Observable-geometric phases and quantum computation
Abstract
This paper presents 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 quantum geometry of the observable space evolving according to the Heisenberg equation. They are indeed distinct from Berry's phase \cite{Berry1984, Simon1983} as the system evolves adiabatically. It is shown that the observable-geometric phases can be used to realize a universal set of quantum gates in quantum computation. This scheme leads to the same gates as the Abelian geometric gates of Zhu and Wang \cite{ZW2002,ZW2003}, but based on the quantum geometry of the observable space beyond the state space.
Cite
@article{arxiv.1710.03913,
title = {Observable-geometric phases and quantum computation},
author = {Zeqian Chen},
journal= {arXiv preprint arXiv:1710.03913},
year = {2020}
}
Comments
17 pages. References update, minor expanded