Lindbladian Learning with Neural Differential Equations
This work provides a robust method for characterizing open quantum systems, which is crucial for the verification, calibration, and control of quantum processors. It offers a strong specific gain in the field of quantum computing.
This paper addresses the challenge of inferring the dynamical generator of open many-body quantum systems from measurement data, a problem known as Lindbladian learning. The authors propose a maximum-likelihood method using Pauli measurements at transient times, augmented with a neural differential equation term during training. Their method reliably learns open-system dynamics for various Hamiltonians and dissipative parts, robustly inferring systems up to N=6 qubits with fewer than 5e5 shots over noise-to-signal ratios spanning four orders of magnitude.
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.