24 August 2004 Quantum computational geometry
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The prospects for practical quantum computing have improved significantly over the past few years, and there is an increasing motivation for developing quantum algorithms to address problems that are presently impractical to solve using classical computing. In previous work we have indentified such problems in the areas of computer graphics applications, and we have derived quantum-based solutions. In this paper we examine quantum-based solutions to problems arising in the area of computational geometry. These types of problems are important in a variety of scientific, industrial and military applications such as large scale multi-object simulation, virtual reality systems, and multi-target tracking. In particular, we present quantum algorithms for multidimensional searches, convex hull construction, and collision detection.
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Marco Lanzagorta, Marco Lanzagorta, Jeffrey K. Uhlmann, Jeffrey K. Uhlmann, } "Quantum computational geometry", Proc. SPIE 5436, Quantum Information and Computation II, (24 August 2004); doi: 10.1117/12.541624; https://doi.org/10.1117/12.541624

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