Geometrically robust linear optics from non-Abelian geometric phases

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 of how any linear optical quantum computation can be made geometrically robust in terms of adiabatic or nonadiabatic geometric phases.

Automated summary

We have developed a unified operator framework for quantum holonomies generated from bosonic systems. By considering systems with a Hamiltonian that is bilinear in the creation and annihilation operators, we have discovered a holonomy group that is solely determined by a set of selected orthonormal modes obeying a stronger version of the adiabatic theorem. This photon-number independent approach provides a deeper understanding and computational advantage compared to the standard formalism on geometric phases. Additionally, we have found a strong analogy between quantum holonomies and linear optical networks, offering a specific recipe for making any linear optical quantum computation geometrically robust in terms of adiabatic or nonadiabatic geometric phases.