It has been shown [Minsky and Papert, 1969] that, even though feed-forward
networks might contain a non-linearity, they must have at least two
layers of non-linear units if they are to be able to compute
non-linearly-separable functions, which can be as simple as the
function XOR (exclusive OR). Thus, for any reasonably powerful form
of quantum learning, it might be better to think of a quantum
beam/barrier/screen apparatus as implementing one unit in a layered
network of units. Any units in a layer beyond the input layer would
not have their input slits positions determined by the input sample
x directly, but rather by the outputs of the units in the previous
layer. In such a case, it would be typical to take the output of a
unit to be uni-dimensional, usually soft-thresholded.
This would differ substantially from standard feed-forward networks, in that each weight would modulate all inputs to a unit. In standard networks, each weight only modulates the input from one other unit. This has the result of making the derivative computation during learning a relatively local computation. Whether or not this difference can be avoided, or whether it would be disadvantageous if it could not, has yet to be worked out.