This paper discusses the time-dependent quantum description of logical operations based on channelled atomic particles. We envisage particle traps in the form of grooves which steer atoms or ions, make them switch potential channels or interact with each other. Thus the presence of a particle can act as a control bit steering a target particle from one course into another. This phenomenon may be used to effect conditional logic operations. We discuss the quantum dynamics of the system using a simple analytic model whose proposed behaviour is verified by wave packet calculation.