Spacetime Emergence in the Memory of a Learning Agent

We show that the causal structure of spacetime can emerge within the memory of a learning agent performing a quantum information task. We train a model-based reinforcement-learning agent to maximize the quantum mutual information between localized quantum probes interacting with a quantum field in Minkowski spacetime, without directly providing it with information regarding the spacetime metric or causal structure. In learning to accomplish this task, the reinforcement-learning agent constructs an internal predictive model whose planner develops the characteristic null structure of spacetime, allowing us to reconstruct the causal structure of the Minkowski metric with high accuracy. Within this task, spacetime geometry is obtained from an agent's successful predictions and actions, providing a first step toward showing that spacetime concepts emerge from operational quantum experience.