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arxiv: 2512.24393 · v2 · submitted 2025-12-30 · 🪐 quant-ph

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

Riccardo Cantone , Shreyasi Mukherjee , Luigi Giannelli , Elisabetta Paladino , Giuseppe A. Falci This is my paper

Pith reviewed 2026-05-16 18:42 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum optimal controlnon-Markovian noisegreybox modelneural networksopen quantum systemsqubit controlRandom Telegraph noiseOrnstein-Uhlenbeck noise
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The pith

A greybox method merges physical qubit models with neural networks trained on synthetic data to reach over 90 percent gate fidelity under non-Markovian noise.

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

The paper develops a control technique for a qubit that faces external noise with memory, called non-Markovian noise. It combines a known physical model of the system with a neural network that learns from simulated noise trajectories. This hybrid setup produces control pulses that keep gate errors low even when the noise correlations persist over time. A reader would care because standard optimal-control methods often assume noise forgets its past quickly, an assumption that fails in many real devices. The authors test the approach on two common noise processes and note practical limits of moving from simulation to hardware.

Core claim

The central claim is that a greybox framework, formed by embedding a whitebox physical model inside a neural-network blackbox trained exclusively on synthetic data, successfully captures non-Markovian noise dynamics and yields gate fidelities above 90 percent for a single qubit driven by Random Telegraph or Ornstein-Uhlenbeck noise.

What carries the argument

The greybox framework that integrates a whitebox physical model of the open quantum system with a neural-network blackbox trained on synthetic noise trajectories to generate optimal control pulses.

If this is right

  • Gate fidelities above 90 percent are obtained for both Random Telegraph and Ornstein-Uhlenbeck noise models.
  • Non-Markovian memory effects are incorporated without requiring a fully Markovian approximation.
  • The method extends standard quantum optimal control to open systems where noise has temporal correlations.
  • Critical implementation issues, such as model mismatch between simulation and experiment, are identified for further work.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the synthetic-to-real transfer holds, experimenters could reduce the amount of detailed noise spectroscopy needed before running control sequences.
  • The same hybrid structure might be applied to multi-qubit gates where cross-talk creates additional memory effects.
  • Retraining the network on a mixture of synthetic and limited experimental data could improve robustness when the physical noise deviates from the assumed models.

Load-bearing premise

A neural network trained only on synthetic noise data will correctly reproduce the non-Markovian dynamics that actually occur inside a physical qubit device.

What would settle it

Apply the learned control pulses to a real qubit in a laboratory setting under calibrated Random Telegraph or Ornstein-Uhlenbeck noise and measure whether the observed gate fidelity remains above 90 percent.

Figures

Figures reproduced from arXiv: 2512.24393 by Elisabetta Paladino, Giuseppe A. Falci, Luigi Giannelli, Riccardo Cantone, Shreyasi Mukherjee.

Figure 1
Figure 1. Figure 1: The transformer-based graybox architecture we used to model Markovian and non-Markovian open-system qubit dynamics. OU Case. The model exhibited similar performance, with low and stable MSE values across all g, confirming robustness to different noise types. Optimal control results mir￾rored those of the RTN case, with fidelities exceeding 99% at low g and remaining above 90% even at stronger coupling. Whi… view at source ↗
read the original abstract

We apply a machine-learning-enhanced greybox framework to a quantum optimal control protocol for open quantum systems. Combining a whitebox physical model with a neural-network blackbox trained on synthetic data, the method captures non-Markovian noise effects and achieves gate fidelities above 90% under Random Telegraph and Ornstein-Uhlenbeck noise. Critical issues of the approach are discussed.

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

1 major / 2 minor

Summary. The manuscript presents a machine-learning-enhanced greybox framework for optimal control of a qubit under non-Markovian external noise. It integrates a whitebox physical model with a neural-network blackbox trained exclusively on synthetic trajectories from Random Telegraph and Ornstein-Uhlenbeck processes, reporting gate fidelities above 90% for these noise models while discussing critical issues of the approach.

Significance. If the numerical results hold, the hybrid greybox construction offers a reproducible route to augment incomplete open-system models with data-driven corrections for memory effects, potentially aiding control design in simulated noisy quantum systems. The explicit use of synthetic data for both training and testing is a methodological strength that supports controlled verification, though broader applicability hinges on how well the learned corrections transfer beyond the training noise manifold.

major comments (1)
  1. [Numerical results] The headline fidelity claim (>90%) is demonstrated only under the same Random Telegraph and Ornstein-Uhlenbeck processes used to generate the training data. To establish that the neural-network correction genuinely captures non-Markovian features rather than memorizing the training distribution, the results section should include at least one out-of-distribution test (e.g., 1/f or quasistatic noise) and report the corresponding fidelity relative to the pure whitebox baseline.
minor comments (2)
  1. [Abstract] The abstract states the fidelity result but supplies no numerical values, baseline comparison, or reference to the specific figures/tables that contain the data; adding these details would improve immediate readability.
  2. [Methods] Notation for the combined whitebox-plus-blackbox dynamics (e.g., the precise form of the memory kernel or the input features to the neural network) should be defined explicitly in the methods section to allow readers to reproduce the greybox construction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and the constructive suggestion regarding numerical validation. We address the major comment below and will revise the manuscript to incorporate the requested out-of-distribution tests.

read point-by-point responses

  1. Referee: [Numerical results] The headline fidelity claim (>90%) is demonstrated only under the same Random Telegraph and Ornstein-Uhlenbeck processes used to generate the training data. To establish that the neural-network correction genuinely captures non-Markovian features rather than memorizing the training distribution, the results section should include at least one out-of-distribution test (e.g., 1/f or quasistatic noise) and report the corresponding fidelity relative to the pure whitebox baseline.

    Authors: We agree that out-of-distribution testing is necessary to substantiate that the neural-network component learns genuine non-Markovian corrections rather than overfitting to the training distributions. In the revised manuscript we will add results for 1/f noise and quasistatic noise, reporting gate fidelities for the greybox model together with the corresponding whitebox baseline values. These new experiments will be placed in the results section with updated figures and discussion. revision: yes

Circularity Check

0 steps flagged

No significant circularity: greybox NN trained on external synthetic RT/OU trajectories yields reported fidelities without definitional reduction

full rationale

The paper's central construction trains a neural-network blackbox exclusively on synthetic trajectories generated from the Random Telegraph and Ornstein-Uhlenbeck processes and then reports gate fidelities above 90% when the combined whitebox+blackbox controller is applied to the same noise classes. No equation in the provided text equates the learned correction to the input noise statistics by construction, nor does any self-citation supply a uniqueness theorem that forces the result. The fidelity metric is computed on simulated trajectories drawn from the training distribution, which is a standard supervised-learning evaluation rather than a circular re-derivation of the inputs. Because the derivation chain remains self-contained against the external synthetic benchmark and contains no load-bearing self-citation or ansatz smuggling, the circularity score is 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the method is described at the level of combining an existing physical model with a trained network.

pith-pipeline@v0.9.0 · 5363 in / 968 out tokens · 56055 ms · 2026-05-16T18:42:51.580368+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages · 1 internal anchor

  1. [1]

    Paz-Silva, and Christopher Ferrie

    Akram Youssry, Gerardo A. Paz-Silva, and Christopher Ferrie. Characterization and control of open quantum systems beyond quantum noise spectroscopy.npj (Nature Partner Journals) Quantum Information, 2020

    work page 2020

  2. [2]

    Gomez, Lukasz Kaiser, and Illia Polosukhin

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, 4 Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need.Pro- ceedings of the 31st Conference on Neural Information Processing Systems (NIPS 2017), 2017

    work page 2017

  3. [3]

    A tutorial on optimal control and reinforcement learning methods for quantum technologies.Physics Letters A, 2022

    Luigi Giannelli, Pierpaolo Sgroi, Jonathon Brown, Gheorghe Sorin Paraoanu, Mauro Paternostro, Elisabetta Paladino, and Giuseppe Falci. A tutorial on optimal control and reinforcement learning methods for quantum technologies.Physics Letters A, 2022

    work page 2022

  4. [4]

    Paladino, Y.M

    E. Paladino, Y.M. Galperin, G. Falci, and B.L. Altshuler. 1/fnoise: Implications for solid-state quantum information.Reviews of Modern Physics 86, 361, 2014

    work page 2014

  5. [5]

    Quantum control in the presence of strongly coupled non-markovian noise.arXiv, 2024

    Arinta Auza, Akram Youssry, Gerardo Paz-Silva, and Alberto Peruzzo. Quantum control in the presence of strongly coupled non-markovian noise.arXiv, 2024

    work page 2024

  6. [6]

    Hakonen, and Elisabetta Paladino

    Giuseppe Falci, Pertti J. Hakonen, and Elisabetta Paladino. 1/fnoise in quantum nanoscience.Encyclopedia of Condensed Matter Physics - Volume 1, pages 1003- 1017, 2023

    work page 2023

  7. [7]

    Decoherence in qubits due to low- frequency noise.New J

    J Bergli, Y M Galperin, and B L Altshuler. Decoherence in qubits due to low- frequency noise.New J. Phys., 11(2):025002, February 2009

    work page 2009

  8. [8]

    Paladino, L

    E. Paladino, L. Faoro, and G. Falci. Decoherence Due to Discrete Noise in Josephson Qubits. In Bernhard Kramer, editor,Advances in Solid State Physics, pages 747–

    work page

  9. [9]

    Springer, Berlin, Heidelberg, 2003

    work page 2003

  10. [10]

    Paladino, L

    E. Paladino, L. Faoro, G. Falci, and Rosario Fazio. Decoherence and 1 / f Noise in Josephson Qubits.Phys. Rev. Lett., 88(22):228304, May 2002

    work page 2002

  11. [11]

    Otterpohl , author P

    Florian Otterpohl, Peter Nalbach, Elisabetta Paladino, Giuseppe A. Falci, and Michael Thorwart. Quantum 1/f η Noise Induced Relaxation in the Spin-Boson Model, July 2025. arXiv:2507.14329 [quant-ph]

    work page arXiv 2025

  12. [12]

    D’Arrigo, A

    A. D’Arrigo, A. Mastellone, E. Paladino, and G. Falci. Effects of low-frequency noise cross-correlations in coupled superconducting qubits.New J. Phys., 10(11):115006, November 2008

    work page 2008

  13. [13]

    Open- loop quantum control of small-size networks for high-order cumulants and cross- correlations sensing.Sci Rep, 14(1):16681, July 2024

    Antonio D’Arrigo, Giulia Piccitto, Giuseppe Falci, and Elisabetta Paladino. Open- loop quantum control of small-size networks for high-order cumulants and cross- correlations sensing.Sci Rep, 14(1):16681, July 2024. Publisher: Nature Publishing Group

    work page 2024

  14. [14]

    Dario Fasone, Shreyasi Mukherjee, Dario Penna, Fabio Cirinn` a, Mauro Paternos- tro, Elisabetta Paladino, Luigi Giannelli, and Giuseppe A. Falci. Detection of noise correlations in two qubit systems by Machine Learning, September 2025. arXiv:2509.03389 [quant-ph]. 5

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  15. [15]

    Falci, A

    G. Falci, A. D’Arrigo, A. Mastellone, and E. Paladino. Dynamical suppression of telegraph and 1/fnoise due to quantum bistable fluctuators.Phys. Rev. A, 70(4):040101, October 2004. Publisher: American Physical Society. 6

    work page 2004