Supervised Machine Learning for Predicting Open Quantum System Dynamics and Detecting Non-Markovian Memory Effects

We present a novel and scalable supervised machine learning framework to predict open-quantum system dynamics and detect non-Markovian memory using only local ancilla measurements. A system qubit is coherently coupled to an ancilla via a symmetric XY Hamiltonian; the ancilla interacts with a noisy environment and is the only qubit we measure. A feedforward neural network, trained on short sliding windows of supplementary data from the past, forecasts the observable system ⟨Z(S)​(t)⟩ without state tomography or knowledge of the bath.

To quantify memory, we introduce a normalized revival-based metric that counts upward ’turn-backs’ in predicted ⟨Z(S)​(t)⟩ and reports the fraction of evaluated samples that exceeds a small threshold. This bounded score provides an interpretable, model-independent indicator of non-Markovianity.

We demonstrate the method on two representative noise channels, non-unital amplitude damping and unital dephasing from random telegraph noise (RTN). Under matched conditions, the model accurately reproduces the dynamics and flags memory effects, with RTN exhibiting a larger normalized revival score than amplitude damping. Overall, the approach is experimentally realistic and readily extensible, enabling real-time, interpretable non-Markovian diagnostics from accessible local measurements.