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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Upper and lower bounds determined for energy eigenvalues using Hamiltonian operators and projections on manifolds in Hilbert regions
Singular nonself-adjoint differential operator of second order eigenvalues
Eigenvalue problem for beams and rectangular plates with linearly varying in-plane and axial load
State variable approach for analysis of linear multivariable system with multiple eigenvalues
Upper and lower bounds for eigenvalues of vibrating beams and flat plates with varying axial load
Nonlinear system evaluation by observing eigenvalue motion
Mathematical procedure leading to better and simpler approximation expansion terms in eigenvalues problem of Ritz and Bubnov- Galerkin method
Nonhomogeneous heat-conduction equation transformation into discrete spectrum eigenvalue form
Quantum mechanical perturbation theory calculation of upper and lower bounds of energy eigenvalues using partitioning methods
Modification of Potter method of Gaussian elimination for solving eigenvalue problems of buckling and free vibrations of shells of revolution
Lower bound procedure in quantum mechanical energy equation eigenvalue problem by partitioning and bracketing Hilbert space
Parameter and domain dependence of eigenvalues of elliptic partial differential equations
Characterization of eigenvalues of singular nonself-adjoint differential operator of second order
Radio frequency interference (RFI) can corrupt passive remote sensing measurements taken with microwave radiometers. With the increasingly utilized spectrum and the push for larger bandwidth radiometers, the likelihood of RFI contamination has grown significantly. In this work, an eigenvalue-based algorithm is developed to detect the presence of RFI and provide estimates of RFI-free radiation levels. Simulated tests show that the proposed detector outperforms conventional kurtosis-based RFI detectors in the low-to-medium interference-to-noise-power-ratio (INR) regime under continuous wave (CW) and quadrature phase shift keying (QPSK) RFIs.
Radio frequency interference (RFI) can corrupt passive remote sensing measurements taken with microwave radiometers. With the increasingly utilized spectrum and the push for larger bandwidth radiometers, the likelihood of RFI contamination has grown significantly. In this work, an eigenvalue-based algorithm is developed to detect the presence of RFI and provide estimates of RFI-free radiation levels. Simulated tests show that the proposed detector outperforms conventional kurtosis-based RFI detectors in the low-to-medium interferece-to-noise-power-ratio (INR) regime under continuous wave (CW) and quadrature phase shift keying (QPSK) RFIs.
Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases, enabling the characterization of strongly correlated ground states with arbitrary spatial geometry. The energy is converged via a gradient-free generalized sweep algorithm based on quantum subspace diagonalization, with a potentially exponential speedup in the off-diagonal matrix element contractions upon translation into compact quantum circuits of linear depth in the number of qubits. Chemical accuracy is attained in numerical experiments for both a stretched water molecule and an octahedral arrangement of hydrogen atoms, achieving substantially better correlation energies compared to a unitary coupled-cluster benchmark, with orders of magnitude reductions in quantum resource estimates and a surprisingly high tolerance to shot noise. This proof-of-concept study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.
We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed with the fewest number of gates. We present the general theory of controlled gate networks and show that, under quite general conditions, it can significantly reduce the number of two-qubit gates needed to produce linear combinations of unitary operators. The first example we consider is a variational subspace calculation for a two-qubit system. The second example is estimating the eigenvalues of a two-qubit Hamiltonian via the rodeo algorithm (Choi et al. in Phys Rev Lett 127(4):040505, 2021. https://doi.org/10.1103/PhysRevLett.127.040505) using operators that we call controlled reversal gates. We use the Quantinuum H1-2 and IBM Perth devices to realize the quantum circuits. The third example is the application of controlled gate networks to the controlled time evolution of a free nucleon on a three-dimensional lattice. For all of the examples, we show very substantial reductions in the number of two-qubit gates required. Our work demonstrates that controlled gate networks are a useful tool for reducing gate complexity in quantum algorithms for quantum many-body problems such as those relevant to nuclear physics.
Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.