  Recent research shows that quasiparticle-induced decoherence of
superconducting qubits depends on the superconducting-gap asymmetry originating
from the different thicknesses of the top and bottom films in Al/AlO$_x$/Al
junctions. Magnetic field is a key tuning knob to investigate this dependence
as it can change the superconducting gaps in situ. We present measurements of
the parity-switching time of a field-resilient 3D transmon with in-plane field
up to 0.41T. At low fields, small parity splitting requires qutrit pulse
sequences for parity measurements. We measure a non-monotonic evolution of the
parity lifetime with in-plane magnetic field, increasing up to 0.2T, followed
by a decrease at higher fields. We demonstrate that the superconducting-gap
asymmetry plays a crucial role in the observed behavior. At zero field, the
qubit frequency is nearly resonant with the superconducting-gap difference,
favoring the energy exchange with the quasiparticles and so enhancing the
parity-switching rate. With a higher magnetic field, the qubit frequency
decreases and gets detuned from the gap difference, causing the initial
increase of the parity lifetime, while photon-assisted qubit transitions
increase, producing the subsequent decrease at higher fields. Besides giving a
deeper insight into the parity-switching mechanism in conventional transmon
qubits, we establish that Al-AlO$_x$-Al JJs could be used in architectures for
the parity-readout and manipulation of topological qubits based on Majorana
zero modes.
