  Quantum memories capable of faithfully storing and recalling quantum states
on-demand are powerful ingredients in bulding quantum networks
[arXiv:0806.4195] and quantum information processors [arXiv:1109.3743]. As in
conventional computing, key attributes of such memories are high storage
density and, crucially, random access, or the ability to read from or write to
an arbitrarily chosen register. However, achieving such random access with
quantum memories [arXiv:1904.09643] in a dense, hardware-efficient manner
remains a challenge, for example requiring dedicated cavities per qubit
[arXiv:1109.3743] or pulsed field gradients [arXiv:0908.0101]. Here we
introduce a protocol using chirped pulses to encode qubits within an ensemble
of quantum two-level systems, offering both random access and naturally
supporting dynamical decoupling to enhance the memory lifetime. We demonstrate
the protocol in the microwave regime using donor spins in silicon coupled to a
superconducting cavity, storing up to four multi-photon microwave pulses and
retrieving them on-demand up to 2~ms later. A further advantage is the natural
suppression of superradiant echo emission, which we show is critical when
approaching unit cooperativity. This approach offers the potential for
microwave random access quantum memories with lifetimes exceeding seconds
[arXiv:1301.6567, arXiv:2005.09275], while the chirped pulse phase encoding
could also be applied in the optical regime to enhance quantum repeaters and
networks.
