  We study the implementation of arbitrary excitation-conserving linear
transformations between two sets of $N$ stationary bosonic modes, which are
connected through a photonic quantum channel. By controlling the individual
couplings between the modes and the channel, an initial $N$-partite quantum
state in register $A$ can be released as a multiphoton wave packet and,
successively, be reabsorbed in register $B$. Here we prove that there exists a
set of control pulses that implement this transfer with arbitrarily high
fidelity and, simultaneously, realize a prespecified $N\times N$ unitary
transformation between the two sets of modes. Moreover, we provide a numerical
algorithm for constructing these control pulses and discuss the scaling and
robustness of this protocol in terms of several illustrative examples. By being
purely control-based and not relying on any adaptations of the underlying
hardware, the presented scheme is extremely flexible and can find widespread
applications, for example, for boson-sampling experiments, multiqubit state
transfer protocols or in continuous-variable quantum computing architectures.
