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arxiv: 1906.10175 · v1 · pith:KPIT5N2Cnew · submitted 2019-06-21 · 🪐 quant-ph

Machine learning methods in quantum computing theory

D. V. Fastovets , Yu. I. Bogdanov , B. I. Bantysh , V. F. Lukichev This is my paper

Pith reviewed 2026-05-25 19:02 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum machine learningquantum tomographytree tensor networkneural networksnoise mitigationhybrid quantum-classical methodsIBM quantum processor
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The pith

Neural networks can reconstruct quantum states from measurement data while excluding noise influence.

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

The paper explores hybrid classical-quantum machine learning approaches that apply classical algorithms to quantum data and problems. It introduces a multiclass tree tensor network algorithm and tests it on an IBM quantum processor. It also presents a neural network method for quantum tomography that predicts the true quantum state without noise effects from the measurements. These techniques seek to identify hidden links between input data and output results in quantum experiments. A sympathetic reader would value them as practical tools for dealing with noise in real quantum hardware.

Core claim

The authors show that neural networks trained on quantum measurement outcomes can predict the underlying quantum state while excluding noise influence, and that a multiclass tree tensor network algorithm can be implemented and tested on quantum processors for classification tasks.

What carries the argument

Neural network trained to separate true quantum state signal from noise in measurement outcomes.

If this is right

  • The tomography method can be applied in various experiments to reveal latent dependence between input data and output measurement results.
  • Hybrid classical-quantum methods can analyze quantum states directly rather than classical data alone.
  • Tree tensor network algorithms enable multiclass classification tasks on available quantum processors.

Where Pith is reading between the lines

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

  • Noise-excluding tomography may allow more accurate state reconstruction on noisy intermediate-scale devices without requiring full noise model calibration.
  • The hybrid approach could extend to other quantum tasks such as parameter estimation or circuit optimization under realistic noise.
  • Demonstration on IBM hardware indicates these methods are feasible on current cloud-accessible quantum computers.

Load-bearing premise

The neural network can be trained to separate the true quantum state signal from noise in measurement outcomes without the separation relying on post-hoc data selection or assumptions about the noise model that are not independently validated.

What would settle it

Prepare known quantum states on hardware, add controlled noise with independently measured parameters, feed the outcomes to the trained network, and check whether the output states match the known inputs when noise strength or type is varied.

Figures

Figures reproduced from arXiv: 1906.10175 by B. I. Bantysh, D. V. Fastovets, V. F. Lukichev, Yu. I. Bogdanov.

Figure 2
Figure 2. Figure 2: Quantum circuit of quantum minimization algorithm. Firstly, we randomly select point 1 x and set threshold y f x 11    using minimized function f . Next, we apply Hadamard (see [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Training and test datasets (4 classes) used for modeling quantum KNN algorithm [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Confusion matrices for different values of SWAP-test iterations and QMA iterations. Let n - training set size, m - test set size, k - number of clusters and d - space dimension. Then, classical KNN computational complexity is O nm k d     . Quantum approaches can improve this value. The quantum KNN complexity is O nm k d    log  . Here we can see the computational advantage. But if we take into a… view at source ↗
Figure 6
Figure 6. Figure 6: Unlabeled dataset with 4 classes. Our clusterization results (using quantum version of k-means algorithm) are shown on [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Clusterization results for different values of SWAP-test iterations and QMA iterations [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: Parameterized TTN quantum circuit for Fisher’s iris dataset. All parameters           1 2 3 4 5 6 7 , , , , , ,  are optimized to correctly classify training dataset (usually represented by 70% of the original dataset). Such result obtains by loss function minimization     2 1 r L y y ii i     , (5) where r is a training set size. Loss function usually optimized by stochastic gradient … view at source ↗
Figure 11
Figure 11. Figure 11: Training process: loss function optimization. Using other nr  vectors (test set) allows us to obtain accuracy of models. Accuracy is a basic metric for evaluating classification models. Therefore, accuracy is the fraction of predictions our model got right. In our case, accuracy between setosa and versicolor classes is A  1 , between setosa and virginica classes is A  1 too, and between versicolor and … view at source ↗
Figure 12
Figure 12. Figure 12: Generalized TTN circuit for 3-class classification [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Neurotomography and MLE tomography comparison. Number of experiments: 2000. Sample size: 105 . The basic tomography methods, developed in our laboratory [21,22] (based on maximum likelihood estimation (MLE)) work better then neural network approach (Fig. 13a). But it is true for ideal quantum systems. Neurotomography allows us to reconstruct quantum state amplitudes in noisy quantum systems also (without … view at source ↗
read the original abstract

Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. The quantum machine learning includes hybrid methods that involve both classical and quantum algorithms. Quantum approaches can be used to analyze quantum states instead of classical data. On other side, quantum algorithms can exponentially improve classical data science algorithm. Here, we show basic ideas of quantum machine learning. We present several new methods that combine classical machine learning algorithms and quantum computing methods. We demonstrate multiclass tree tensor network algorithm, and its approbation on IBM quantum processor. Also, we introduce neural networks approach to quantum tomography problem. Our tomography method allows us to predict quantum state excluding noise influence. Such classical-quantum approach can be applied in various experiments to reveal latent dependence between input data and output measurement results.

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 / 1 minor

Summary. The manuscript surveys intersections between classical machine learning and quantum computing, outlines basic ideas of quantum machine learning, presents a multiclass tree tensor network algorithm with an experimental demonstration on an IBM quantum processor, and introduces a neural-network approach to quantum state tomography that is claimed to predict the underlying quantum state while excluding the influence of noise.

Significance. If the neural-network tomography method can be shown to separate signal from noise without relying on post-hoc selection or unvalidated noise-model assumptions, the result would be of interest for practical quantum state reconstruction on noisy hardware; the tree-tensor-network demonstration on IBM hardware is a standard but useful benchmark exercise. The manuscript does not supply the technical detail needed to evaluate either claim.

major comments (2)
  1. [Abstract] Abstract: the central claim that the neural-network tomography method 'allows us to predict quantum state excluding noise influence' is presented without any description of training-data construction (e.g., whether paired noisy/noiseless measurements are used), loss function, network architecture, or any test that the learned mapping remains accurate under noise statistics different from the training distribution. This leaves the claimed noise-exclusion capability unassessable.
  2. [Abstract] Abstract / methods: no equations, dataset sizes, error bars, or comparison baselines are supplied for either the tree-tensor-network multiclass algorithm or the tomography network, making it impossible to verify the reported IBM-hardware demonstration or the tomography performance.
minor comments (1)
  1. [Abstract] Abstract contains several grammatical issues ('among of the most', 'On other side') that should be corrected for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed comments. We address each major point below and will revise the manuscript to supply the requested technical details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the neural-network tomography method 'allows us to predict quantum state excluding noise influence' is presented without any description of training-data construction (e.g., whether paired noisy/noiseless measurements are used), loss function, network architecture, or any test that the learned mapping remains accurate under noise statistics different from the training distribution. This leaves the claimed noise-exclusion capability unassessable.

    Authors: We agree that the abstract lacks these specifics. In revision we will expand both the abstract and main text to describe the training-data construction (paired noisy and noiseless measurement sets), the loss function, network architecture, and explicit tests of generalization to unseen noise distributions, thereby making the noise-exclusion claim assessable. revision: yes

  2. Referee: [Abstract] Abstract / methods: no equations, dataset sizes, error bars, or comparison baselines are supplied for either the tree-tensor-network multiclass algorithm or the tomography network, making it impossible to verify the reported IBM-hardware demonstration or the tomography performance.

    Authors: We acknowledge that the submitted version omits these quantitative elements. The revised manuscript will include the defining equations for both the multiclass tree-tensor-network algorithm and the neural-network tomography method, together with dataset sizes, error bars on the IBM-processor results, and baseline comparisons to permit verification. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain; claims rest on empirical NN performance without self-referential reduction

full rationale

The paper introduces a neural-network tomography method claimed to predict quantum states while excluding noise, along with a tree tensor network algorithm tested on IBM hardware. No equations, parameter-fitting procedures, or derivation steps are exhibited that reduce a 'prediction' to a fitted input by construction. No self-citations, uniqueness theorems, or ansatzes imported from prior author work appear in the provided text. The central claim is an empirical assertion about NN training outcomes rather than a mathematical derivation that collapses to its own inputs; therefore the work is self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities. The central claims rest on the unstated assumption that the described algorithms function as claimed on real hardware and that noise can be excluded via the neural network without further specification.

pith-pipeline@v0.9.0 · 5692 in / 1171 out tokens · 21553 ms · 2026-05-25T19:02:01.770933+00:00 · methodology

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Reference graph

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