  We construct a unified operator framework for quantum holonomies generated
from bosonic systems. For a system whose Hamiltonian is bilinear in the
creation and annihilation operators, we find a holonomy group determined only
by a set of selected orthonormal modes obeying a stronger version of the
adiabatic theorem. This photon-number independent description offers deeper
insight as well as a computational advantage when compared to the standard
formalism on geometric phases. In particular, a strong analogy between quantum
holonomies and linear optical networks can be drawn. This relation provides an
explicit recipe how any linear optical quantum computation can be made
geometrically robust in terms of adiabatic or nonadiabatic geometric phases.
