  Linear optical networks are devices that turn classical incident modes by a
linear transformation into outgoing ones. In general, the quantum version of
such transformations may mix annihilation and creation operators. We derive a
simple formula for the effective Hamiltonian of a general linear quantum
network, if such a Hamiltonian exists. Otherwise we show how the scattering
matrix of the network is decomposed into a product of three matrices that can
be generated by Hamiltonians.
