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arxiv: 2509.03389 · v2 · submitted 2025-09-03 · 🪐 quant-ph · cond-mat.other

Detection of noise correlations in two qubit systems by Machine Learning

Dario Fasone , Shreyasi Mukherjee , Dario Penna , Fabio Cirinn\`a , Mauro Paternostro , Elisabetta Paladino , Luigi Giannelli , Giuseppe A. Falci This is my paper

Pith reviewed 2026-05-18 19:19 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.other
keywords machine learningquantum sensingnoise correlationstwo-qubit systemsMarkovian noisenon-Markovian noisecoherent population transfer
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The pith

Machine learning classifies noise correlations in two ultrastrongly coupled qubits with over 94 percent accuracy from three final measurements.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a protocol that uses machine learning to classify spatial and temporal correlations of classical noise affecting two ultrastrongly coupled qubits. It considers six distinct classes of Markovian and non-Markovian noise and relies on measuring final transfer efficiencies from a coherent population transfer protocol run under three different driving conditions. These three numbers are fed into a shallow neural network that achieves at least 94 percent classification accuracy, with near-perfect separation of Markovian from non-Markovian cases. The method requires only simple final-state measurements and no time-series data, which matters because it reduces the experimental overhead for characterizing noise in quantum hardware by extracting information from protocol non-idealities.

Core claim

The final transfer efficiencies obtained from a coherent population transfer protocol applied under three distinct driving conditions contain sufficient information for a shallow neural network to discriminate among six classes of Markovian and non-Markovian noise in two ultrastrongly coupled qubits, reaching at least 94 percent classification accuracy.

What carries the argument

A shallow neural network that takes the three measured final transfer efficiencies as inputs and outputs the predicted noise class.

Load-bearing premise

The six different noise classes must imprint sufficiently distinct patterns on the three final transfer efficiencies for the neural network to learn a reliable mapping.

What would settle it

Applying the trained network to new data from two qubits driven by one of the six independently verified noise types and obtaining classification accuracy substantially below 94 percent.

Figures

Figures reproduced from arXiv: 2509.03389 by Dario Fasone, Dario Penna, Elisabetta Paladino, Fabio Cirinn\`a, Giuseppe A. Falci, Luigi Giannelli, Mauro Paternostro, Shreyasi Mukherjee.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representation of the sensor consisting of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 6
Figure 6. Figure 6: We anticipate that non-ideal features emerging [PITH_FULL_IMAGE:figures/full_fig_p002_6.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy levels of the two-qubit sensor, for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Efficiency of the STIRAP-like protocol versus the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Accuracy, and (b) value of the cost function, [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. . Confusion matrix of the MLP model for classifying [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Contour plot of the efficiency of the STIRAP-like [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

We introduce and validate a machine-learning assisted quantum sensing protocol to classify spatial and temporal correlations of classical noise affecting two ultrastrongly coupled qubits. We consider six distinct classes of Markovian and non-Markovian noise. Leveraging the sensitivity of a coherent population transfer protocol under three distinct driving conditions, the various forms of noise are discriminated by only measuring the final transfer efficiencies. Our approach achieves $\gtrsim 94\%$ accuracy in classification providing a near-perfect discrimination between Markovian and non-Markovian noise. The method requires minimal experimental resources, relying on a simple driving scheme providing three inputs to a shallow neural network with no need of measuring time-series data or real-time monitoring. The machine-learning data analysis acquires information from non-idealities of the coherent protocol highlighting how combining these techniques may significantly improve the characterization of quantum-hardware.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a machine-learning protocol to classify six classes of Markovian and non-Markovian spatial and temporal noise correlations affecting two ultrastrongly coupled qubits. It uses final transfer efficiencies measured under only three distinct driving conditions in a coherent population-transfer protocol as inputs to a shallow neural network, reporting ≳94% classification accuracy without requiring time-series data.

Significance. If the quantitative results hold under rigorous validation, the work demonstrates a low-resource method for noise characterization that extracts information from non-idealities of a coherent protocol. This could be useful for quantum hardware diagnostics, particularly for distinguishing Markovian from non-Markovian regimes with minimal experimental overhead.

major comments (2)
  1. [Methods/Results] Methods/Results sections: The central claim of ≳94% accuracy (and near-perfect Markovian/non-Markovian discrimination) is presented without any description of training-data generation, the ranges of noise correlation parameters sampled, the simulation method for the two-qubit dynamics, validation-split ratios, or cross-validation procedure. These details are load-bearing for assessing whether the reported performance reflects genuine separability or overfitting on the three-dimensional feature vector.
  2. [Driving conditions / feature extraction] Section on driving conditions and feature extraction: The assumption that three scalar final efficiencies suffice to distinguish temporal correlation timescales (including decay rates and oscillation frequencies of non-Markovian noise) is not supported by any sensitivity analysis or injectivity argument. Two noise correlation functions differing primarily in memory time can produce nearly identical integrated populations under fixed Rabi frequencies and total evolution time, undermining the claim that the chosen conditions yield an injective mapping for the selected noise families.
minor comments (2)
  1. [Abstract/Introduction] The abstract and introduction use 'non-idealities of the coherent protocol' without defining the term or linking it explicitly to the three chosen driving conditions.
  2. [Notation] Notation for the six noise classes and the precise form of the correlation functions should be introduced earlier and used consistently in the results tables or figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help improve the clarity and rigor of the work. We address each major comment below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: [Methods/Results] Methods/Results sections: The central claim of ≳94% accuracy (and near-perfect Markovian/non-Markovian discrimination) is presented without any description of training-data generation, the ranges of noise correlation parameters sampled, the simulation method for the two-qubit dynamics, validation-split ratios, or cross-validation procedure. These details are load-bearing for assessing whether the reported performance reflects genuine separability or overfitting on the three-dimensional feature vector.

    Authors: We agree that the current manuscript would benefit from expanded details on these aspects to strengthen reproducibility and address potential concerns about overfitting. In the revised version, we will add a dedicated subsection in Methods describing: the generation of training data (including sampling ranges for correlation parameters such as decay rates and oscillation frequencies), the numerical integration method for the two-qubit master equation under the coherent population transfer protocol, the train/validation/test split ratios used, and the cross-validation procedure. This will allow readers to evaluate the robustness of the ≳94% accuracy. revision: yes

  2. Referee: [Driving conditions / feature extraction] Section on driving conditions and feature extraction: The assumption that three scalar final efficiencies suffice to distinguish temporal correlation timescales (including decay rates and oscillation frequencies of non-Markovian noise) is not supported by any sensitivity analysis or injectivity argument. Two noise correlation functions differing primarily in memory time can produce nearly identical integrated populations under fixed Rabi frequencies and total evolution time, undermining the claim that the chosen conditions yield an injective mapping for the selected noise families.

    Authors: We acknowledge that the manuscript does not include a formal sensitivity analysis or injectivity proof. However, the classification is performed empirically via machine learning on the six specific noise classes, and the reported accuracy indicates practical distinguishability within the sampled parameter space rather than a general injective mapping for arbitrary correlation functions. To address the referee's concern, we will include additional sensitivity analysis (e.g., distributions of efficiencies for varied memory times) in the revised manuscript and clarify the distinction between empirical classification performance and theoretical injectivity. We believe this will sufficiently support the chosen driving conditions for the noise families studied. revision: partial

Circularity Check

0 steps flagged

No circularity: classification accuracy obtained from supervised training on simulated efficiencies under fixed driving protocols.

full rationale

The paper simulates qubit dynamics for six noise classes, extracts three scalar final transfer efficiencies under distinct driving conditions, trains a shallow neural network on those features, and reports test-set classification accuracy. This workflow does not reduce any claimed result to a fitted parameter by construction, nor does it rely on a self-citation chain or imported uniqueness theorem for its central claim. The derivation chain consists of standard numerical simulation followed by standard supervised learning; the reported ≳94% accuracy is an empirical performance metric on held-out simulated data, not a tautological renaming or self-definition. No load-bearing step equates the output to the input by algebraic identity or by re-labeling a fit as a prediction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard models of classical noise acting on two coupled qubits and on the assumption that the coherent population transfer protocol remains sensitive to those noise classes under the chosen driving conditions. No explicit free parameters or invented entities are stated in the abstract.

axioms (2)
  • domain assumption Classical noise affects the two ultrastrongly coupled qubits according to one of six predefined Markovian or non-Markovian correlation classes.
    The classification task is defined over these six classes; the abstract treats their existence and distinguishability as given.
  • domain assumption Final population transfer efficiencies under three driving conditions contain sufficient information to discriminate the noise classes.
    This premise is required for the protocol to work with only end-point measurements.

pith-pipeline@v0.9.0 · 5698 in / 1382 out tokens · 55252 ms · 2026-05-18T19:19:14.903821+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Machine Learning-Aided Optimal Control of a Qubit Subjected to External Noise

    quant-ph 2025-12 unverdicted novelty 5.0

    A greybox framework combining whitebox physics with a neural-network blackbox trained on synthetic data achieves over 90% gate fidelity for a qubit under non-Markovian noise.

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