Quantum Feature Space of a Qubit Coupled to an Arbitrary Bath

TL;DR

This paper introduces an efficient quantum feature space for qubit-bath interactions that enables effective noise classification and analysis without complex neural networks, facilitating real-time quantum noise diagnostics.

Contribution

It presents a novel, scalable parameterization of the qubit's noise influence, allowing simple machine learning methods to classify noise types and analyze control pulse effects.

Findings

Quantum feature space effectively classifies noise processes.

Euclidean distance in feature space correlates with noise similarity.

Control pulse parameters map meaningfully into the feature space.

Abstract

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 \textit{quantum 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.