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Quantum jump data associated with the article "Solomon equation for qubit and two-level systems" by M. Spiecker et al. acquired and prepared at the Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany. The quantum jump data was extracted from the qubit relaxation available at https://doi.org/10.5281/zenodo.7817552 associated with the article "Two-level system hyperpolarization using a quantum Szilard engine" (arXiv:2204.00499). We use the relaxation data from 5ms onwards where the qubit and the TLSs are close to thermal equilibrium. The data is stored in NumPy binary compressed .npz format in the shape (run, polarization time, polarization to excited/ground state, qubit initialization to excited/ground state, repetitions, quantum jump trace). The video shows the quantum jump statistics evolving in time. Each frame in the video corresponds to taking a histogram over all quantum jumps within a quantum jump trace and all repetitions. For additional information please contact: martin.spiecker@kit.edu or ioan.pop@kit.edu.

We demonstrate flux-bias locking and operation of a gradiometric fluxonium artificial atom using two symmetric granular aluminum (grAl) loops to implement the superinductor. The gradiometric fluxonium shows two orders of magnitude suppression of sensitivity to homogeneous magnetic fields, which can be an asset for hybrid quantum systems requiring strong magnetic field biasing. By cooling down the device in an external magnetic field while crossing the metal-to-superconductor transition, the gradiometric fluxonium can be locked either at $0$ or $\Phi_0/2$ effective flux bias, corresponding to an even or odd number of trapped fluxons, respectively. At mK temperatures, the fluxon parity prepared during initialization survives to magnetic field bias exceeding $100 \,\Phi_0$. However, even for states biased in the vicinity of $1 \,\Phi_0$, we observe unexpectedly short fluxon lifetimes of a few hours, which cannot be explained by thermal or quantum phase slips. When operating in a deep-underground cryostat of the Gran Sasso laboratory, the fluxon lifetimes increase to days, indicating that ionizing events activate phase slips in the grAl superinductor.