  We propose and experimentally demonstrate a scheme for implementation of a
maximally entangling quantum controlled-Z gate between two weakly interacting
systems. We conditionally enhance the interqubit coupling by quantum
interference. Both before and after the interqubit interaction, one of the
qubits is coherently coupled to an auxiliary quantum system, and finally it is
projected back onto qubit subspace. We experimentally verify the practical
feasibility of this technique by using a linear optical setup with weak
interferometric coupling between single-photon qubits. Our procedure is
universally applicable to a wide range of physical platforms including hybrid
systems such as atomic clouds or optomechanical oscillators coupled to light.
