  The control of flying qubits is at the core of quantum networks. As often
carried by single-photon fields, the flying-qubit control involves not only
their logical states but also their shapes. In this paper, we explore a variety
of flying-qubit control problems using a three-level atom with time-varying
tunable couplings to two input-output channels. It is shown that one can tune
the couplings of a $\Lambda$-type atom to distribute a single photon into the
two channels with arbitrary shapes, or use a $V$-type atom to catch an
arbitrary-shape distributed single photon. The $\Lambda$-type atom can also be
designed to transfer a flying qubit from one channel to the other, with both
the central frequency and the photon shape being converted. With a $\Xi$-type
atom, one can use the tunable coupling to shape a pair of correlated photons
via cascaded emission. In all cases, analytical formulas are derived for the
coupling functions to fulfil these control tasks, and their physical
limitations are discussed as well. These results provide useful control
protocols for high-fidelity quantum information transmission over complex
quantum networks.
