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We report continuous measurements of quasiparticles trapping and clearing from Andreev Bound States in aluminum nanobridge Josephson junctions integrated into a superconducting-qubit-like device. We find that trapping is well modeled by independent spontaneous emission events. Above 80 mK the clearing process is well described by absorption of thermal phonons, but other temperature-independent mechanisms dominate at low temperature. We find complex structure in the dependence of the low-temperature clearing rate on the Andreev Bound State energy. Our results shed light on quasiparticle behavior in qubit-like circuits.

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