Lindbladian Learning with Neural Differential Equations

TL;DR

This paper introduces a neural differential equation-based maximum-likelihood method for learning Lindbladian dynamics of open quantum systems from transient measurement data, effectively handling noise and system complexity.

Contribution

It presents a novel neural differential equation approach for Lindbladian learning that captures open-system quantum dynamics from transient data with high robustness.

Findings

Successfully learns open-system dynamics for various quantum models.

Robustly infers dissipative processes over high noise levels.

Handles systems up to 6 qubits with limited measurement shots.

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.