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.Comment: 5 pages, 2 figures, supplementary material at the end of the
document. Comments and feedback are highly welcom