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arXiv · 2511.22437

Sum rule for non-adiabatic geometric phases

Adam Fredriksson·Erik Sjöqvist
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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.

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Adam Fredriksson, Erik Sjöqvist. 2025-11-27. Sum rule for non-adiabatic geometric phases. https://doi.org/10.1016/j.physleta.2026.131345

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