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.
As the year-to-year gains in speeds of classical computers continue to taper off, computational chemists are increasingly examining quantum computing as a possible route to achieve greater computational performance. Quantum computers, built upon the properties of superposition, interference, and entanglement of quantum bits, offer, in principle, the possibility to outperform classical computers for solving many important classes of problems. In the field of chemistry, quantum algorithm development offers promising propositions for solving classically intractable problems in areas such as electronic structure, chemical quantum dynamics, spectroscopy, and cheminformatics. However, physical implementations of quantum computers are still in their infancy and have yet to outperform classical computers for useful computations. Still, quantum software development for chemistry is a highly active area of research. In this perspective, we summarize recent progress in the areas of quantum computing algorithms, hardware, and software, and we describe the challenges that remain for useful implementations of quantum computing for chemical applications.