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Quantum Feature Space of a Qubit Coupled to an Arbitrary Bath

Chris Wise, Akram Youssry, Alberto Peruzzo, Jo Plested, Matt Woolley

TL;DR

This work introduces the Quantum Feature Space (QFS), a compact, physics-informed parameterization of qubit-bath interactions that replaces expensive neural networks with a tractable, observable-based feature space. By deriving a bath-influenced operator tilde{O}(T) and its parameters from measurement data, the authors enable efficient noise classification and control-pulse mapping using simple methods like Euclidean distance and random forests. They validate the approach with a fast, GPU-accelerated simulator, a set of noise-process simulations (including non-stationary and coloured noise), and demonstrated high classification accuracy with minimal data and model complexity. The QFS framework offers a scalable, robust alternative for quantum noise spectroscopy and control optimization, with potential extensions to multi-qubit systems.

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.

Quantum Feature Space of a Qubit Coupled to an Arbitrary Bath

TL;DR

This work introduces the Quantum Feature Space (QFS), a compact, physics-informed parameterization of qubit-bath interactions that replaces expensive neural networks with a tractable, observable-based feature space. By deriving a bath-influenced operator tilde{O}(T) and its parameters from measurement data, the authors enable efficient noise classification and control-pulse mapping using simple methods like Euclidean distance and random forests. They validate the approach with a fast, GPU-accelerated simulator, a set of noise-process simulations (including non-stationary and coloured noise), and demonstrated high classification accuracy with minimal data and model complexity. The QFS framework offers a scalable, robust alternative for quantum noise spectroscopy and control optimization, with potential extensions to multi-qubit systems.

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.
Paper Structure (17 sections, 47 equations, 3 figures, 7 tables)

This paper contains 17 sections, 47 equations, 3 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Theoretical Results
  3. Open System Dynamics
  4. Deriving the Quantum Feature Space
  5. Experimental Results
  6. Efficiency of QFS Derivation
  7. Quantum Simulation Implementation
  8. Creation of QFS Data
  9. Black Box Classification of Bath Through QFS
  10. Explicit Comparison to Previous Work
  11. Decision Tree for Noise Characterisation
  12. Properties of the QFS
  13. Conclusion and Future Work
  14. Data and Code Availability
  15. References
  16. ...and 2 more sections

Figures (3)

  • Figure 1: The diagram illustrates an iterative process for characterising and learning noise properties in quantum systems. Starting with a PSD (top), noise realisations are generated (right) and combined with control pulses in a quantum simulation. The outcomes of these simulations are mapped onto a QFS (bottom), where data points encode the effects of the noise. This feature space is used by regression models such as decision trees to infer key noise properties, including type and stationarity (left). These inferred properties refine the PSD model used in subsequent iterations. This closed-loop framework enables the classification and clustering of noise processes. It facilitates tailored noise mitigation strategies, leveraging machine learning techniques like decision trees, k-means clustering, and neural networks for enhanced quantum control.
  • Figure 2: Control pulses used in the simulations. (a) shows the ideal CPMG pulses, and (b) shows the realistic CPMG pulses.
  • Figure 3: (a) Visualisation of the QFS with widening Gaussian-shaped control pulses, with the fraction indicating the scale factor. (b) Visualisation of the QFS with interpolation between noise processes implemented by utilising a linear combination of the '$1/f$ + bump' and coloured Gaussian noise processes. (c) Visualisation of the quantum parameter space with two different noise processes, '$1/f$ + bump' and coloured Gaussian, with colour saturation representing increasing energy.