  Although universal continuous-variable quantum computation cannot be achieved
via linear optics (including squeezing), homodyne detection and feed-forward,
inclusion of ideal photon counting measurements overcomes this obstacle. These
measurements are sometimes described by arrays of beam splitters to distribute
the photons across several modes. We show that such a scheme cannot be used to
implement ideal photon counting and that such measurements necessarily involve
nonlinear evolution. However, this requirement of nonlinearity can be moved
"off-line," thereby permitting universal continuous-variable quantum
computation with linear optics.
