  We propose a tunable coupler consisting of N fixed-frequency qubits, which
can tune and even amplify the effective interaction between two superconducting
quantum circuits. The tuning range of the interaction is proportional to N,
with a minimum value of zero and a maximum that can exceed the physical
coupling rates between the coupler and the circuits. The effective coupling
rate is determined by the collective magnetic quantum number of the qubit
ensemble, which takes only discrete values and is free from collective decay
and decoherence. Using single-photon pi-pulses, the coupling rate can be
switched between arbitrary choices of the initial and final values within the
dynamic range in a single step without going through intermediate values. A
cascade of the couplers for amplifying small interactions or weak signals is
also discussed. These results should not only stimulate interest in exploring
the collective effects in quantum information processing, but also enable
development of applications in tuning and amplifying the interactions in a
general cavity-QED system.
