Sum rule for non-adiabatic geometric phases
arXiv:2511.22437 · doi:10.1016/j.physleta.2026.131345
Abstract
Berry monopoles always cancel when summing over a complete set of energy eigenstates. We demonstrate that analogous sum rules exist for geometric phases and their underlying 2-forms in non-adiabatic evolution. Our result has implications for qudit computation as it limits the types of gates that can be implemented by purely geometric means.
Minor revision, journal reference added