Solving the Quantum Many-Body Lindbladian Learning Problem With Neural Differential Equations

Abstract

Learning open quantum many-body dynamics is challenging: full Liouvillian models grow exponentially with system size, and dissipation and dephasing force us to follow mixed states from noisy, limited data. These factors make routine characterisation and control difficult, so we need methods that are data-efficient, scalable, and easy to interpret. We present an interpretable, robust framework for learning Lindbladian dynamics from minimal, hardwarefriendly data. The method pairs a physics-first CPTP Lindblad model with a small Neural Differential Equation (NDE) residual and uses a two-stage curriculum (neural warm-up, then analytic-only refinement) to reliably recover coherent and dissipative parameters on challenging 1D benchmarks. There are two ways in which robustness emerges in Lindladian learning: modest physical dissipation that smoothens loss landscapes via steady-state attraction, and the NDE residual that resolves remaining nonconvexity when paired with an optimizer reset. A transient infidelity metric shows short-time power-law error and small steady-state plateaus. Extending beyond CPTP to a stochastic dissipative qubit shows failures in noise-induced or deep PT-unbroken phases that are information-limited, not optimization-limited