Coherent time evolution and boundary conditions of two-photon quantum walks

Multiphoton quantum walks in integrated optics comprise an attractive controlled quantum system, that can mimic less readily accessible quantum systems and exhibit behavior that cannot in general be accurately replicated by classical light without an exponential overhead in resources. The ability to observe the time evolution of such systems is important for characterizing multiparticle quantum dynamics - notably this includes the effects of boundary conditions for walks in spaces of finite size. Here we demonstrate the coherent evolution of quantum walks of two indistinguishable photons using planar arrays of 21 evanescently coupled waveguides fabricated in silicon oxynitride technology. We compare three time evolutions, that follow closely a model assuming unitary evolution, corresponding to three different lengths of the array - in each case we observe quantum interference features that violate classical predictions. The longest array includes reflecting boundary conditions.