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Results for “tensor network theory”

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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Geometrical approach to neural net control of movements and posture

In one approach to modeling brain function, sensorimotor integration is described as geometrical mapping among coordinates of non-orthogonal frames that are intrinsic to the system; in such a case sensors represent (covariant) afferents and motor effectors represent (contravariant) motor efferents. The neuronal networks that perform such a function are viewed as general tensor transformations among different expressions and metric tensors determining the geometry of neural functional spaces. Although the non-orthogonality of a coordinate system does not impose a specific geometry on the space, this "Tensor Network Theory of brain function" allows for the possibility that the geometry is non-Euclidean. It is suggested that investigation of the non-Euclidean nature of the geometry is the key to understanding brain function and to interpreting neuronal network function. This paper outlines three contemporary applications of such a theoretical modeling approach. The first is the analysis and interpretation of multi-electrode recordings. The internal geometries of neural networks controlling external behavior of the skeletomuscle system is experimentally determinable using such multi-unit recordings. The second application of this geometrical approach to brain theory is modeling the control of posture and movement. A preliminary simulation study has been conducted with the aim of understanding the control of balance in a standing human. The model appears to unify postural control strategies that have previously been considered to be independent of each other. Third, this paper emphasizes the importance of the geometrical approach for the design and fabrication of neurocomputers that could be used in functional neuromuscular stimulation (FNS) for replacing lost motor control.

Review↗
NASA NTRS1980

Theory of electromagnetic transmission structures. I - Relativistic foundation and network formalisms

A new theorem on a class of four-dimensional skew-symmetric tensors is demonstrated. Coupled with the relativistic covariant form of Maxwell's equations, this theorem consolidates the classifications of guided waves by combining the three types - TE, TM, TEM - under a uniform condition applied to the generating four-potential which is Lorentz invariant. Each type corresponds to a potential of which a pair of the four components vanishes in a particular frame. Through appropriate normalization conditions, the resulting time-domain equations for the field amplitudes are readily reduced to modified telegraphist equations, which in turn lead to distributed network representations for each of the three types. The ambiguity of distributed network formalisms in general is elucidated and the concept of network parameter densities such as traditionally employed in TEM transmission line theory is questioned.

Gabriel, G. J.↗
NASA NTRSDate not supplied

Ab initio ground states of strongly-correlated materials on quantum computers

The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving accurate many-body Hamiltonians including strong correlations, representing a subspace of interest of a material, using density functional theory calculations as a starting point. However, the solution of these material-specific models can scale exponentially on classical computers, constituting a challenge. Here we propose that utilizing quantum computers for obtaining the properties of downfolded Hamiltonians yields an accurate description of the ground state properties of strongly-correlated systems, while circumventing the exponential scaling problem. We benchmark the solution of Hubbard-like models obtained through downfolding by utilizing a classical tensor network implementation of variational quantum eigensolvers (VQE), and we reveal a strategy for driving the optimization through a hybrid minimization of the energy and maximization of the overlap with an approximate solution obtained through low-cost computational methods. This results in a reduction of the energy error by orders of magnitude compared to conventional VQE approaches, and allows us to reproduce long-range correlations for the first time. We demonstrate our first-principles approach for diverse strongly-correlated materials, correctly predicting the antiferromagnetic state of one-dimensional cuprate Ca 2 CuO 3 , the excitonic ground state of monolayer WTe2, and the charge-ordered state of correlated metal SrVO 3 . Our efficient computational implementation allows us to simulate large systems with up to 54 qubits and encompassing up to four correlated bands, which is indicative of the complexity that our framework can address.

Antonios M Alvertis↗