# Quantum Feature Space of a Qubit Coupled to an Arbitrary Bath

arXiv: https://arxiv.org/abs/2505.03397 · HTML: https://mlsanity.com/paper/2505.03397/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 6 May 2025.

## Builds on (most cited first, 6 of 6)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models](https://mlsanity.com/paper/2312.04410/) (2023)
- [Machine learning classification of non-Markovian noise disturbing quantum dynamics](https://mlsanity.com/paper/2101.03221/) (2021)
- [Deep learning enhanced noise spectroscopy of a spin qubit environment](https://mlsanity.com/paper/2301.05079/) (2023)
- [Multi-Axis Control of a Qubit in the Presence of Unknown Non-Markovian Quantum Noise](https://mlsanity.com/paper/2208.03058/) (2022)

## Built on by (most cited first, 2 of 2)

- [Singularity-free dynamical invariants-based quantum control](https://mlsanity.com/paper/2510.15340/) (2025)
- [Bayesian quantum sensing using graybox machine learning](https://mlsanity.com/paper/2601.17465/) (2026)

## Abstract (arXiv)

Qubit control protocols have traditionally leveraged a characterisation of the qubit-bath coupling via its power spectral density. Previous work proposed the inference of noise operators that characterise the influence of a classical bath using a grey-box approach that combines deep neural networks with physics-encoded layers. This overall structure is complex and poses challenges in scaling and real-time operations. Here, we show that no expensive neural networks are needed and that this noise operator description admits an efficient parameterisation. We refer to the resulting parameter space as the textitquantum feature space of the qubit dynamics resulting from the coupled bath. We show that the Euclidean distance defined over the quantum feature space provides an effective method for classifying noise processes in the presence of a given set of controls. Using the quantum feature space as the input space for a simple machine learning algorithm (random forest, in this case), we demonstrate that it can effectively classify the stationarity and the broad class of noise processes perturbing a qubit. Finally, we explore how control pulse parameters map to the quantum feature space.