Universal time-dependent control scheme for realizing arbitrary linear bosonic transformations

Abstract: 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.