  As in conventional computing, key attributes of quantum 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 in a dense, hardware-efficient manner remains a
challenge, for example requiring dedicated cavities per qubit or pulsed field
gradients. 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 in distinct memory modes 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, while the chirped pulse phase encoding could also
be applied in the optical regime to enhance quantum repeaters and networks.
