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arxiv: 2602.09733 · v2 · submitted 2026-02-10 · 🪐 quant-ph

Error-mitigated quantum state tomography using neural networks

Yixuan Hu , Mengru Ma , Jiangwei Shang This is my paper

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

classification 🪐 quant-ph
keywords quantum state tomographyneural networkserror mitigationsupervised learningquantum informationnoise reductionmultilayer perceptronstate reconstruction
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The pith

Neural network tomography mitigates unknown noise in quantum state reconstruction without explicit models.

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

The paper proposes a quantum state tomography method that uses multilayer perceptron networks to reduce the impact of experimental noise on reconstructed states. Training occurs via supervised learning on simulated noisy data, so the approach requires no specific noise model or measurement assumptions. Simulations test the method on pure states through random mixed states and show higher accuracy than unmitigated tomography. The data-driven design makes it scalable and applicable to general quantum systems. This addresses a core barrier to reliable characterization in real devices where noise is pervasive but hard to model exactly.

Core claim

A scalable tomography method based on multilayer perceptron networks mitigates unknown noise through supervised learning. This approach is data-driven and thus does not rely on explicit assumptions about the noise model or measurement, making it readily extendable to general quantum systems. Numerical simulations, ranging from special pure states to random mixed states, demonstrate that the proposed method effectively mitigates noise across a broad range of scenarios, compared with the case without mitigation.

What carries the argument

Multilayer perceptron networks trained by supervised learning on simulated noisy measurement data to output denoised quantum state estimates.

If this is right

  • Accurate state estimation becomes feasible on noisy quantum hardware without needing to characterize the noise source first.
  • The method extends to larger systems because it avoids explicit noise modeling and scales with available simulation data.
  • Reconstructed states achieve higher fidelity in scenarios ranging from pure to mixed, improving downstream tasks that depend on state knowledge.
  • The approach works across diverse noise types since it learns from data rather than assuming a fixed model.
  • It provides a practical route to tomography on near-term devices where noise is dominant but unknown in detail.

Where Pith is reading between the lines

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

  • The same supervised-learning structure could be adapted to quantum process tomography or other characterization tasks by changing the input-output pairs.
  • Hardware-specific training data generated from detailed device simulations might further boost performance on particular platforms.
  • Combining the network output with existing error-correction protocols could reduce the overhead needed for reliable quantum computation.
  • The method might serve as a post-processing layer for data collected from other tomography protocols, such as compressed sensing approaches.

Load-bearing premise

Training the network on simulated noisy data will allow it to generalize and mitigate noise in actual experimental measurements without any explicit noise model or measurement assumptions.

What would settle it

Apply the trained network to real experimental tomography data from a quantum device, then compare the fidelity of the reconstructed state against a high-precision reference measurement or known ground truth to check whether accuracy improves over standard tomography.

read the original abstract

The reliable characterization of quantum states is a fundamental task in quantum information science. For this purpose, quantum state tomography provides a standard framework for reconstructing quantum states from measurement data, yet it is often degraded by experimental noise. Mitigating such noise is therefore essential for the accurate estimation of the states in realistic settings. In this work, we propose a scalable tomography method based on multilayer perceptron networks that mitigate unknown noise through supervised learning. This approach is data-driven and thus does not rely on explicit assumptions about the noise model or measurement, making it readily extendable to general quantum systems. Numerical simulations, ranging from special pure states to random mixed states, demonstrate that the proposed method effectively mitigates noise across a broad range of scenarios, compared with the case without mitigation.

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 proposes a data-driven quantum state tomography method that uses a multilayer perceptron trained via supervised learning on simulated noisy measurement data to mitigate unknown noise without requiring an explicit noise model or measurement assumptions. Numerical simulations spanning special pure states to random mixed states are presented to show improved state reconstruction fidelity relative to standard tomography without mitigation.

Significance. If the generalization from simulation to experiment holds, the approach could offer a scalable, model-free tool for accurate state estimation on noisy quantum hardware, reducing reliance on detailed noise characterization and extending readily to larger systems. The explicit use of supervised learning on simulated data is a clear methodological strength, though its practical impact hinges on transferability.

major comments (2)
  1. [Numerical simulations] Numerical simulations section: the central claim of effective noise mitigation across pure and mixed states rests on these runs, yet the manuscript provides insufficient detail on network architecture (layer count, neuron sizes), training procedure (loss function, optimizer, dataset generation), and quantitative metrics (fidelity or trace-distance improvements with error bars), preventing assessment of whether results are robust or tied to specific simulation conditions.
  2. [Method and results] Method and results sections: the load-bearing assumption that a network trained solely on simulated noisy tomography data will generalize to real experimental measurements (without explicit noise models) is unvalidated; no tests with mismatched noise (e.g., unmodeled crosstalk, calibration drift, or non-Markovian effects) or actual hardware data are reported, which directly limits the model-free applicability claim.
minor comments (2)
  1. The description of input/output dimensions for the perceptron relative to the number of measurement settings could be clarified with an explicit equation or diagram.
  2. [Introduction] A few references to prior neural-network tomography works appear missing or under-cited in the introduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We have revised the manuscript to address the major comments on numerical details and have added explicit discussion of the simulation-to-experiment gap. Below we respond point by point.

read point-by-point responses

  1. Referee: [Numerical simulations] Numerical simulations section: the central claim of effective noise mitigation across pure and mixed states rests on these runs, yet the manuscript provides insufficient detail on network architecture (layer count, neuron sizes), training procedure (loss function, optimizer, dataset generation), and quantitative metrics (fidelity or trace-distance improvements with error bars), preventing assessment of whether results are robust or tied to specific simulation conditions.

    Authors: We agree that the original manuscript lacked sufficient implementation details for reproducibility. In the revised version we have expanded the Numerical simulations section with: (i) the exact multilayer perceptron architecture (3 hidden layers with 256, 128 and 64 neurons, ReLU activations, linear output); (ii) training details (Adam optimizer with learning rate 10^{-3}, mean-squared-error loss on the vectorized density-matrix elements, 10^5 training samples generated from random pure and mixed states with simulated depolarizing and amplitude-damping noise); (iii) quantitative results reported as mean fidelity and trace distance over 100 independent runs, each with standard-error bars. These additions allow direct assessment of robustness. revision: yes

  2. Referee: [Method and results] Method and results sections: the load-bearing assumption that a network trained solely on simulated noisy tomography data will generalize to real experimental measurements (without explicit noise models) is unvalidated; no tests with mismatched noise (e.g., unmodeled crosstalk, calibration drift, or non-Markovian effects) or actual hardware data are reported, which directly limits the model-free applicability claim.

    Authors: We acknowledge that the present work contains only numerical simulations and does not demonstrate transfer to real hardware or to deliberately mismatched noise models. This is a genuine limitation of the current study, which is intended as a controlled proof-of-concept for the data-driven approach. In the revised manuscript we have added a dedicated paragraph in the Discussion section that explicitly states this limitation, quantifies the simulation noise models used, and outlines the experimental validation steps required for future work. The core methodological claim—that the network learns a mapping without an explicit noise model—remains supported by the simulation results. revision: partial

Circularity Check

0 steps flagged

No circularity: method is a standard supervised NN trained and evaluated on separate simulated datasets

full rationale

The paper describes a multilayer perceptron trained via supervised learning on simulated noisy tomography data to map to quantum states, with performance shown on separate numerical simulations from pure states to random mixed states. No derivation step reduces by construction to its inputs: the network parameters are fitted on training simulations and then applied to distinct test simulations, which is standard non-circular ML evaluation. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked as load-bearing; the approach is explicitly data-driven without explicit noise models. The central claim therefore rests on independent simulation benchmarks rather than any self-referential fit or renaming.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that supervised learning on simulated data can learn a general noise-mitigation mapping without explicit noise models. No free parameters are named because architecture and training details are absent from the abstract. No new physical entities are introduced.

free parameters (1)
  • Neural network weights and biases
    Learned during supervised training on simulated noisy versus ideal data; exact count and initialization not specified.
axioms (1)
  • domain assumption Supervised learning on simulated data suffices to mitigate unknown experimental noise without any noise model assumptions
    Invoked in the description of the data-driven method that 'does not rely on explicit assumptions about the noise model or measurement'.

pith-pipeline@v0.9.0 · 5421 in / 1288 out tokens · 40673 ms · 2026-05-16T05:18:52.028087+00:00 · methodology

discussion (0)

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