On 28 December 2003, the scientific community will celebrate the 100-th anniversary of John von Neumann's birthday. On this occasion, we are reminded of his achievements as outstanding mathematician and creator of Game Theory, but even more that he laid the very conceptional foundations of the digital computer. His concept had the fortune - contrary to Konrad Zuse's in Germany - that the transistor was invented in 1947, just when JvN wrote his famous reports on the digital computer, at Bell Labs thus giving rise to the extraordinary technological development of microelectronics pushed further by other inventions like photolithography and integrated circuits in the years to come. Since decades, the exponential growth of the power of microchips - every 18 months, the integration density of transistors on the chips is doubling -is steering the also exponential growth of computer power. The top computers have surpassed the teraflops level by far today targeting towards 100 teraflops or even petaflops. The computer has become ubiquitous, and protagonists of robotics and artificial intelligence are tempted to attribute to it omnipotent capabilities which will lead to autonomous "humanoids" (Moravec, Kurzweil) on the one hand and threatening horror scenarios on the other (Joy). The predictions of the semiconductor industry tell us that "Moore's Law" describing the exponential evolution in microelectronics might remain valid for other 10 to 15 years. Beyond Moore's Law, quantum effects will definitely end the orderly functioning of "classical" circuits. In 1982, Richard Feyn-man pointed out that certain quantum mechanical systems could not be simulated efficiently on a "classical" digital computer how powerful it may evolve. This led to speculations that computation in general could be done, in principle and even more efficiently, if a novel computer could make thorough use of quantum effects, thus providing a challenging option for parallel computing by exploiting the exponential speedup through quantum parallelism. Peter Shor's factorization algorithm of 1994 showed that the quantum computer is capable to solve NP-hard problems efficiently. Experimentalists work on different physical concepts to realize quantum computation; for instance, quantum dots, trapped ions, superconducting devices, and NMR technology have been shown to provide the principles and the technology to build quantum computers.
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