On the possibility of quantum computation based on photon exchange interactions

We examine several proposed schemes by Franson et al. for quantum logic gates based on non-local exchange interactions between two photons in a medium. In these schemes the presence of a {\em single} photon in a given mode is supposed to induce a large phase shift on another photon propagating in the same medium. We conclude that the schemes proposed so far are not able to produce the required conditional phase shift, even though the proposals contain many stimulating and intriguing ideas.