  Universal quantum computation is usually associated with interaction among
two-level quantum subsystems, as this interaction is commonly viewed as a
necessity to achieve universal quantum computation. In this work, we show that,
contrary to this intuition, universal quantum computation can be achieved
without interaction among initially independent two-level quantum subsystems.
We call it counterfactual universal quantum computation. As special cases, we
show how to achieve counterfactual communication of quantum states,
counterfactual quantum swapping, and counterfactual quantum erasure codes. To
ease practical implementation, we analyze counterfactual universal quantum
computation with realistic devices, including the effects of finite execution
time, photon loss, and atom missing. Besides the theoretical interest of
illustrating the mysterious and counterintuitive nature of quantum physics, our
work has practical applications to color imaging of ancient arts, upon which
light is forbidden to shine.
