Image classification via a quantum-inspired strategy involving a mixture of experts

Apoorva D. Patel; Kumari Jyoti; Rohith Babu

REVIEW 3 major objections 4 minor 17 references

A quantum-inspired mixture of experts halves image-classification failure rates versus classical diffusion-plus-pooling on MNIST and Fashion-MNIST.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-10 19:06 UTC pith:6J6NH54H

load-bearing objection Solid hybrid pipeline with a real joint-vs-independent expert result, but the factor-of-two claim rests on a deliberately weak classical diffuser, not competitive CNNs. the 3 major comments →

arxiv 2607.07754 v1 pith:6J6NH54H submitted 2026-07-08 cs.LG quant-ph

Image classification via a quantum-inspired strategy involving a mixture of experts

Kumari Jyoti , Rohith Babu , Apoorva D. Patel This is my paper

classification cs.LG quant-ph

keywords supervised machine learningquantum-inspired algorithmmixture of expertsamplitude encodingunitary convolutionstabiliser codeimage classificationMNIST

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that classical CNN-style feature extraction loses too much information through diffusion-based smearing and block-wise pooling. It replaces those steps with amplitude encoding of images into few-qubit states, non-lossy local unitary convolution performed by multiple experts with different smearing parameters, and syndrome extraction from a quantum stabilizer code. The resulting compact features are fed jointly into a fully connected network. On the standard MNIST and Fashion-MNIST benchmarks the joint-expert version roughly halves the class-prediction failure rate relative to a classical diffusion baseline while only moderately increasing GPU runtime, and joint decisions consistently beat independent majority-vote experts. The authors present this hybrid pipeline as a practical alternative that can also be executed on a quantum processor.

Core claim

Joint analysis of features produced by multiple experts—each applying distinct unitary-smearing parameters to amplitude-encoded images and extracting [[5,1,3]] stabilizer syndromes—outperforms both independent experts and classical diffusion-plus-block-pooling, cutting image-class prediction failure rates by about a factor of two on MNIST (≈97.6 % vs ≈95 %) and Fashion-MNIST (≈86 % vs ≈76–77 %) with only moderate computational overhead.

What carries the argument

Quantum Mixture of Experts (QMoE): amplitude-encoded 10-qubit image states are unitarily smeared by even-odd local unitaries whose parameters label distinct experts; each expert’s 16 stabilizer-syndrome expectation values become the compact features that a classical fully-connected network then classifies jointly.

Load-bearing premise

The classical baseline of nearest-neighbor diffusion with a single scalar rate and fixed 3-by-3 weighted pooling is taken as representative of existing classical schemes, so that beating it establishes practical superiority.

What would settle it

Replace the classical baseline with a modern multi-layer CNN of comparable parameter count and depth; if the quantum-inspired pipeline no longer reduces failure rate by roughly half, the claimed practical advantage disappears.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Solid hybrid pipeline with a real joint-vs-independent expert result, but the factor-of-two claim rests on a deliberately weak classical diffuser, not competitive CNNs.

read the letter

The useful core here is the specific stack: thresholded amplitude encoding of 32×32 images into 10 qubits, even/odd local unitary smearing with experts whose θ ranges are clamped, [[5,1,3]] syndrome expectations as the 16 pooling features per expert/layer, then a joint FCL on the concatenated features. That combination is not in the two QMoE papers they cite, and the joint-vs-independent comparison is clean and consistent: joint wins, and the numbers (≈97.6% MNIST, ≈86% Fashion-MNIST at the chosen N_exp/N_lyr points) are internally coherent with the confusion matrices.

They also give an explicit gate-level appendix for the unitary blocks, coordinate shifts, and syndrome extraction, so the quantum-inspired claim is not hand-wavy. GPU overhead is moderate, which matches what they report.

The soft spot is exactly the one the stress-test flags, and it is load-bearing for the abstract’s “practical alternative / factor-of-two failure-rate reduction” language. Their classical baseline is nearest-neighbor diffusion with a single α, T≈1, and fixed 3×3 weighted pooling down to 16 features. That is a fair ablation of the classical analogue of their own pipeline, but it is not a competitive CNN. Modern shallow nets already sit well above their quantum numbers on both datasets, so the headline practical claim does not survive a stronger baseline. No error bars, no seeds, no code release—standard for this venue but still a gap.

Everything else is proportionate: free parameters are declared, circularity is low, citations are honest. This is for people who care about hybrid feature extractors and stabilizer-as-pooling ideas, not for anyone looking for SOTA image classification. I would send it to referees; they will force a stronger baseline and a clearer framing, but the joint-expert and syndrome design are worth the time. Engage if that is your lane; otherwise skim the appendix and move on.

Referee Report

3 major / 4 minor

Summary. The paper introduces a hybrid classical–quantum-inspired image classifier. Grey-scale images are thresholded and amplitude-encoded into 10-qubit states; local unitary convolutions (even/odd bipartite mixing controlled by angles θ) are applied by multiple experts with distinct θ intervals; 16 features per expert per layer are extracted as expectation values of the four [[5,1,3]] stabilizer generators on each axis; these features are jointly fed to a fully-connected network (512-256-128-10) for 10-class prediction. On MNIST and Fashion-MNIST the joint-expert pipeline is reported to outperform both independent experts and a classical diffusion-plus-3 imes3-pooling baseline, roughly halving the failure rate (optimal points ~97.6 % vs ~95 % MNIST, ~86 % vs ~76–77 % Fashion-MNIST) at moderate GPU cost; an appendix sketches a quantum-processor realization of the unitary and stabilizer stages.

Significance. If the reported gains survive stronger classical baselines, the work would supply a concrete, implementable demonstration that non-lossy unitary smearing, stabilizer-code syndromes, and joint multi-expert analysis can improve feature extraction relative to simple diffusion/pooling inside a CNN-style pipeline. Systematic sweeps of N_exp and N_lyr, confusion matrices, joint-versus-independent comparisons, and explicit quantum-circuit decompositions are genuine strengths that make the proposal reproducible and extensible. The practical-alternative claim, however, currently rests on a deliberately simplified classical baseline, so the significance for the broader machine-learning community remains conditional on that comparison being strengthened or the claim being appropriately narrowed.

major comments (3)

[Abstract, §III.C–D, Table II] Abstract, §III.C–D and Table II: the central claim that the method “reduces the failure rate y around a factor of two” and is therefore “a practical alternative to existing classical schemes” is supported solely by comparison with a hand-crafted classical baseline (nearest-neighbour diffusion with scalar α, T=1, fixed 3 imes3 weighted pooling to 16 features). Modern CNNs (even shallow ones with learned kernels) routinely exceed 99 % on MNIST and 92–94 % on Fashion-MNIST; against those numbers the reported 97.6 % / 86.2 % no longer constitute a factor-of-two reduction. Either add competitive CNN baselines with comparable feature budgets or reframe the claim to “outperforms a simple diffusion baseline.”
[§III, Tables I–II] §III and Tables I–II: all accuracies are single-run point estimates with no error bars, multiple random seeds, or statistical tests. The joint-versus-independent and quantum-versus-classical gaps are therefore difficult to assess for significance, especially given the many free parameters (θ intervals, N_exp, N_lyr, FCL hyper-parameters). At least three independent seeds with standard deviations should be reported for the headline configurations.
[§II.E] §II.E: the text states that “we perform a binary classification analysis … and repeat that for each of the 10 classes,” yet the network ends with a 10-way softmax, CrossEntropyLoss is used, and all confusion matrices are 10 imes10 multi-class. The description and the actual training objective are inconsistent; clarify whether one-versus-rest or true multi-class training was performed.

minor comments (4)

[Figs. 4–15] Figs. 4–5 and 6–15: captions and axis labels are sparse; numerical values of θ, N_exp and N_lyr should appear in every panel so that the figures are self-contained.
[§II.A, Eq. (1)] Eq. (1) and §II.A: the binarization threshold that converts grey-scale pixels to ±1 is never stated; a short sensitivity check would be useful.
[Appendix] Appendix circuits (Figs. 16–17): gate counts and ancilla overhead for the full multi-layer, multi-expert pipeline are not estimated; a brief resource table would help readers judge near-term feasibility.
[throughout] Typographical: “stabiliser”/“stabilizer” spelling is mixed; “28times28” appears once; the manuscript date is listed as July 2026.

Circularity Check

1 steps flagged

No significant circularity: performance claims are empirical test-set measurements on external benchmarks; only a minor non-load-bearing self-citation of the unitary-smearing subroutine.

specific steps

self citation load bearing [§II.B (Convolutional Smearing), Eqs. (3)–(6) and citation [11]]
"Instead, we process the quantum image states by a non-lossy unitary smearing, using the transformation described in [11]. Local unitary smearing can be carried out for a hypercubic structure in any dimension, by a bipartite splitting of the data into even and odd subsets…"

The concrete 4 imes4 Hamiltonians and the even/odd unitary operators U_o(e) are taken from prior work whose author list overlaps the present paper. This is a methodological self-citation, not a load-bearing uniqueness claim: the operators merely define the smearing subroutine; the accuracy numbers that constitute the paper's main result are measured independently on test data and do not reduce to the citation by construction.

full rationale

The paper's central claims (joint experts outperform independent experts; failure rate roughly halved vs. classical diffusion+pooling on MNIST/Fashion-MNIST) are obtained by training variational parameters (θ intervals, FCL weights) on the labeled training split and evaluating accuracy/confusion matrices on the held-out test split. These quantities are not forced by construction from any fitted constant or definitional identity; they are ordinary supervised-learning measurements against public external data. The classical baseline (scalar-α diffusion, fixed 3×3 pooling) is deliberately simple, but that is a strength-of-evidence issue, not circularity. The sole self-reference is the adoption of the even-odd unitary blocks from the authors' earlier quantum-walk paper [11]; that citation supplies a concrete 4×4 gate, not a uniqueness theorem or a numerical prediction that is later re-used as input. No equation equates a reported accuracy gain to a fitted parameter by definition, no ansatz is smuggled as a theorem, and no result is a renaming of a known empirical pattern. Hence the derivation chain is self-contained against external benchmarks and scores at most 1.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 1 invented entities

The accuracy claims rest on standard ML training assumptions plus several design choices treated as fixed: thresholded amplitude encoding, the particular even/odd unitary mixers, the [[5,1,3]] code as feature map, and a weak classical diffusion baseline. Free parameters include expert θ ranges, layer counts, and FCL hyperparameters fitted on the same benchmarks. No new physical particles or forces are invented; ‘experts’ are parameter clones of the same unitary pipeline.

free parameters (5)

Expert smear angles θ_i (and per-layer θ)
Clamped in [(i−1)π/N_exp, iπ/N_exp] and optimized via FCL backprop; central to multi-expert performance.
N_exp and N_lyr
Grid-searched; optimal points (e.g. 16×16 MNIST, 18×16 Fashion-MNIST) chosen from accuracy heatmaps on the same datasets.
Classical diffusion rate α and steps T
Baseline tuned (α∈{0.5,1.0,1.5}, T=1–10); best classical numbers used for comparison.
FCL architecture and training hyperparameters
512→256→128→10, dropout 0.2, batch norm, Adam lr 0.002, label smoothing 0.05, 30 epochs—chosen experimentally.
Binarization threshold for grey-scale → ±1
Unspecified numerical threshold; maps continuous pixels to c_{x,y}=±1 before amplitude encoding.

axioms (5)

domain assumption Amplitude encoding of thresholded 32×32 images into a normalized 10-qubit state is a valid lossless embedding of the binarized image for subsequent unitary processing.
§II.A Eq. (1); discards grey levels and assumes binarized structure suffices for class labels.
domain assumption Local even/odd unitary mixers U_o, U_e with real c,s parameters implement non-lossy convolutional smearing that preserves classification-relevant structure better than discrete Laplacian diffusion.
§II.B Eqs. (3)–(6); load-bearing for claiming less information degradation than classical diffusion.
ad hoc to paper Expectation values of the four [[5,1,3]] stabilizer generators on each axis yield 16 features sufficient for 10-class discrimination after FCL.
§II.D; replaces pooling by construction; logical-qubit feature is ignored.
domain assumption Standard supervised learning on MNIST/Fashion-MNIST with CrossEntropyLoss and Adam yields generalizable accuracy comparisons.
§II.E–III; usual ML training assumptions.
standard math Linear algebra of Pauli operators, unitary evolution, and stabilizer codes as in standard quantum information texts.
Used throughout §II and Appendix; Preskill notes [12], DiVincenzo–Shor [14].

invented entities (1)

Quantum Mixture of Experts (this paper’s QMoE pipeline) no independent evidence
purpose: Multiple unitary-smearing experts with distinct θ, joint FCL over concatenated stabilizer features.
Named framework combining known pieces; related QMoE works exist [7,8] but this stabilizer+unitary stack is paper-specific. Not a new physical object.

pith-pipeline@v1.1.0-grok45 · 15886 in / 3686 out tokens · 43449 ms · 2026-07-10T19:06:32.236368+00:00 · methodology

0 comments

read the original abstract

Pattern recognition problems arise in a variety of physical image processing situations, and convolutional neural networks are a popular scheme for the required feature extraction and classification tasks. The classical networks use diffusion-based smearing and block-wise pooling to downsample the image data and capture important structural features. In this work, we propose and demonstrate a more efficient quantum-inspired strategy involving a mixture of experts. It is a hybrid classical-quantum framework. The quantum part consists of amplitude encoding of the images, convolution using local unitary operations, multiple experts processing the same image with different parameters, and feature extraction using quantum stabiliser codes. The classical part then jointly processes the features extracted by different experts using a standard fully connected neural network for image class prediction. Using MNIST and Fashion-MNIST datasets as benchmarks, we demonstrate that the joint expert analysis outperforms the individual expert one, as well as reduces the failure rate of image class prediction by around a factor of two. The overhead of our quantum-inspired strategy is only moderate on GPU workstations, which makes our proposal a practical alternative to existing classical schemes. We also point out how the quantum part of our framework can be executed on a quantum processor.

Figures

Figures reproduced from arXiv: 2607.07754 by Apoorva D. Patel, Kumari Jyoti, Rohith Babu.

**Figure 2.** Figure 2: FIG. 2. Pixel weights for classical pooling using a 3 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Confusion matrix for the MNIST dataset in case of classical diffusion with [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Unitary convolution of MNIST images for 3 layers, with [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Unitary convolution of Fashion-MNIST images for 3 layers, with [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Quantum joint expert performance for the test [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Heatmap for quantum joint expert performance for [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Confusion matrix for the optimal quantum joint expert analysis of the MNIST test dataset [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12. Quantum joint expert performance for the test Fash [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14. Heatmap for quantum joint expert performance for [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15. Confusion matrix for the optimal quantum joint expert analysis of Fashion-MNIST test dataset [PITH_FULL_IMAGE:figures/full_fig_p010_15.png] view at source ↗

**Figure 16.** Figure 16: FIG. 16. Two-qubit logic gate circuit for the operator [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗

**Figure 17.** Figure 17: FIG. 17. Reversible logic circuit for adding 1 to (left) and subtracting 1 from (right) a 5-qubit register. They are inverses of [PITH_FULL_IMAGE:figures/full_fig_p013_17.png] view at source ↗

**Figure 18.** Figure 18: FIG. 18. Block circuit diagram for the full multi-expert image classification algorithm [PITH_FULL_IMAGE:figures/full_fig_p014_18.png] view at source ↗

discussion (0)

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages · 6 internal anchors

[1]

for loops

For the MNIST dataset, the test accuracy peaked at a 95.02% forα= 1.5, and was worse at 94.62% forα= 1.0 and 93.27% forα= 0.5. For the Fashion-MNIST dataset, the test accuracy remained smaller, around 76%. A particular example of the confusion matrix, which specifies misidentified class labels, is shown in Fig. 3. Results for classification accuracy for d...

work page
[2]

6 and 7 in graphical form and in Figs

MNIST Dataset Our classification accuracy results for the training and test datasets, while varyingN exp andN lyr, are presented in Figs. 6 and 7 in graphical form and in Figs. 8 and 9 as heatmaps. Going up from small values ofN exp andN lyr, the classification accuracy initially increases substantially but then levels off. Giving more emphasis to the tes...

work page
[3]

Quantum Algorithms and Simulations

Fashion-MNIST Dataset Our classification accuracy results for the training and test datasets, while varyingN exp andN lyr, are presented in Figs. 11 and 12 in graphical form and in Figs. 13 and 14 as heatmaps. The Fashion-MNIST dataset has more complex features than the MNIST dataset, with somewhat ambiguous shapes of spatial boundaries, and so provides a...

work page
[4]

ImageNet Classification with Deep Convolutional Neural Networks

A. Krizhevsky, I. Sutskever and G.E. Hinton, “ImageNet Classification with Deep Convolutional Neural Networks”, Ad- vances Neural Information Processing Systems (NeurIPS) 25 (2012)

work page 2012
[5]

Deep Learning

Y. LeCun, Y. Bengio and G. Hinton, “Deep Learning”, Nature 521, 436-444 (2015)

work page 2015
[6]

Quantum Convolutional Neural Networks are Effectively Classically Simulable

P. Bermejo, P. Braccia, M.S. Rudolph, Z. Holmes, L. Cincio and M. Cerezo, “Quantum Convolutional Neural Networks are Effectively Classically Simulable”, Phys. Rev. X Quantum 7, 020304 (2026)

work page 2026
[7]

Better than classical? The subtle art of benchmarking quantum machine learning models

J. Bowles, S. Ahmed and M. Schuld, “Better than Classical? The Subtle Art of Benchmarking Quantum Machine Learning Models”, [preprint arXiv:2403.07059] (2024)

work page internal anchor Pith review Pith/arXiv arXiv 2024
[8]

Advances in Machine Learning: Where Can Quantum Techniques Help?

R.K. Ramakrishnan, S. Kashyap, K. Jyoti and A.D. Patel, “Advancing in Machine Learning: Where can Quantum Techniques Help?”, [preprint arXiv:2507.08379] (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[9]

Quantum Advantage in Learning from Experiments

H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill and J.R. Mcclean, “Quantum Advantage in Learning from Experiments”, Science 376, 1182-1186 (2022)

work page 2022
[10]

QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networks

H.-Q. Nguyen et al., “QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networks”, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE), Albuquerque, NM, USA, pp. 223-228 [preprint arXiv:2507.05190] (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[11]

Solving MNIST with a globally trained Mixture of Quantum Experts

P.A.X. Tognini et al., “Solving MNIST with a Globally Trained Mixture of Quantum Experts”, [preprint arXiv:2505.14789] (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[12]

Gradient-based Learning Applied to Document Recognition

Y. LeCun, L. Bottou, Y. Bengio and P. Haffner, “Gradient-based Learning Applied to Document Recognition”, Proc. IEEE 86(11), 2278-2324 (1998). Image database: http://kaggle.com/datasets/hojjatk/mnist-dataset 12

work page 1998
[13]

Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms

H. Xiao, K. Rasul and R. Vollgraf, “Fashion-MNIST: A Novel Image Dataset for Benchmarking Machine Learning Algo- rithms”, [preprint arXiv:1708.07747] (2017). Image database: http://kaggle.com/datasets/zalando-research/fashionmnist

work page internal anchor Pith review Pith/arXiv arXiv 2017
[14]

Quantum Random Walks without a Coin Toss

A. Patel, K.S. Raghunathan and P. Rungta, “Quantum Random Walks without a Coin Toss”, Proc. Workshop on Quantum Information, Computation and Communication (QICC2005), Kharagpur, India, Allied Publishers, pp. 41-55, [preprint arXiv:0506221 (quant-ph)] (2005)

work page 2005
[15]

Chapter 7: Quantum Error Correction,

John Preskill, “Chapter 7: Quantum Error Correction,” Lecture notes for Ph219/CS219: Quan- tum Information and Computation, California Institute of Technology, 2020. Available online: https://www.preskill.caltech.edu/ph229/notes/chap7.pdf

work page 2020
[16]

Adam: A Method for Stochastic Optimization

D.P. Kingma and J. Ba, “Adam: A method for stochastic optimization”, [preprint arXiv:1412.6980] (2014)

work page internal anchor Pith review Pith/arXiv arXiv 2014
[17]

Fault-Tolerant Error Correction with Efficient Quantum Codes

D.P. DiVincenzo and P.W. Shor, “Fault-Tolerant Error Correction with Efficient Quantum Codes”, Phys. Rev. Lett. 77, 3260 (1996). APPENDIX Here we describe how various quantum-inspired parts of our algorithm can be implemented on a quantum processor. A. Amplitude Encoding We have opted for amplitude encoding of the quantum state after thresholding. That fi...

work page 1996

[1] [1]

for loops

For the MNIST dataset, the test accuracy peaked at a 95.02% forα= 1.5, and was worse at 94.62% forα= 1.0 and 93.27% forα= 0.5. For the Fashion-MNIST dataset, the test accuracy remained smaller, around 76%. A particular example of the confusion matrix, which specifies misidentified class labels, is shown in Fig. 3. Results for classification accuracy for d...

work page

[2] [2]

6 and 7 in graphical form and in Figs

MNIST Dataset Our classification accuracy results for the training and test datasets, while varyingN exp andN lyr, are presented in Figs. 6 and 7 in graphical form and in Figs. 8 and 9 as heatmaps. Going up from small values ofN exp andN lyr, the classification accuracy initially increases substantially but then levels off. Giving more emphasis to the tes...

work page

[3] [3]

Quantum Algorithms and Simulations

Fashion-MNIST Dataset Our classification accuracy results for the training and test datasets, while varyingN exp andN lyr, are presented in Figs. 11 and 12 in graphical form and in Figs. 13 and 14 as heatmaps. The Fashion-MNIST dataset has more complex features than the MNIST dataset, with somewhat ambiguous shapes of spatial boundaries, and so provides a...

work page

[4] [4]

ImageNet Classification with Deep Convolutional Neural Networks

A. Krizhevsky, I. Sutskever and G.E. Hinton, “ImageNet Classification with Deep Convolutional Neural Networks”, Ad- vances Neural Information Processing Systems (NeurIPS) 25 (2012)

work page 2012

[5] [5]

Deep Learning

Y. LeCun, Y. Bengio and G. Hinton, “Deep Learning”, Nature 521, 436-444 (2015)

work page 2015

[6] [6]

Quantum Convolutional Neural Networks are Effectively Classically Simulable

P. Bermejo, P. Braccia, M.S. Rudolph, Z. Holmes, L. Cincio and M. Cerezo, “Quantum Convolutional Neural Networks are Effectively Classically Simulable”, Phys. Rev. X Quantum 7, 020304 (2026)

work page 2026

[7] [7]

Better than classical? The subtle art of benchmarking quantum machine learning models

J. Bowles, S. Ahmed and M. Schuld, “Better than Classical? The Subtle Art of Benchmarking Quantum Machine Learning Models”, [preprint arXiv:2403.07059] (2024)

work page internal anchor Pith review Pith/arXiv arXiv 2024

[8] [8]

Advances in Machine Learning: Where Can Quantum Techniques Help?

R.K. Ramakrishnan, S. Kashyap, K. Jyoti and A.D. Patel, “Advancing in Machine Learning: Where can Quantum Techniques Help?”, [preprint arXiv:2507.08379] (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025

[9] [9]

Quantum Advantage in Learning from Experiments

H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill and J.R. Mcclean, “Quantum Advantage in Learning from Experiments”, Science 376, 1182-1186 (2022)

work page 2022

[10] [10]

QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networks

H.-Q. Nguyen et al., “QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networks”, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE), Albuquerque, NM, USA, pp. 223-228 [preprint arXiv:2507.05190] (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025

[11] [11]

Solving MNIST with a globally trained Mixture of Quantum Experts

P.A.X. Tognini et al., “Solving MNIST with a Globally Trained Mixture of Quantum Experts”, [preprint arXiv:2505.14789] (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025

[12] [12]

Gradient-based Learning Applied to Document Recognition

Y. LeCun, L. Bottou, Y. Bengio and P. Haffner, “Gradient-based Learning Applied to Document Recognition”, Proc. IEEE 86(11), 2278-2324 (1998). Image database: http://kaggle.com/datasets/hojjatk/mnist-dataset 12

work page 1998

[13] [13]

Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms

H. Xiao, K. Rasul and R. Vollgraf, “Fashion-MNIST: A Novel Image Dataset for Benchmarking Machine Learning Algo- rithms”, [preprint arXiv:1708.07747] (2017). Image database: http://kaggle.com/datasets/zalando-research/fashionmnist

work page internal anchor Pith review Pith/arXiv arXiv 2017

[14] [14]

Quantum Random Walks without a Coin Toss

A. Patel, K.S. Raghunathan and P. Rungta, “Quantum Random Walks without a Coin Toss”, Proc. Workshop on Quantum Information, Computation and Communication (QICC2005), Kharagpur, India, Allied Publishers, pp. 41-55, [preprint arXiv:0506221 (quant-ph)] (2005)

work page 2005

[15] [15]

Chapter 7: Quantum Error Correction,

John Preskill, “Chapter 7: Quantum Error Correction,” Lecture notes for Ph219/CS219: Quan- tum Information and Computation, California Institute of Technology, 2020. Available online: https://www.preskill.caltech.edu/ph229/notes/chap7.pdf

work page 2020

[16] [16]

Adam: A Method for Stochastic Optimization

D.P. Kingma and J. Ba, “Adam: A method for stochastic optimization”, [preprint arXiv:1412.6980] (2014)

work page internal anchor Pith review Pith/arXiv arXiv 2014

[17] [17]

Fault-Tolerant Error Correction with Efficient Quantum Codes

D.P. DiVincenzo and P.W. Shor, “Fault-Tolerant Error Correction with Efficient Quantum Codes”, Phys. Rev. Lett. 77, 3260 (1996). APPENDIX Here we describe how various quantum-inspired parts of our algorithm can be implemented on a quantum processor. A. Amplitude Encoding We have opted for amplitude encoding of the quantum state after thresholding. That fi...

work page 1996