Unraveling quantum environments: Transformer-assisted learning in Lindblad dynamics

Understanding dissipation in open quantum systems is crucial for the development of robust quantum technologies. In this work, we introduce a transformer-based machine learning framework to infer time-dependent dissipation rates in systems governed by the Lindblad master equation. Our method requires only time series of observable quantities, such as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>〈</a:mo> <a:msub> <a:mi>σ</a:mi> <a:mi>x</a:mi> </a:msub> <a:mrow> <a:mo>(</a:mo> <a:mi>t</a:mi> <a:mo>)</a:mo> </a:mrow> <a:mo>〉</a:mo> </a:mrow> </a:math> , <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mo>〈</b:mo> <b:msub> <b:mi>σ</b:mi> <b:mi>y</b:mi> </b:msub> <b:mrow> <b:mo>(</b:mo> <b:mi>t</b:mi> <b:mo>)</b:mo> </b:mrow> <b:mo>〉</b:mo> </b:mrow> </b:math> , and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mo>〈</c:mo> <c:msub> <c:mi>σ</c:mi> <c:mi>z</c:mi> </c:msub> <c:mrow> <c:mo>(</c:mo> <c:mi>t</c:mi> <c:mo>)</c:mo> </c:mrow> <c:mo>〉</c:mo> </c:mrow> </c:math> , and does not require prior knowledge of the initial quantum state or the system Hamiltonian during inference. We demonstrate the effectiveness of our approach across a hierarchy of open quantum models, including single-qubit systems with time-independent and time-dependent jump rates, two-qubit interacting systems (e.g., Heisenberg and transverse Ising models), and the Jaynes-Cummings model with cavity loss and time-dependent decay. Our method accurately reconstructs both fixed and time-varying dissipation profiles from observable trajectories. We further show that under reasonable assumptions, the jump rates in these models are uniquely determined by a small set of measurable observables. The results suggest that transformer-based learning provides a scalable and data-driven route for identifying environmental effects in open quantum systems.