Projective holonomic quantum computation

Nonadiabatic holonomic quantum computing is a novel and promising framework for the implementation and efficient and robust execution of quantum gates based on purely geometric principles. However, the parallel transport condition that is central to nonadiabatic holonomic quantum computing has shortcomings. In this paper, we address some of these shortcomings and show that a projectivization of the standard gauge theory of nonadiabatic holonomic quantum computation eliminates them. In addition, we extend the isoholonomic inequality to projective gates and establish a minimum execution time-a quantum speed limit-for projective holonomic quantum gates.