Indexed on: 21 Dec '15Published on: 21 Dec '15Published in: Quantum Physics
Geometric quantum computation is the idea that geometric phases can be used to perform quantum computation. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, geometric quantum computation can as well be realized at high-speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we examine some conceptual issues that naturally arise in the realizations of geometric gates. First, we examine the role played by dynamical phases in certain realizations of geometric quantum computation. Secondly, we delineate the relation between Abelian and non-Abelian geometric phase gates and find an explicit physical example where the two types of gates coincide. Finally, we identify similarities and differencies between adiabatic and nonadiabatic realizations of quantum computation based upon non-Abelian geometric phases.