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Quantum sampling algorithms, phase transitions, and computational complexity
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Numerical evidence against advantage with quantum fidelity kernels on classical data
Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential “flattening” of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter-tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data that lacks special structure.
Effects of noise on the overparametrization of quantum neural networks
Overparametrization is one of the most surprising and notorious phenomena in machine learning. Recently, there have been several efforts to study if, and how, quantum neural networks (QNNs) acting in the absence of hardware noise can be overparametrized. In particular, it has been proposed that a QNN can be defined as overparametrized if it has enough parameters to explore all available directions in state space. That is, if the rank of the quantum Fisher information matrix (QFIM) for the QNN's output state is saturated. Here, we explore how the presence of noise affects the overparametrization phenomenon. Our results show that noise can “turn on” previously zero eigenvalues of the QFIM. This enables the parametrized state to explore directions that were otherwise inaccessible, thus potentially turning an overparametrized QNN into an underparametrized one. For small noise levels, the QNN is quasioverparametrized, as large eigenvalues coexists with small ones. Then, we prove that as the magnitude of noise increases all the eigenvalues of the QFIM become exponentially suppressed, indicating that the state becomes insensitive to any change in the parameters. As such, there is a pull-and-tug effect where noise can enable new directions but also suppress the sensitivity to parameter updates. Finally, our results imply that current QNN capacity measures are ill-defined when hardware noise is present. Published by the American Physical Society 2024
ARMing the Edge: Designing Edge Computing–Capable Machine Learning Algorithms to Target ARM Doppler Lidar Processing
Abstract There is a need for long-term observations of cloud and precipitation fall speeds in validating and improving rainfall forecasts from climate models. To this end, the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility Southern Great Plains (SGP) site at Lamont, Oklahoma, hosts five ARM Doppler lidars that can measure cloud and aerosol properties. In particular, the ARM Doppler lidars record Doppler spectra that contain information about the fall speeds of cloud and precipitation particles. However, due to bandwidth and storage constraints, the Doppler spectra are not routinely stored. This calls for the automation of cloud and rain detection in ARM Doppler lidar data so that the spectral data in clouds can be selectively saved and further analyzed. During the ARMing the Edge field experiment, a Waggle node capable of performing machine learning applications in situ was deployed at the ARM SGP site for this purpose. In this paper, we develop and test four algorithms for the Waggle node to automatically classify ARM Doppler lidar data. We demonstrate that supervised learning using a ResNet50-based classifier will classify 97.6% of the clear-air images and 94.7% of cloudy images correctly, outperforming traditional peak detection methods. We also show that a convolutional autoencoder paired with k -means clustering identifies 10 clusters in the ARM Doppler lidar data. Three clusters correspond to mostly clear conditions with scattered high clouds, and seven others correspond to cloudy conditions with varying cloud-base heights.
How to Benchmark Quantum Computers with Any Quantum Algorithm.
Abstract not provided.
Simulation and analysis of optimal self-paced second order control systems
Local variation of dynamic programming algorithm and computer simulation of optimal second-order self-pace control systems
Algorithms for the numerical computation of the time responses of a system from its transfer function by state variable techniques
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Numerical algorithms for finite element computations on arrays of microprocessors
The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.
A new algorithm for tuning of computed radiances for HIRS2/MSU
Small biases of the order of 1 C exist in brightness temperatures computed for a number of atmospheric sounding channels using radiosonde reports of atmospheric temperature humidity profile compared to those of collocated HIRS2/MSU observations on TIROS N. These biases are attributed to errors in the computed atmospheric transmittances functions. Channel dependent empirical tuning coefficients were found such that the biases in the channel brightness temperatures are removed if the transmittances used to calculate these brightness temperatures are modified. Possible shortcomings of this method are that some of the bias errors may be due to instrumental calibration problems and that the part that is computational may not be of the form assumed in the equation used. Form of tuning was implemented in the calculation which has the potential of distinguishing between calibration and calculation errors and is also computationally faster and more easily vectorizable.
Numerical algorithms for finite element computations on concurrent processors
The work of several graduate students which relate to the NASA grant is briefly summarized. One student has worked on a detailed analysis of the so-called ijk forms of Gaussian elemination and Cholesky factorization on concurrent processors. Another student has worked on the vectorization of the incomplete Cholesky conjugate method on the CYBER 205. Two more students implemented various versions of Gaussian elimination and Cholesky factorization on the FLEX/32.
Parallel algorithms and archtectures for computational structural mechanics
The determination of the fundamental (lowest) natural vibration frequencies and associated mode shapes is a key step used to uncover and correct potential failures or problem areas in most complex structures. However, the computation time taken by finite element codes to evaluate these natural frequencies is significant, often the most computationally intensive part of structural analysis calculations. There is continuing need to reduce this computation time. This study addresses this need by developing methods for parallel computation.
A Simple Physical Optics Algorithm Perfect for Parallel Computing Architecture
A reflector antenna computer program based upon a simple discreet approximation of the radiation integral has proven to be extremely easy to adapt to the parallel computing architecture of the modest number of large-gain computing elements such as are used in the Intel iPSC and Touchstone Delta parallel machines.
Computationally Efficient Learning of Large Scale Dynamical Systems: A Koopman Theoretic Approach
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In general, the Koopman operator is obtained as a solution to a least-squares problem, and as such, the Koopman operator can be expressed as a closed-form solution that involves the computation of Moore-Penrose inverse of a matrix. For high dimensional systems and also if the size of the obtained data-set is large, the computation of the Moore-Penrose inverse becomes computationally challenging. In this paper, we provide an algorithm for computing the Koopman operator for high dimensional systems in a time-efficient manner. We further demonstrate the efficacy of the proposed approach on two different systems, namely a network of coupled oscillators (with state-space dimension up to 2500) and IEEE 68 bus system (with state-space dimension 204 and up to 24,000 time-points).
Fundamental Algorithmic Research for Quantum Computing (FAR-QC): Project Overview.
Abstract not provided.
Improved Diagnosis of Precipitation Type with LightGBM Machine Learning
Abstract Existing precipitation-type algorithms have difficulty discerning the occurrence of freezing rain and ice pellets. These inherent biases are not only problematic in operational forecasting but also complicate the development of model-based precipitation-type climatologies. To address these issues, this paper introduces a novel light gradient-boosting machine (LightGBM)-based machine learning precipitation-type algorithm that utilizes reanalysis and surface observations. By comparing it with the Bourgouin precipitation-type algorithm as a baseline, we demonstrate that our algorithm improves the critical success index (CSI) for all examined precipitation types. Moreover, when compared with the precipitation-type diagnosis in reanalysis, our algorithm exhibits increased F1 scores for snow, freezing rain, and ice pellets. Subsequently, we utilize the algorithm to compute a freezing-rain climatology over the eastern United States. The resulting climatology pattern aligns well with observations; however, a significant mean bias is observed. We interpret this bias to be influenced by both the algorithm itself and assumptions regarding precipitation processes, which include biases associated with freezing drizzle, precipitation occurrence, and regional synoptic weather patterns. To mitigate the overall bias, we propose increasing the precipitation cutoff from 0.04 to 0.25 mm h −1 , as it better reflects the precision of precipitation observations. This adjustment yields a substantial reduction in the overall bias. Finally, given the strong performance of LightGBM in predicting mixed precipitation episodes, we anticipate that the algorithm can be effectively utilized in operational settings and for diagnosing precipitation types in climate model outputs. Significance Statement Freezing rain can have significant impacts on transportation and infrastructure, making accurate prediction of precipitation types crucial. In this study, we use a machine learning method known as LightGBM to predict precipitation types. We show that the new algorithm performs better than the existing methods for all precipitation types examined. Additionally, we compute a freezing-rain climatology over the eastern United States. Although the resulting climatology pattern corresponds well to observations, the algorithm overpredicts freezing-rain occurrence. We argue that this bias can be substantially reduced by increasing the precipitation cutoff from 0.04 to 0.25 mm h −1 . Overall, this work highlights the potential of the LightGBM algorithm for both weather forecasting and diagnosing precipitation types in climate models.
Improving reproducibility in synchrotron tomography using implementation-adapted filters
For reconstructing large tomographic datasets fast, filtered backprojection-type or Fourier-based algorithms are still the method of choice, as they have been for decades. These robust and computationally efficient algorithms have been integrated in a broad range of software packages. The continuous mathematical formulas used for image reconstruction in such algorithms are unambiguous. However, variations in discretization and interpolation result in quantitative differences between reconstructed images, and corresponding segmentations, obtained from different software. This hinders reproducibility of experimental results, making it difficult to ensure that results and conclusions from experiments can be reproduced at different facilities or using different software. In this paper, a way to reduce such differences by optimizing the filter used in analytical algorithms is proposed. These filters can be computed using a wrapper routine around a black-box implementation of a reconstruction algorithm, and lead to quantitatively similar reconstructions. Use cases for this approach are demonstrated by computing implementation-adapted filters for several open-source implementations and applying them to simulated phantoms and real-world data acquired at the synchrotron. Our contribution to a reproducible reconstruction step forms a building block towards a fully reproducible synchrotron tomography data processing pipeline.
Rectilinear partitioning of irregular data parallel computations
New mapping algorithms for domain oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns are described. Researchers consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network. Discussed here is an improved algorithm for finding the optimal partitioning in one dimension, new algorithms for partitioning in two dimensions, and optimal partitioning in three dimensions. The application of these algorithms to real problems are discussed.