Geometrically robust linear optics from non-Abelian geometric phases

TL;DR

This paper introduces a unified framework for quantum holonomies in bosonic systems, enabling the design of geometrically robust linear optical quantum computations through adiabatic and nonadiabatic geometric phases.

Contribution

It develops a photon-number independent operator formalism for quantum holonomies, linking quantum holonomies with linear optical networks for robust quantum computation.

Findings

Holonomy group determined by selected orthonormal modes

Provides a computational advantage over standard geometric phase formalism

Explicit recipe for geometrically robust linear optical quantum computation

Abstract

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.