Geometric phases for the observable and quantum computing
Zeqian Chen · arXiv (Cornell University) · 2017
This paper presents an alternative approach to geometric phase beyond wavefunctions. Precisely, we introduce the concept of geometric phase for an observable, which is defined as a sequence of phases associated with a complete set of eigenstates of the observable. The geometric phases of the observable are shown to be connected with the geometry of the quantal observable space described by the Heisenberg equation. As an application, we show that the geometric phases of the observable can be used to realize a universal set of quantum gates in quantum computation. This sheds a new light on the topology and geometry for the quantum system.