Simple digital quantum algorithm for symmetric first order linear hyperbolic systems

This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first order linear hyperbolic systems, thanks to the reservoir technique. The reservoir technique is a method designed to avoid artificial diffusion generated by first order finite volume methods approximating hyperbolic systems of conservation laws. For some class of hyperbolic systems, namely those with constant matrices in several dimensions, we show that the combination of i) the reservoir method and ii) the alternate direction iteration operator splitting approximation, allows for the derivation of algorithms only based on simple unitary transformations, thus perfectly suitable for an implementation on a quantum computer. The same approach can also be adapted to scalar one-dimensional systems with non-constant velocity by combining with a non-uniform mesh. The asymptotic computational complexity for the time evolution is determined and it is demonstrated that the quantum algorithm is more efficient than the classical version. However, in the quantum case, the solution is encoded in probability amplitudes of the quantum register. As a consequence, as with other similar quantum algorithms, a post-processing mechanism has to be used to obtain general properties of the solution because a direct reading cannot be performed as efficiently as the time evolution.Comment: 28 pages, 12 figures, major rewriting of the section describing the numerical method, simplified the presentation and notation, reorganized the sections, comments are welcome

Estimating mean dynamic topography in the tropical Pacific Ocean from gravity and altimetry satellites

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel W 1190 (59) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Estimating mean dynamic topography in the tropical Pacific Ocean from gravity and altimetry satellites

International audienceA new geoid model, combining the CHAMP satellite gravity data and an accurate altimetric mean sea surface, was used to investigate the 1993–1999 mean dynamic topography in the tropical Pacific Ocean. The mean dynamic topography, represented by a spherical harmonic expansion to degree 60 appear to be consistent with our knowledge of the tropical circulation, notably the South Equatorial Counter Current which is clearly visible in the western Pacific. This satellite solution, validated with in‐situ data, is independent from any climatology and has a resolution similar to other classical mean dynamic topographies. Altimetry combined with geodesy can thus provide an absolute sea level which will be useful for data assimilation and tropical oceanography