  We theoretically investigate and experimentally demonstrate a procedure for
conditional control and enhancement of an interferometric coupling between two
qubits encoded into states of bosonic particles. Our procedure combines local
coupling of one of the particles to an auxiliary mode and single-qubit quantum
filtering. We experimentally verify the proposed procedure using a linear
optical setup where qubits are encoded into quantum states of single photons
and coupled at a beam splitter with a fixed transmittance. With our protocol,
we implement a range of different effective transmittances, demonstrate both
enhancement and reduction of the coupling strength, and observe dependence of
two-photon bunching on the effective transmittance. To make our analysis
complete, we also theoretically investigate a more general scheme where each
particle is coupled to a separate auxiliary mode and show that this latter
scheme enables to achieve higher implementation probability. We show that our
approach can be extended also to other kinds of qubit-qubit interactions.
