Time-dependent driving of topological quantum circuits

Time-dependent control of superconducting quantum circuits is a prerequisite for building scalable quantum hardware. The quantum description of these circuits is complicated due to the electromotive force (emf) induced by time-varying magnetic fields. Here, using a perturbative approach, we examine how the emf modifies the fractional Josephson effect between two weakly coupled topological superconductors. We show that, at low frequencies, a time-varying flux introduces a new term that can be probed via charge and current measurements in open-circuit and closed-loop geometries, respectively. This term depends on both the geometry of the circuit and the time-dependent magnetic field. Finally, we generalize to an intermediate frequency regime with numerical methods and study how the supercurrent depends on the induced emf.