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QCLAB is an object-oriented MATLAB package for creating and representing quantum circuits. QCLAB can be used for rapid prototyping and testing of quantum algorithms, and allows for fast algorithm development and discovery. QCLAB provides I/O through openQASM making it compatible with quantum hardware. It is uniquely targeted at MATLAB users who so far didn't have any native MATLAB options for developing quantum computing applications.
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This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. Furthermore, the results demonstrate the advantage of the algorithm in finding high-precision solutions.
Standard computed tomography (CT) reconstruction algorithms such as filtered back projection (FBP) and Feldkamp-Davis-Kress (FDK) require many views for producing high-quality reconstructions, which can slow image acquisition and increase cost in non-destructive evaluation (NDE) applications. Over the past 20 years, a variety of methods have been developed for computing high-quality CT reconstructions from sparse views. However, the problem of how to select the best views for CT reconstruction remains open. In this paper, we present a novel view covariance loss (VCL) function that measures the joint information of a set of views by approximating the normalized mean squared error (NMSE) of the reconstruction. We present fast algorithms for computing the VCL along with an algorithm for selecting a subset of views that approximately minimizes its value. Our experiments on simulated and measured data indicate that for a fixed number of views our proposed view covariance loss selection (VCLS) algorithm results in reconstructions with lower NRMSE, fewer artifacts, and greater accuracy than current alternative approaches.
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.
Cryo-electron tomography (cryo-ET) enables structural characterization of biomolecules under near-native conditions. Existing approaches for interpreting the resulting three-dimensional volumes are computationally expensive and have difficulty interpreting density associated with small proteins/complexes. To explore alternate approaches for identifying proteins in cryo-ET data we pursued a Graph Network and topologically invariant approach. Here, we report on a fast algorithm that classifies particles by searching for nuances of evolutionarily conversed motifs and the geometrical characteristics of protein structure. GRIP-Tomo 2.0 is a machine-learning pipeline that extracts interpretable topological features of protein structures within noisy experimental backgrounds. Compared to version 1.0, the new pipeline includes three upgrades that significantly improve performance including synthetic tomogram generation simulating realistic noise, graph-based persistent feature extraction as protein fingerprints, and high-performance computing acceleration. GRIP-Tomo 2.0 achieves over 90% accuracy in classifying between proteins and noise using both real and synthetic datasets which represents a foundational step toward advancing cryo-ET workflows and empowering automated visual proteomics.
In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.
Standard MCNP particle tracking takes place along straight-line trajectories from interaction point to interaction point. There is a feature within MCNP that is planned for deprecation that provides surface boundary conditions for approximating gravity for planetary cases, but this feature is not applicable to a cold neutron beam. A new extension has been developed to track particles along parabolic trajectories with a constant acceleration. MCNP contains 1st and 2nd-order surfaces as well as a special case of 4th-order surfaces for simple tori, and the intersection of parabolic trajectories with these surfaces becomes 2nd, 4th, and 8th-order equations in time, respectively. Solving these equations utilizes a fast algorithm for finding the roots of polynomials. Finally, the theory, MCNP input card, and examples of using this new feature will be discussed.
One of the challenges of high granularity calorimeters, such as that to be built to cover the endcap region in the CMS Phase-2 Upgrade for HL-LHC, is that the large number of channels causes a surge in the computing load when clustering numerous digitized energy deposits (hits) in the reconstruction stage. In this article, we propose a fast and fully parallelizable density-based clustering algorithm, optimized for high-occupancy scenarios, where the number of clusters is much larger than the average number of hits in a cluster. The algorithm uses a grid spatial index for fast querying of neighbors and its timing scales linearly with the number of hits within the range considered. We also show a comparison of the performance on CPU and GPU implementations, demonstrating the power of algorithmic parallelization in the coming era of heterogeneous computing in high-energy physics.
The proposed project aimed to develop faster algorithms for FHE and zk-SNARKs processing. The research team previously developed a fast Number Theoretic Transform (NTT) and other fast arithmetic algorithms. The project team explored using these fast algorithms to enable FHE and zk-SNARKSs acceleration, with specific attention to how the algorithms would need to be integrated into specific FHE and zk-SNARKs software packages to become useful. Existing FHE/zk-SNARKs software packages have been written for CPUs, however this project’s technology targeted FPGAs and GPUs. The team explored how to modify existing CPU software to support FPGAs/GPUs as well as ways they could implement entirely new software stacks that run purely on FPGAs/GPUs.
Machine learning methods have shown initial promise in constitutive modeling for single crystals or homogenized polycrystals, delivering notable computational efficiency. However, existing machine learning-based constitutive models often lack generalizability, limiting their application across diverse boundary value problems. This study introduces a thermodynamics-informed artificial neural network model to accelerate rate-tangent crystal plasticity fast Fourier transform simulations for cross-scale deformation behaviors of polycrystals under complex loading. Our model integrates microstructural variability and local interactions effectively. To address local effects in each grain, we employ K-means clustering to group Gauss points within the microstructure into clusters assumed to be in similar mechanical states. This approach, based on self-clustering analysis, extends model scope from macroscopic stress response to the granular level, capturing mechanical responses and orientation evolution across grains. This reduces the number of nonlinear problems to solve, with cluster responses propagated throughout each group. The thermodynamics-based artificial neural network-extracted features are further processed using local material state clusters to account for history-dependent deformation and evolving microstructures. Additionally, representative volume element simulations with rate-tangent crystal plasticity fast Fourier transform provide reliable datasets for model training. The proposed model demonstrates high efficiency, accuracy, self-consistency, and enhanced generalizability in predicting strain–stress responses and orientation evolution at both individual grain and aggregate scales under complex loading conditions, such as biaxial tension and arbitrary loading scenarios.
Neutrino oscillation experiments will be entering the precision era in the next decade with the advent of high statistics experiments like DUNE, HK, and JUNO. Correctly estimating the confidence intervals from data for the oscillation parameters requires very large Monte Carlo datasets involving calculating the oscillation probabilities in matter many, many times. In this paper, we leverage past work to present a new, fast, precise technique for calculating neutrino oscillation probabilities in matter optimized for long-baseline neutrino oscillations in the Earth’s crust including both accelerator and reactor experiments. For ease of use by theorists and experimentalists, we provide fast ++ and codes . Published by the American Physical Society 2024
As a result of climate change, extreme weather events are occurring more frequently and with increasing impact. This trend poses a significant challenge for distribution utilities and system operators to ensure that there is uninterrupted power supply to critical loads in their networks; thus, the level of proactive preparation of the distribution system to be able to handle severe impacts of extreme weather events represents the system's resilience. One method that distribution system planners can use to prepare for future extreme events is to plan multiple microgrids which can use local generation as much as possible to supply critical loads. But partitioning an existing distribution system such that multiple feasible islands are planned and which are capable of supporting critical loads is still challenging for distribution systems - first, because of the size of the network graph partitioning problem and, second, because of the difficulty in properly formulating the desired attributes of such islands or microgrids. Therefore, this paper presents a genetic algorithm based approach that facilitates incorporating multiple objectives for grid partitioning by formulating two types of problems - node allocation and edge elimination - and it considers multiple topological and resilience-enhancing objectives. The performance of the proposed genetic algorithm-based approach is numerically evaluated on multiple test systems as well as on a real distribution feeder in Colorado, United States.
The integration of hybrid photovoltaic (PV) and energy storage system (ESS) based plants has become a promising way of solving the intermittency of PV plants and providing frequency support to the power grid. The multi-port autonomous reconfigurable solar power plant (MARS) can integrate the PV systems and ESSs to an ac grid and dc lines. The proposed isolated MARS incorporates an isolated converter that connects to the PV arrays and is based on the dual active bridge (DAB) converter. The high frequency switching in the DAB and the means to control the DAB converter using delays between switching signals lead to the need for a small timestep in simulations. Moreover, several hundreds of modules that include a DAB converter are present in the MARS. The small timestep and the presence of several hundreds of modules lead to a significant rise in the overall simulation time. To address this issue, simulation algorithms like numerical stiffness-based hybrid discretization and the hysteresis relaxation technique are applied to the switched system model of isolated MARS. Additionally, an event-driven interpolating method is introduced to help increase the minimum timestep to simulate the conventional DAB converter model while maintaining high accuracy in the simulation results. The developed model is validated by comparison with its reference model built in the PSCAD/EMTDC and MATLAB software environments using library components.
In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.