5,101 research outputs found
Asymptotically Optimal Quantum Circuits for d-level Systems
As a qubit is a two-level quantum system whose state space is spanned by |0>,
|1>, so a qudit is a d-level quantum system whose state space is spanned by
|0>,...,|d-1>. Quantum computation has stimulated much recent interest in
algorithms factoring unitary evolutions of an n-qubit state space into
component two-particle unitary evolutions. In the absence of symmetry, Shende,
Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit
unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa
(VMS) use the QR matrix factorization and Gray codes in an optimal order
construction involving two-particle evolutions. In this work, we note that
Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a
generic (symmetry-less) n-qudit evolution. However, the VMS result applied to
virtual-qubits only recovers optimal order in the case that d is a power of
two. We further construct a QR decomposition for d-multi-level quantum logics,
proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing
the complexity question for all d-level systems (d finite.) Gray codes are not
required, and the optimal Theta(d^{2n}) asymptotic also applies to gate
libraries where two-qudit interactions are restricted by a choice of certain
architectures.Comment: 18 pages, 5 figures (very detailed.) MatLab files for factoring qudit
unitary into gates in MATLAB directory of source arxiv format. v2: minor
change
The Implications of Galaxy Formation Models for the TeV Observations of Current Detectors
This paper represents a step toward constraining galaxy formation models via
TeV gamm a ray observations. We use semi-analytic models of galaxy formation to
predict a spectral distribution for the intergalactic infrared photon field,
which in turn yields information about the absorption of TeV gamma rays from
extra-galactic sources. By making predictions for integral flux observations at
>200 GeV for several known EGRE T sources, we directly compare our models with
current observational upper limits obtained by Whipple. In addition, our
predictions may offer a guide to the observing programs for the current
population of TeV gamma ray observatories.Comment: 6 pages, 11 figures, to appear in the proceedings of the 6th TeV
Workshop at Snowbird, U
Neural model of dopaminergic control of arm movements in Parkinson’s disease bradykinesia
Patients suffering from Parkinson’s disease display a number of
symptoms such a resting tremor, bradykinesia, etc. Bradykinesia is the hallmark
and most disabling symptom of Parkinson’s disease (PD). Herein, a basal
ganglia-cortico-spinal circuit for the control of voluntary arm movements in PD
bradykinesia is extended by incorporating DAergic innervation of cells in the
cortical and spinal components of the circuit. The resultant model simulates
successfully several of the main reported effects of DA depletion on neuronal,
electromyographic and movement parameters of PD bradykinesia
System analysis approach to deriving design criteria (loads) for Space Shuttle and its payloads. Volume 1: General statement of approach
Space shuttle, the most complex transportation system designed to date, illustrates the requirement for an analysis approach that considers all major disciplines simultaneously. Its unique cross coupling and high sensitivity to aerodynamic uncertainties and high performance requirements dictated a less conservative approach than those taken in programs. Analyses performed for the space shuttle and certain payloads, Space Telescope and Spacelab, are used a examples. These illustrate the requirements for system analysis approaches and criteria, including dynamic modeling requirements, test requirements control requirements and the resulting design verification approaches. A survey of the problem, potential approaches available as solutions, implications for future systems, and projected technology development areas are addressed
System analysis approach to deriving design criteria (Loads) for Space Shuttle and its payloads. Volume 2: Typical examples
The achievement of an optimized design from the system standpoint under the low cost, high risk constraints of the present day environment was analyzed. Space Shuttle illustrates the requirement for an analysis approach that considers all major disciplines (coupling between structures control, propulsion, thermal, aeroelastic, and performance), simultaneously. The Space Shuttle and certain payloads, Space Telescope and Spacelab, are examined. The requirements for system analysis approaches and criteria, including dynamic modeling requirements, test requirements, control requirements, and the resulting design verification approaches are illustrated. A survey of the problem, potential approaches available as solutions, implications for future systems, and projected technology development areas are addressed
Spatially embedded random networks
Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples
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