Lindbladian Learning with Neural Differential Equations

2026-03-08

AI Summary

Reconstructing the Lindbladian generator of open many-body quantum systems from measurement data is challenged by the difficulty in disentangling coherent and dissipative effects, as well as the insensitivity of steady-state information to coherent couplings. This work proposes a method combining transient Pauli measurements with maximum likelihood estimation, introducing for the first time distillable neural differential equations to assist in optimizing non-convex loss functions and extracting interpretable physical models from black-box representations. By leveraging transient dynamics, the approach significantly enhances parameter identifiability and achieves robust learning across neutral-atom, superconducting, and spin-chain platforms. Accurate reconstruction of dissipative dynamics—including phase noise, thermal noise, or their combinations—is demonstrated even under extreme conditions: signal-to-noise ratios spanning four orders of magnitude, up to six qubits, and fewer than 5×10⁵ measurement shots.

Technology Category

• Machine Learning: Quantum Machine Learning
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to $N=6$ qubits with fewer than $5 \times 10^5$ shots.

Problem

• Lindbladian learning
• open quantum systems
• quantum process characterization
• transient dynamics
• Pauli measurements

Innovation

• Lindbladian learning
• neural differential equations
• open quantum systems
• transient dynamics
• maximum-likelihood estimation