  Delay lines that store quantum information are crucial for advancing quantum
repeaters and hardware efficient quantum computers. Traditionally, they are
realized as extended systems that support wave propagation but provide limited
control over the propagating fields. Here, we introduce a parametrically
addressed delay line for microwave photons that provides a high level of
control over the stored pulses. By parametrically driving a three-wave mixing
circuit element that is weakly hybridized with an ensemble of resonators, we
engineer a spectral response that simulates that of a physical delay line,
while providing fast control over the delay line's properties. We demonstrate
this novel degree of control by choosing which photon echo to emit, translating
pulses in time, and even swapping two pulses, all with pulse energies on the
order of a single photon. We also measure the noise added from our parametric
interactions and find it is much less than one photon.
