  Central to the success of adaptive systems is their ability to interpret
signals from their environment and respond accordingly -- they act as agents
interacting with their surroundings. Such agents typically perform better when
able to execute increasingly complex strategies. This comes with a cost: the
more information the agent must recall from its past experiences, the more
memory it will need. Here we investigate the power of agents capable of quantum
information processing. We uncover the most general form a quantum agent need
adopt to maximise memory compression advantages, and provide a systematic means
of encoding their memory states. We show these encodings can exhibit extremely
favourable scaling advantages relative to memory-minimal classical agents,
particularly when information must be retained about events increasingly far
into the past.
