Discrete control of capacitance in quantum circuits

Precise in-situ control of system parameters is indispensable for all quantum hardware applications. The capacitance in a circuit, however, is usually a simple consequence of electrostatics, and thus quite literally cast in stone. We here propose a way to control the charging energy of a given island by exploiting recently predicted Chern insulator physics in common Cooper-pair transistors, where the capacitance switches between discrete values given by the Chern number. We identify conditions for which the discrete control benefits from exponentially reduced noise sensitivity to implement protected tunable qubits.