Dimension Reduction for Quantum Adaptive Agents
Adaptive agents realise complex reactive behaviours by using a memory of past input stimuli and output actions to guide structured future responses. Quantum adaptive agents can operate while storing less information in memory than optimal classical counterparts; yet, this does not necessarily translate into a reduced dimension of the memory that must be physically realised. We introduce a route-truncate-repair procedure that converts entropic quantum memory advantages into reductions in memory dimension. Routing a reference input process through an agent yields a temporal matrix product state representation whose canonical bond is identified with the agent's memory. Truncating this bond and locally repairing the resulting dynamics produces a smaller, physically-valid agent that remains capable of responding to arbitrary input sequences. A fidelity-divergence certificate quantifies the resulting trade-off between accuracy and memory dimension. Benchmark adaptive processes exhibit substantial dimension reduction whilst preserving the underlying behaviour with high fidelity. These results establish a route from entropic memory advantages to practical, dimension-reduced adaptive quantum agents.