# Unraveling Quantum Environments: Transformer-Assisted Learning in Lindblad Dynamics

arXiv: https://arxiv.org/abs/2505.06928 · HTML: https://mlsanity.com/paper/2505.06928/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 11 May 2025.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Path sampling of recurrent neural networks by incorporating known physics](https://mlsanity.com/paper/2203.00597/) (2022)

## Built on by (most cited first, 4 of 4)

- [Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold](https://mlsanity.com/paper/2605.03573/) (2026)
- [Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations](https://mlsanity.com/paper/2512.13913/) (2025)
- [Lindbladian Learning with Neural Differential Equations](https://mlsanity.com/paper/2603.07778/) (2026)
- [Transformer-Based Time-Series Inference of Lindblad Dynamics in Open Quantum Systems](https://mlsanity.com/paper/2610.05647/) (2026)

## Abstract (arXiv)

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 quantum systems governed by the Lindblad master equation. Our approach uses time series of observable quantities, such as expectation values of single Pauli operators, as input to learn dissipation profiles without requiring knowledge of the initial quantum state or even the system Hamiltonian. We demonstrate the effectiveness of our approach on a hierarchy of open quantum models of increasing complexity, including single-qubit systems with time-independent or time-dependent jump rates, two-qubit interacting systems (e.g., Heisenberg and transverse Ising models), and the Jaynes--Cummings model involving light--matter interaction and cavity loss with time-dependent decay rates. Our method accurately reconstructs both fixed and time-dependent decay rates from observable time series. To support this, we prove that under reasonable assumptions, the jump rates in all these models are uniquely determined by a finite set of observables, such as qubit and photon measurements. In practice, we combine Transformer-based architectures with lightweight feature extraction techniques to efficiently learn these dynamics. Our results suggest that modern machine learning tools can serve as scalable and data-driven alternatives for identifying unknown environments in open quantum systems.