Geometric nature in adiabatic evolution of dark eigenstates

Abstract

In a recent Letter [Phys. Rev. Lett. {\bf 95}, 080502 (2005)], an interesting scheme was proposed to implement a type of conditional quantum phase gates with built-in fault-tolerant feature via adiabatic evolution of dark eigenstates. In this comment we elaborate the geometric nature of the gate scheme and clarify that it still belongs to a class of conventional geometric quantum computation.