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Giant planets such as Jupiter and Saturn in our solar system have attracted a renewed lively interest since the discovery of extrasolar planets. The study of planetary formation processes, of the internal structure and evolution of giant planets are challenging problems in this context. Furthermore, the interior of giant planets is a perfect laboratory to study matter at high energy densities. For instance, pressure and temperature inside Jupiter rise from almost normal conditions in the outer atmosphere up to about 20 000 K and 40 Mbar in the central core region. We have performed ab initio quantum molecular dynamics simulations to calculate highly accurate equation of state data for the most abundant planetary materials hydrogen, helium, and water in this warm dense matter region. The influence of this new data on the internal structure of Jupiter and other giant planets is investigated and compared with state-of-the- art results within a three-layer model which is consistent with astrophysical observations for, e.g., the mass, the radius, and the gravitational moments. We study also interesting high- pressure effects such as the nonmetal-to-metal transition in hydrogen and helium, the demixing of hydrogen and helium as well as the exotic phase diagram of high-pressure water with a possible superionic phase (proton conductor). Our new ab initio results for the thermophysical properties of warm dense matter will improve our present understanding of the internal structure of hydrogen-rich planets.