Computation with quantum systems

Summary form only given. In 1994, Peter Shor showed that a computer based on the rules that govern quantum systems could efficiently factorize large numbers. Because of the implications of this idea on the security of data encryption, funding for the development of such a device increased significantly and sparked research for other applications of quantum information processing (QIP). Since then, the elementary logic operations and simple algorithms for such a device have been demonstrated, but building a useful quantum computer is an extremely daunting task due to the necessity of overcoming decoherence of the inherent large entangled quantum superposition states. Nevertheless, in the near term, the principles of QIP are finding applications in metrology (such as for atomic clocks) and may also provide a way to efficiently simulate other quantum systems of interest, a motivation that intrigued Richard Feynman in the early 1980´s. A number of physical systems are currently considered for building a quantum computer; this talk will focus on the use of registers of atomic ions, but connections to other possible physical implementations are rather direct.