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We derive the structure of the Landau-Zener-St\"uckelberg-Majorana (LZSM)interference pattern for a qubit that experiences quantum dissipation and isadditionally subjected to time-periodic but otherwise general driving. Aspin-boson Hamiltonian serves as model which we treat with a Bloch-Redfieldmaster equation in Floquet basis. It predicts a peak structure that dependssensitively on the operator through which the qubit couples to the bath. TheFourier transforms of the LZSM patterns exhibit arc structures which reflectthe shape of the driving. These features are captured by an effectivetime-independent Bloch equation which provides an analytical solution.Moreover, we determine the decay of these arcs as a function of dissipationstrength and temperature.

Qubit interference at avoided crossings: The role of driving shape and bath coupling