  Tunable two-qubit couplers offer an avenue to mitigate errors in multiqubit
superconducting quantum processors. However, most couplers operate in a narrow
frequency band and target specific couplings, such as the spurious $ZZ$
interaction. We introduce a superconducting coupler that alleviates these
limitations by suppressing all two-qubit interactions with an exponentially
large on-off ratio and without the need for fine-tuning. Our approach is based
on a bus mode supplemented by an ancillary nonlinear resonator mode. Driving
the ancillary mode leads to a coupler-state-dependent field displacement in the
resonator which, in turn, results in an exponential suppression of real and
virtual two-qubit interactions with respect to the drive power. A
superconducting circuit implementation supporting the proposed mechanism is
presented.
