Solvable Quantum Circuits with non-Markovian Influence Matrices

What the math gives to ML

The paper provides a constructive hierarchy of exactly solvable influence matrices: one-column conditions produce temporally factorized Markovian baths, while two-column CDU3 conditions produce non-Markovian temporal correlations whose influence state remains an efficiently representable matrix product state with bond dimension bounded by \(\chi\le q^2\). The transferable mechanism is a recurrent memory module whose temporal influence functional has finite tensor-network rank rather than a single-step hidden-state transition. A neural implementation can use a bounded-bond MPS memory core, optionally constrained to be contractive or isometric, and test whether increasing temporal interaction width produces measurable long-horizon gains without exponential memory growth.