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At least 343 records · Page 19

Time-dependent variational principle for mixed matrix product states in the thermodynamic limit

Here, we describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Land Surface Temperature Measurements form EOS MODIS Data

We have developed a physics-based land-surface temperature (LST) algorithm for simultaneously retrieving surface band-averaged emissivities and temperatures from day/night pairs of MODIS (Moderate Resolution Imaging Spectroradiometer) data in seven thermal infrared bands. The set of 14 nonlinear equations in the algorithm is solved with the statistical regression method and the least-squares fit method. This new LST algorithm was tested with simulated MODIS data for 80 sets of band-averaged emissivities calculated from published spectral data of terrestrial materials in wide ranges of atmospheric and surface temperature conditions. Comprehensive sensitivity and error analysis has been made to evaluate the performance of the new LST algorithm and its dependence on variations in surface emissivity and temperature, upon atmospheric conditions, as well as the noise-equivalent temperature difference (NE(Delta)T) and calibration accuracy specifications of the MODIS instrument. In cases with a systematic calibration error of 0.5%, the standard deviations of errors in retrieved surface daytime and nighttime temperatures fall between 0.4-0.5 K over a wide range of surface temperatures for mid-latitude summer conditions. The standard deviations of errors in retrieved emissivities in bands 31 and 32 (in the 10-12.5 micrometer IR spectral window region) are 0.009, and the maximum error in retrieved LST values falls between 2-3 K. Several issues related to the day/night LST algorithm (uncertainties in the day/night registration and in surface emissivity changes caused by dew occurrence, and the cloud cover) have been investigated. The LST algorithms have been validated with MODIS Airborne Simulator (MAS) dada and ground-based measurement data in two field campaigns conducted in Railroad Valley playa, NV in 1995 and 1996. The MODIS LST version 1 software has been delivered.

Wan, Zhengming↗

Observability and Estimation of Distributed Space Systems via Local Information-Exchange Networks

Spacecraft formation flying involves the coordination of states among multiple spacecraft through relative sensing, inter-spacecraft communication, and control. Most existing formation-flying estimation algorithms can only be supported via highly centralized, all-to-all, static relative sensing. New algorithms are proposed that are scalable, modular, and robust to variations in the topology and link characteristics of the formation exchange network. These distributed algorithms rely on a local information exchange network, relaxing the assumptions on existing algorithms. Distributed space systems rely on a signal transmission network among multiple spacecraft for their operation. Control and coordination among multiple spacecraft in a formation is facilitated via a network of relative sensing and interspacecraft communications. Guidance, navigation, and control rely on the sensing network. This network becomes more complex the more spacecraft are added, or as mission requirements become more complex. The observability of a formation state was observed by a set of local observations from a particular node in the formation. Formation observability can be parameterized in terms of the matrices appearing in the formation dynamics and observation matrices. An agreement protocol was used as a mechanism for observing formation states from local measurements. An agreement protocol is essentially an unforced dynamic system whose trajectory is governed by the interconnection geometry and initial condition of each node, with a goal of reaching a common value of interest. The observability of the interconnected system depends on the geometry of the network, as well as the position of the observer relative to the topology. For the first time, critical GN&C (guidance, navigation, and control estimation) subsystems are synthesized by bringing the contribution of the spacecraft information-exchange network to the forefront of algorithmic analysis and design. The result is a formation estimation algorithm that is modular and robust to variations in the topology and link properties of the underlying formation network.

Fathpour, Nanaz↗

Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers

Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number n of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size 2 n − 2 can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.

Shkolnikov, V. O.↗

Development of Global Operational Snow Analysis at the US Air Force 557th Weather Wing

The outdated SNODEP snow depth retrieval algorithm is replaced by the Foster et al. (1997; 2005) approach, which considers the effects of variations in forest cover. The simple blending algorithm (IDW) is replaced by the Bratseth scheme, a successive correction algorithm that converges to the solution provided by Optimal Interpolation (OI). Outdated quality control datasets are updated and quality control algorithms are reorganized to ensure the performance of the snow analysis. The spatial resolution of snow and ice estimates are increased from 25-km to 10-km.USAF-SI are fully integrated into the global operational land analysis configuration at the USAF 557th WW.

Yoon, Yeosang↗

Detect and correct bias in multi-site neuroimaging datasets

The desire to train complex machine learning algorithms and to increase the statistical power in association studies drives neuroimaging research to use ever-larger datasets. The most obvious way to increase sample size is by pooling scans from independent studies. However, simple pooling is often ill-advised as selection, measurement, and confounding biases may creep in and yield spurious correlations. In this work, we combine 35,320 magnetic resonance images of the brain from 17 studies to examine bias in neuroimaging. In the first experiment, Name That Dataset, we provide empirical evidence for the presence of bias by showing that scans can be correctly assigned to their respective dataset with 71.5% accuracy. Given such evidence, we take a closer look at confounding bias, which is often viewed as the main shortcoming in observational studies. In practice, we neither know all potential confounders nor do we have data on them. Hence, we model confounders as unknown, latent variables. Kolmogorov complexity is then used to decide whether the confounded or the causal model provides the simplest factorization of the graphical model. Finally, we present methods for dataset harmonization and study their ability to remove bias in imaging features. In particular, we propose an extension of the recently introduced ComBat algorithm to control for global variation across image features, inspired by adjusting for unknown population stratification in genetics. Overall, our results demonstrate that harmonization can reduce dataset-specific information in image features. Further, confounding bias can be reduced and even turned into a causal relationship. However, harmonization also requires caution as it can easily remove relevant subject-specific information. Code is available at https://github.com/ai-med/Dataset-Bias.

42 ENGINEERING↗

Long-time simulations for fixed input states on quantum hardware

Publicly accessible quantum computers open the exciting possibility of experimental dynamical quantum simulations. While rapidly improving, current devices have short coherence times, restricting the viable circuit depth. Despite these limitations, we demonstrate long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on Rigetti and IBM quantum computers, maintaining a fidelity over 0.9 for 150 times longer than is possible using the iterated Trotter method. Our simulations use an algorithm we call fixed state Variational Fast Forwarding (fsVFF). Recent work has shown an approximate diagonalization of a short time evolution unitary allows a fixed-depth simulation. fsVFF substantially reduces the required resources by only diagonalizing the energy subspace spanned by the initial state, rather than over the total Hilbert space. We further demonstrate the viability of fsVFF through large numerical simulations, and provide an analysis of the noise resilience and scaling of simulation errors.

97 MATHEMATICS AND COMPUTING↗

Ab initio molecular dynamics on quantum computers

Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann-Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H-2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum Computer-Aided Design: Digital Quantum Simulation of Quantum Processors

With the increasing size of quantum processors, submodules that constitute the processor hardware will become too large to accurately simulate on a classical computer. Therefore, one would soon have to fabricate and test each new design primitive and parameter choice in time-consuming coordination between design, fabrication, and experimental validation. Here we show how one can design and test the performance of next-generation quantum hardware—by using existing quantum computers. Focusing on superconducting transmon processors as a prominent hardware platform, we compute the static and dynamic properties of individual and coupled transmons. We show how the energy spectra of transmons can be obtained by variational hybrid quantum-classical algorithms that are well suited for near-term noisy quantum computers. In addition, single- and two-qubit gate simulations are demonstrated via Suzuki-Trotter decomposition. Our methods pave a promising way towards designing candidate quantum processors when the demands of calculating submodule properties exceed the capabilities of classical computing resources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Extracting off-diagonal order from diagonal basis measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multiscale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. Published by the American Physical Society 2024

1-dimensional systems↗

Optimum structural design with plate bending elements - A survey

A survey is presented of recently published papers in the field of optimum structural design of plates, largely with respect to the minimum-weight design of plates subject to such constraints as fundamental frequency maximization. It is shown that, due to the availability of powerful computers, the trend in optimum plate design is away from methods tailored to specific geometry and loads and toward methods that can be easily programmed for any kind of plate, such as finite element methods. A corresponding shift is seen in optimization from variational techniques to numerical optimization algorithms. Among the topics covered are fully stressed design and optimality criteria, mathematical programming, smooth and ribbed designs, design against plastic collapse, buckling constraints, and vibration constraints.

Haftka, R. T.↗

Precipitating electron energy flux and auroral zone conductances - An empirical model

Data from the low energy electron (LEE) experiments on the Atmosphere Explorer C and D satellites have been used to determine the average global distribution of the energy flux of precipitating auroral electrons and their average energy for different levels of geomagnetic activity. Measurements from the Atmosphere Explorer unified abstract file (15-s resolution) have been binned according to invariant latitude (in the range 50-90 deg), magnetic local time, and geomagnetic activity as measured by the Kp and auroral electrojet (AE) indices, separately. Bin-averaged values of precipitating energy flux and average energy have been calculated, and a smoothing algorithm used to reduce stochastic variations in the raw data. The results indicate that, for the parameters studied, the AE inces does a superior job of ordering the data with regard to geomagnetic activity. The global distribution of the auroral enhancement porition of the Pedersen and Hall conductances were inferred from the data by means of an empirical fit to detailed energy deposition calculations.

Spiro, R. W.↗

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Bailey, David H.↗

Measurement of a zonal wind profile on Titan by Doppler tracking of the Cassini entry probe

A program, called the Cassini mission, intended to study the Saturn system by utilizing a Saturn orbiter and a probe descending to the surface of Titan, is discussed. Winds are expected to cause perturbations to the probe local horizontal velocity, resulting in an anomalous drift in the probe location and a shift in the frequency of the probe telemetry, due to the Doppler effect. By using an iterative algorithm, in which the time variation of the probe telemetry frequency is monitored throughout the descent, and the probe trajectory is updated to reflect the effect of wind on the probe location, a highly accurate relative wind profile can be recovered. By adding a single wind velocity, measured by independent means, an absolute wind profile can be obtained. However, the accuracy of the zonal winds recovery is limited by errors in trajectory, and frequency.

Atkinson, D. H.↗

Measurement of subresolution terrain displacements using SPOT panchromatic imagery

It is shown that satellite-derived imagery can be used to measure subresolution horizontal terrain displacements associated with present-day earthquakes, sand dune migration, glacial motion, coastal sediment transport, and pre-eruptive volcanic processes. This use of these data allows the detection of change and the determination of rates of many environmental processes worldwide. The premise of the method is that areally extensive, subresolution spatial differences in ground patterns between images acquired at different times can be accurately measured to high precision and can be distinguished from systematic image differences, such as those due to sensing-system attitude variations. Thus far, a preliminary algorithm has been tested that shows that the approach is reasonable.

Crippen, Robert E.↗

New Global Electron Density Observations from GPS-RO in the D- and E-Region Ionosphere

A novel retrieval technique is developed for electron density (N(sub e)) in the D- and E-region (80-120 km) using the high-quality 50-Hz GPS radio occultation (GPS-RO) phase measurements. The new algorithm assumes a slow, linear variation in the F-region background when the GPS-RO passes through the D- and E-region, and extracts the N(sub e) profiles at 80-130 km from the phase advance signal caused by N(sub e). Unlike the conventional Abel function, the new approach produces a sharp N(sub e) weighting function in the lower ionosphere, and the N(sub e) retrievals are in good agreement with the IRI (International Reference Ionosphere) model in terms of monthly maps, zonal means and diurnal variations. The daytime GPS-RO N(sub e) profiles can be well characterized by the alpha-Chapman function of three parameters (N(sub mE), h(sub mE) and H), showing that the bottom of E-region is deepening and sharpening towards the summer pole. At high latitudes the monthly GPS-RO N(sub e) maps at 80-120 km reveal clear enhancement in the auroral zones, more prominent at night, as a result of energetic electron precipitation (EEP) from the outer radiation belt. The D-/E-region auroral N(sub e) is strongly correlated with K(sub p) on a daily basis. The new N(sub e) data allow further comprehensive analyses of the sporadic E (E(sub s)) phenomena in connection with the background N(sub e) in the E-region. The layered (2-10 km) and fluctuated (less than 2 km) E(sub s) components, namely N(sub e_Layer) than N(sub e_Pert), are extracted with respect to the background N( sub e_Region) on a profile-by-profile basis. The N(sub e_Layer) component has a strong but highly-refined peak at approximately 105 km, with an amplitude smaller than N(sub e_Region) approximately by an order of magnitude. The N(sub e_Pert) component, which was studied extensively in the past, is approximately 2 orders of magnitude weaker than N(sub e_Layer). Both N(sub e_Layer) and N(sub e_Pert) are subject to significant diurnal and semidiurnal variations, showing downward progression with local time in amplitude. The 11-year solar cycle dominates the N(sub e) interannual variations, showing larger N(sub e_Region) and N(sub e_Layer) but smaller N(sub e_Pert) amplitudes in the solar maximum years. Enhanced Ne profiles are often observed in the polar winter, showing good correlation with solar proton events (SPEs) and geomagnetic activity. The new methodology offers great potential for retrieving low N(sub e) in the D-region, where radio propagation and communication blackouts can occur due to enhanced ionization. For space weather applications it is recommended for GPSRO operations to raise the top of high-rate data acquisition to approximately 140 km in the future.

GSP-R↗

Stochastic Virtual Battery Modeling of Uncertain Electrical Loads using Variational Autoencoder

Effective utilization of flexible loads for grid services, while satisfying end-user preferences and constraints, requires an accurate estimation of the aggregated predictive flexibility offered by the electrical loads. Recently, there have been efforts to quantify the predictive flexibility of thermostatic loads (e.g. residential air-conditioners, electric water-heaters) using the notion of virtual battery (VB), whose state evolution is governed by a first order dynamics including self-dissipation rate, and power and energy capacities. Identifying the VB model parameters for a collection of thermostatic loads, however, is challenging primarily due to uncertainties and lack of information regarding the end-user behavior, underlying device models and parameters. In this paper, we propose a \textit{variational autoencoder}-based deep learning algorithm to identify the parameters of the VB model. Using available sensors and meters data, the proposed algorithm generates not only point estimates of the VB parameters, but also confidence intervals around those values. Effectiveness of the proposed frameworks is demonstrated on a collection of electric water-heater loads, whose operation is driven by uncertain water usage profiles.

virtual battery, deep learning algorithms↗