robust and adaptive to the noisy, resource-limited nature of today’s quantum hardware. To that end, it integrates established error-mitigation methods — such as zero-noise extrapolation and dynamical decoupling — directly into compiler infrastructures. These techniques will be packaged as modules that can automatically adjust and combine based on performance analysis, enabling compilers to explore large design spaces and produce optimized, low-noise quantum programs with minimal manual intervention. In parallel, this project also explores new approaches to analog quantum programming or quantum simulation, and has developed the programming language SimuQ which treats quantum Hamiltonian evolution as the central object.

97 MATHEMATICS AND COMPUTING

Celestial Quantum Error Correction. Part II. From qudits to celestial CFT

A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable fluctuations on the CFT dual. The framework is physically motivated by embedding a chain of qudits in the so-called Klein spacetime and then taking a continuum 𝑁 → ∞ limit. At finite 𝑁 the qudit chain 1) enjoys a discrete version of celestial symmetries and 2) supports a Gottesman-Kitaev-Preskill (GKP) code. The limit results in hard states with quantized BMS hair in the celestial torus forming the logical subspace, robust under errors induced by soft radiation. Technically, the construction leverages the recently studied 𝑤 1+∞ hierarchy of soft currents and its realization from a sigma model in twistor space.

79 ASTRONOMY AND ASTROPHYSICS

Optimization of an Impedance-Matched Test Fixture with the Modal Projection Error

Across many industries and engineering disciplines, components and systems are designed and deployed into their operational environment of intended use. It is the desire of the design agency to be able to predict whether their component or system will function in its shock and vibration environments or if it will fail due to mechanical stresses. One method to determine if the component will survive the shock and vibration environments is to expose the component to the operational environment in a laboratory. One difficulty in executing a representative laboratory test is that the component may not have the same boundary condition in the laboratory as in the operational configuration. This paper examines the use of parameterized optimization to design the test fixture in order to better match the operational configuration. Several frequency and modal-based objective functions are examined for the optimization. The study shows that the Modal Projection Error objective function performs the best of the functions studied. The efficacy of the Modal Projection Error is demonstrated with respect to dynamic test fixture design on several analytical and experimental exemplars.

dynamic

Online randomized interpolative decomposition with a posteriori error estimator for temporal PDE data reduction

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. Here, to address these issues, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. A strategy to improve the accuracy of the reconstructed data gradient, when desired, within the ID framework is also presented. We provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.

Column subset selection

Techno-economic implications and cost of forecasting errors in solar PV power production using optimized deep learning models

Accurate solar Photovoltaic (PV) power forecasting is important for enhancing both the performance and economic feasibility of PV systems. This study evaluates several deep learning models, including Dense Neural Networks (DNN), Long Short-Term Memory (LSTM), Convolutional Neural Networks (CNN), and a hybrid LSTMCNN model, for predicting PV power production one day in advance. Prior to optimization, the models exhibited relatively high errors, with the best model (DNN) achieving a Root Mean Square Error (RMSE) of 31.13 kW and a coefficient of determination (R 2 ) of 62.15 %. After employing Bayesian optimization, the LSTM-CNN model demonstrated the best performance, with the RMSE reduced to 9.79 kW and R 2 improved to 97.62 %, showcasing significant enhancement in predictive accuracy. Here, the economic evaluation considered three cases: rewards for underestimation (0.08 USD/kWh), no rewards, and penalties for both over-and underestimation (120 % of the utility tariff). In the rewards scenario, the LSTM-CNN model reduced the Levelized Cost of Electricity (LCOE) by 4 %, while in the penalty scenario, a backup diesel generator would have increased the LCOE by 49 %. Additionally, the LSTM-CNN model minimized financial losses, achieving the lowest penalties and maximizing net cash flow compared to other models, demonstrating its overall technical and economic superiority.

Deep learning

Overview of oxygen opacity experiments at the National Ignition Facility and investigation of potential systematic errors

Experiments to measure oxygen opacity at stellar interior conditions have been performed at the National Ignition Facility in a Discovery Science campaign. These experiments utilize the Opacity-on-NIF platform with a sample comprised of O, Mg, and Si. The spectral data from the Opacity Spectrometer cover the 1000–2000 eV photon energy range showing bound-free continuum absorption from O and line absorption from Mg and Si. DANTE and the Gated X-ray Detector are employed to measure the sample plasma’s temperature and density, respectively. Initial data show lower transmission than expected by theoretical models, raising questions of whether potential background or data uniformity concerns could produce systematic errors in the inferred transmission. Here, we investigate three concerns thought to be important for the oxygen opacity data, including instrumental scattered background, sample self-emission non-uniformity, and backlight continuum non-uniformity. Additionally, we show the effect of a recently developed method to account for 2nd order crystal reflection. The total effect of these concerns on one experiment is found to be small compared to the observed difference between the inferred transmission and a model calculation at the inferred temperature and density. Thus, we conclude that these potential sources of systematic error cannot account for the observed difference, increasing the likelihood of a real effect due to the high temperature and density conditions. However, because this is only a single experiment, we cannot make a firm conclusion. More experiments measuring the opacity and necessary calibrations are needed to assess the reproducibility and uncertainty of this result.

79 ASTRONOMY AND ASTROPHYSICS

Leveraging interpolation models and error bounds for verifiable scientific machine learning

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. Here, in this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository.

97 MATHEMATICS AND COMPUTING