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We propose a tunable coupler consisting of N fixed-frequency qubits, whichcan tune and even amplify the effective interaction between two superconductingquantum circuits. The tuning range of the interaction is proportional to N,with a minimum value of zero and a maximum that can exceed the physicalcoupling rates between the coupler and the circuits. The effective couplingrate is determined by the collective magnetic quantum number of the qubitensemble, which takes only discrete values and is free from collective decayand decoherence. Using single-photon pi-pulses, the coupling rate can beswitched between arbitrary choices of the initial and final values within thedynamic range in a single step without going through intermediate values. Acascade of the couplers for amplifying small interactions or weak signals isalso discussed. These results should not only stimulate interest in exploringthe collective effects in quantum information processing, but also enabledevelopment of applications in tuning and amplifying the interactions in ageneral cavity-QED system.

Tuning and Amplifying the Interactions in Superconducting Quantum Circuits with Subradiant Qubits