Observable-geometric phases and quantum computation

题目： Observable-geometric phases and quantum computation

报告人：陈泽乾（中国科学院武汉物理与数学研究所）

时间：2019年3月8日(星期五) 下午14:00-15：00

地点：工商楼200-9

摘要： In this talk, we will present an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of eigenstates of the observable. The observable-geometric phases are shown to be connected with the geometry of the observable space evolving according to the Heisenberg equation. It is shown that the observable-geometric phases can be used to realize a universal set of quantum gates in quantum computation. In particular, we show that there is a closed formula between the observable-geometric and topological phases, explicitly exhibiting the relationship of the local and global properties for a quantum system. This sheds a new light on the geometry and topology of a quantum system.