Design of gates for quantum computation: the NOT gate
  We offer an alternative to the conventional network formulation of quantum computing. We advance the analog approach to quantum logic gate/circuit construction. As an illustration, we consider the spatially extended NOT gate as the first step in the development of this approach. We derive an explicit form of the interaction Hamiltonian corresponding to this gate and analyze its properties. We also discuss general extensions to the case of certain time-dependent interactions which may be useful for practical realization of quantum logic gates. 
Dima Mozyrsky, Vladimir Privman, Steven P. Hotaling