On the possibility of quantum computation based on photon exchange interactions

We examine several proposed schemes by Franson et al. for quantum logic gat es based on non-local exchange interactions between two photons in a medium . In these schemes the presence of a single photon in a given mode is suppo sed 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 produ ce the required conditional phase shift, even though the proposals contain many stimulating and intriguing ideas.