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Paper detail

Sum rule for non-adiabatic geometric phases

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.

preprint2026arXivOpen access
Adam FredrikssonErik Sjöqvist
quant-ph
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Adam FredrikssonErik Sjöqvist

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