Devanagari Digit Recognition using Quantum Machine Learning

Sahaj Raj Malla

REVIEW 4 major objections 4 minor 17 references

Devanagari Digit Recognition using Quantum Machine Learning

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A hybrid CNN and 10-qubit variational circuit reaches 99.80% accuracy on Devanagari handwritten digits, the first quantum benchmark for this script.

desk verdict First QML benchmark on Devanagari digits, but the central quantum-advantage claim is unsupported because the hybrid adds a 2.1M-parameter projection that the classical baseline lacks. read the letter →

arxiv 2506.09069 v1 pith:WTVLLLX5 submitted 2025-06-08 quant-ph cs.CVcs.LG

Sahaj Raj Malla This is my paper

classification quant-phcs.CVcs.LG

keywords quantummachinelearninghybridquantum-classicalmodelsvariationalcircuitshandwrittendigitrecognitionDevanagariconvolutionalneuralnetworksamplitudeembeddingDHCD

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to establish that a hybrid quantum-classical model can set a new benchmark for recognizing handwritten Devanagari digits, a script used by hundreds of millions of people but with scarce annotated data. The proposed architecture combines a four-layer convolutional network that extracts 2048 spatial features with a 10-qubit variational quantum circuit that performs amplitude-embedded classification. On the Devanagari Handwritten Character Dataset digit subset, the model reports 99.80% test accuracy, 0.2893 test loss, and an average per-class F1-score of 0.9980, surpassing its classical CNN ablation at 99.03% while using only 100 trainable quantum parameters. If the attribution of that gain to the quantum circuit holds, this is the first demonstration that variational quantum circuits help in a low-resource regional-script recognition task.

What carries the argument

The load-bearing mechanism is a 10-qubit variational quantum circuit (VQC) with amplitude embedding. A normalized 1024-dimensional vector, obtained by a learned linear projection of the CNN's 2048 spatial features, is encoded as the amplitudes of the computational basis states. Five variational layers then apply per-qubit RY and RZ rotations followed by a ring of CNOT entangling gates, and the circuit outputs expectation values of ten single-qubit Z and 45 two-qubit ZZ observables, giving a 55-dimensional quantum feature vector that a final linear layer maps to the ten digit classes. The paper credits this circuit, rather than the surrounding classical layers, for the accuracy edge over the classical CNN.

What would settle it

Train the same CNN and post-processing head but replace the variational circuit with a fixed, untrained quantum circuit (or remove the CNOT gates); if test accuracy remains at or above 99.80%, the reported quantum advantage is not caused by the learned quantum parameters.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that inserting a 10-qubit variational circuit as the classifier head of a CNN improves Devanagari digit recognition without large parameter overhead. The authors report that the full model, with 2,339,092 trainable parameters of which exactly 100 live in the quantum circuit, reaches 99.80% accuracy on the DHCD digit test set, outperforming the classical CNN baseline at 99.03% and beating or matching earlier classical results such as 98.47% and 99.00%. They further report a monotone improvement as qubit count rises from 4 to 10, with test misclassifications dropping from 16 to 6, and interpret this as evidence that quantum feature transformation improves class separability. The paper presents this as the first quantum machine learning benchmark for Devanagari digit recognition.

Load-bearing premise

The load-bearing premise is that the 0.77-percentage-point accuracy advantage over the classical CNN comes from the 10-qubit variational circuit, even though the hybrid model also inserts a learned 2048-to-1024 linear projection with about 2.1 million extra trainable weights before the quantum embedding and the classical baseline's parameter count is never reported.

Editorial extensions

If this is right

If the reported numbers are right, quantum-enhanced classification works on a real regional-script dataset, not just on synthetic or Latin-script benchmarks.
A variational circuit with only 100 trainable parameters can stand in for a dense classification head and match or exceed its accuracy, supporting the paper's parameter-efficiency argument.
The steady accuracy climb from 4 to 10 qubits implies that larger or deeper circuits are a plausible route to even higher accuracy on this task.
The same CNN+VQC pipeline can be carried over to the full Devanagari character set and to other low-resource scripts, the extension the authors name as their next step.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The 0.77-point gap over the classical CNN is not a clean quantum-vs-classical comparison, because the hybrid model adds a learned 2048-to-1024 projection with roughly 2.1 million weights before amplitude embedding; an editorially controlled experiment would match the classical baseline's capacity or remove that projection.
The paper's parameter-efficiency claim is muddled by an internal inconsistency: Table 1 counts 2,339,092 total parameters while Section 6.2 says total parameters are under 94,000; reconciling the count is a prerequisite for comparing against large classical models.
A useful test of entanglement's role would be to rerun the ablation with the VQC's CNOT gates removed or with the circuit parameters frozen; if accuracy stays near 99.8%, the source of the gain lies elsewhere.
Applying the same hybrid architecture to MNIST or to a Latin-script digit dataset, with matched classical capacity, would show whether the apparent advantage is specific to Devanagari's low-resource setting or a generic effect of the extra projection.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The thing to know: this is a standard hybrid CNN+VQC pipeline applied to a new dataset, Devanagari digits. The newness is the dataset and the 99.80% test accuracy claim, not the architecture. The paper is readable and the experimental description is mostly clear. But the headline claims do not hold up under scrutiny.

What it does well: the architecture is described in enough detail to reproduce; the dataset split and metrics are stated; the related work is adequate. The claim of being first to apply QML to Devanagari digits is plausible.

The soft spots are serious. The ablation in Section 6.1 compares CNN+VQC(10) to CNN+linear. But the hybrid inserts a learned 2048-to-1024 projection (Eq. 3) with 2.1M weights before the amplitude embedding; the classical baseline uses a linear head directly on the 2048 features. So the 0.77-point gap cannot be attributed to the 100-parameter VQC. The paper never reports the classical baseline's parameter count, so the comparison is uncontrolled.

There is also an internal contradiction: Table 1 totals 2,339,092 parameters, but Section 6.2 claims total parameters under 94,000. Both cannot be right for the same architecture. And the abstract says 'superior accuracy with significantly fewer parameters'; compared to the classical ablation, the hybrid has more parameters (2.3M vs roughly 260k), so that claim is misleading unless the comparison is against much larger classical models, which is not stated clearly.

The 99.80% number itself is plausible but unverified — no code, no seeds, no multi-run statistics. That would be acceptable in a low-stakes benchmark, but not when the paper is making strong generalization claims.

Bottom line: this is an application paper that deserves a cautious referee. The dataset-specific result may be useful to the QML and OCR communities, but the paper needs matched baselines, corrected parameter accounting, and code/reproducibility before its central claims can be taken seriously. I would not cite it as evidence for quantum advantage. I would still send it to review, because the flaws are fixable and the topic is of legitimate interest.

Referee Report

4 major / 4 minor

Summary. This paper proposes a hybrid quantum-classical model for Devanagari handwritten digit recognition on the DHCD digit subset. A CNN with four convolutional layers extracts a 2048-dimensional feature vector, a learned linear projection maps it to 1024 dimensions for amplitude embedding into a 10-qubit variational circuit, and the circuit's 55 expectation values are passed to a linear classifier. The authors report a test accuracy of 99.80% with an average per-class F1-score of 0.9980, and an ablation replacing the VQC with a linear layer yields 99.03%. The manuscript claims that this hybrid model outperforms equivalent classical CNNs with significantly fewer parameters. Hyperparameters were selected by grid search on a 4-qubit model and scaled to 6, 8, and 10 qubits, with all quantum circuits simulated in PennyLane.

Significance. If the reported accuracy and its attribution to the quantum circuit were supported, this would be a useful first benchmark for QML on Devanagari digit recognition and a concrete example of a hybrid QML pipeline in a low-resource script setting. The paper gives a detailed circuit description, a clear data split, a hyperparameter grid, and an honest statement that all experiments are simulations, which are all strengths. However, the central comparative claims rest on an ablation that is not architecturally matched and on a parameter count that is internally inconsistent. These issues are fixable with additional experiments and corrections, but they must be resolved before the quantum-advantage conclusion can be accepted.

major comments (4)

[§6.1, Table 5, Eq. (3)] The classical baseline in the ablation is not architecturally matched to the hybrid model. The hybrid inserts a learned affine map v' = Wv + b with W in R^{1024x2048} (Eq. 3), adding 2,098,176 weights and 1,024 biases before amplitude embedding, while the classical baseline is described as replacing the VQC with a linear layer on the 2048 features directly. The 0.77 percentage point accuracy gap could therefore come from this extra classical capacity rather than from the 100-parameter quantum circuit. Please report the classical baseline's parameter count and rerun the ablation with the same projection (CNN -> 2048-to-1024 projection -> linear classifier) so that the only difference is the presence of the VQC.
[Table 1 and §6.2] The parameter accounting is internally inconsistent. Table 1 reports 2,338,432 parameters for the 'Classical Feature Extractor' and 2,339,092 total, but §6.2 states that the total model has 'under 94,000' parameters and that the quantum circuits contain 40-100 trainable parameters. Both statements cannot be true for the architecture described in Section 3. This contradiction directly bears on the abstract's claim of 'significantly fewer parameters' and must be resolved by reporting one consistent parameter count for the final 10-qubit model.
[Abstract and §2.1] The parameter-efficiency comparison lacks the necessary baseline numbers. The abstract and Section 2.1 compare the hybrid model with classical CNNs, but no parameter counts are given for those baselines, including the classical CNN in Section 6.1 or the Acharya et al. model. Without these counts, the statement that the hybrid model has 'significantly fewer parameters' is unsupported, especially given the 2.1-million-parameter projection layer that is part of the hybrid's total.
[§4.3 and §5.4] Hyperparameters were selected by grid search on a 4-qubit model and then transferred to the 6-, 8-, and 10-qubit models. The paper does not verify that the optimal learning rate, batch size, or circuit depth transfer across qubit counts, so the monotonic accuracy improvement reported in Table 5 may reflect mismatched hyperparameter settings rather than the benefit of more qubits. Please tune each qubit count separately or provide evidence that the transferred configuration is appropriate for all of them.

minor comments (4)

[§6, first paragraph] The phrase 'Nepali Quantum MNIST dataset' is inconsistent with the rest of the paper, which uses the DHCD digit subset; please correct this to avoid confusion.
[§7, Conclusion] There is a typo in 'avearage per-class F1-scores'; it should be 'average'.
[§6.1, Table 5 sentence] The phrase 'Table 5Table 5' appears to be a duplicated reference; please remove the duplication.
[References and Figure captions] The in-text citation 'Aneja et al. [7]' should match the reference entry, which lists the authors as 'A. Vidwans and S. Aneja'; also verify that Figures 1 and 2 are actually included and legible in the submission, since the text refers to them but they were not visible in the manuscript text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper reports measured test-set results from an empirical benchmark, with no fitted quantity renamed as a prediction and no load-bearing self-citation chain.

full rationale

The paper's central claim is an empirical result: a hybrid CNN+VQC model reaches 99.80% test accuracy on the DHCD digit subset. The accuracy, loss, F1-scores, and confusion-matrix counts are reported as measured test-set quantities, not as quantities derived from the model's definition or from a fitted parameter that is then called a prediction. Hyperparameters were selected by grid search on validation data (Section 4.3), and the final metrics are evaluated on a held-out test set (Section 5), which is standard practice and not circular. The 'first QML application to Devanagari' claim is a novelty statement based on the absence of prior work, not a definition that forces the outcome. The ablation comparing CNN+VQC(10) with CNN+linear is a legitimate experimental design, even if the architecture mismatch (the extra 1024x2048 linear projection of Eq. 3) makes the attribution of the accuracy gap to quantum processing a correctness concern rather than a circular-reasoning concern. Similarly, the internal inconsistency between the reported 2,339,092 total parameters (Table 1) and the claim of 'total model parameters under 94,000' (Section 6.2) is an accounting error or incompatibility, not a circular step. No quoted passage reduces an output to an input by construction, no fitted prediction is relabeled as a prediction, and no load-bearing argument rests on a self-citation. The paper is self-contained against external benchmarks in the sense that its empirical numbers are independently measurable test results; the appropriate assessment is a correctness/control critique, not a circularity finding.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The central claim rests on tuned hyperparameters and domain assumptions about dataset integrity, simulation fidelity, and the label-preserving nature of augmentation.

free parameters (6)

learning rate = 1e-3
Selected by grid search on the 4-qubit model, then transferred to 10 qubits (Section 4.3).
batch size = 32
Selected by grid search on the 4-qubit model, then transferred to 10 qubits (Section 4.3).
dropout rate = 0.0
Selected by grid search on the 4-qubit model, then transferred to 10 qubits (Section 4.3).
label smoothing alpha = 0.05
Selected by grid search on the 4-qubit model, then transferred to 10 qubits (Section 4.3).
quantum circuit depth = 5
Selected by grid search on the 4-qubit model, then transferred to 10 qubits (Section 4.3).
data augmentation settings = rotation +/-20 deg, translation +/-0.1, elastic alpha=50, sigma=5, flip p=0.5
Chosen by hand in Section 4.2; not tuned but affect generalization.

assumptions (4)

domain assumption DHCD digit labels and the 17,000/3,000/3,400 split are accurate and leakage-free
Section 4.1 states the split; no code or data hash is provided to verify.
domain assumption PennyLane statevector simulation exactly represents an ideal 10-qubit circuit
All results are simulated (Section 6.3); real hardware noise is not modeled.
domain assumption Horizontal flips preserve Devanagari digit identity
Section 4.2 applies horizontal flips with probability 0.5; for asymmetric digits this may change the class label, but no analysis of this is given.
ad hoc to paper The learned 2048-to-1024 projection retains enough class information for amplitude embedding
Amplitude embedding (Eq. 4) uses the projected vector; information discarded by the projection is invisible to the quantum circuit.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Devanagari Digit Recognition using Quantum Machine Learning." pith.science (2026). https://pith.science/paper/WTVLLLX5

@misc{pith2026250609069,
  author       = {Pith},
  title        = {Pith review of: Devanagari Digit Recognition using Quantum Machine Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WTVLLLX5}},
  note         = {Machine review of arXiv:2506.09069}
}

read the original abstract

Handwritten digit recognition in regional scripts, such as Devanagari, is crucial for multilingual document digitization, educational tools, and the preservation of cultural heritage. The script's complex structure and limited annotated datasets pose significant challenges to conventional models. This paper introduces the first hybrid quantum-classical architecture for Devanagari handwritten digit recognition, combining a convolutional neural network (CNN) for spatial feature extraction with a 10-qubit variational quantum circuit (VQC) for quantum-enhanced classification. Trained and evaluated on the Devanagari Handwritten Character Dataset (DHCD), the proposed model achieves a state-of-the-art test accuracy for quantum implementation of 99.80% and a test loss of 0.2893, with an average per-class F1-score of 0.9980. Compared to equivalent classical CNNs, our model demonstrates superior accuracy with significantly fewer parameters and enhanced robustness. By leveraging quantum principles such as superposition and entanglement, this work establishes a novel benchmark for regional script recognition, highlighting the promise of quantum machine learning (QML) in real-world, low-resource language settings.

Figures

Figures reproduced from arXiv: 2506.09069 by the authors.

**Figure 2.** Quantum circuit for the 10-qubit VQC (one [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Training and validation loss and accuracy [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Confusion matrix for Devanagari digit classi [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

17 extracted references · 12 canonical work pages

[1]

Gradient-based learning applied to document recognition,

Y . LeCun, L. Bottou, Y . Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,”Proceedings of the IEEE, vol. 86, no. 11, pp. 2278–2324, 2002

2002
[2]

Deep learning based large scale handwritten devanagari character recognition,

S. Acharya, A. K. Pant, and P. K. Gyawali, “Deep learning based large scale handwritten devanagari character recognition,” in2015 9th International Conference on Software, Knowledge, Information Management and Applications (SKIMA). IEEE, 2015, pp. 1–6

work page 2015
[3]

Quantum machine learn- ing,

J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learn- ing,”Nature, vol. 549, no. 7671, pp. 195–202, 2017

work page 2017
[4]

Quantum computing in the nisq era and beyond,

J. Preskill, “Quantum computing in the nisq era and beyond,”Quantum, vol. 2, p. 79, 2018

2018
[5]

Hybrid quantum-classical neural network for calculating ground state ener- gies of molecules,

R. Xia and S. Kais, “Hybrid quantum-classical neural network for calculating ground state ener- gies of molecules,”Entropy, vol. 22, no. 8, p. 828, 2020

work page 2020
[6]

Imagenet classification with deep convolutional neural networks,

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,”Communications of the ACM, vol. 60, no. 6, pp. 84–90, 2017

2017
[7]

Transfer learning using cnn for handwritten devanagari character recognition,

A. Vidwans and S. Aneja, “Transfer learning using cnn for handwritten devanagari character recognition,” in2019 1st International Conference on Advances in Information Technology (ICAIT). IEEE, 2019, pp. 293–296

work page 2019
[8]

Variational quan- tum algorithms,

M. Cerezo, A. Arrasmith, R. Babbush, S. C. Ben- jamin, S. Endo, K. Fujii, J. R. McClean, K. Mi- tarai, X. Yuan, L. Cincioet al., “Variational quan- tum algorithms,”Nature Reviews Physics, vol. 3, no. 9, pp. 625–644, 2021

work page 2021

Show all 17 references

[9]

Quantum circuit learning,

K. Mitarai, M. Negoro, M. Kitagawa, and K. Fu- jii, “Quantum circuit learning,”Physical Review A, vol. 98, no. 3, p. 032309, 2018

2018
[10]

Classification of hybrid quantum-classical com- puting,

F. Phillipson, N. Neumann, and R. Wezeman, “Classification of hybrid quantum-classical com- puting,” inInternational Conference on Computa- tional Science. Springer, 2023, pp. 18–33

2023
[11]

The power of quantum neural networks,

A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Fi- galli, and S. Woerner, “The power of quantum neural networks,”Nature Computational Science, vol. 1, no. 6, pp. 403–409, 2021

2021
[12]

A comparative analysis of hybrid-quantum classical neural networks,

K. Zaman, T. Ahmed, M. A. Hanif, A. Marchi- sio, and M. Shafique, “A comparative analysis of hybrid-quantum classical neural networks,” in World Congress in Computer Science, Computer Engineering & Applied Computing. Springer, 2024, pp. 102–115

2024
[13]

Pennylane: Automatic differentiation of hybrid quantum-classical computations,

V . Bergholm, J. Izaac, M. Schuld, C. Gogolin, S. Ahmed, V . Ajith, M. S. Alam, G. Alonso- Linaje, B. AkashNarayanan, A. Asadiet al., “Pennylane: Automatic differentiation of hybrid quantum-classical computations,”arXiv preprint arXiv:1811.04968, 2018

2018 arXiv
[14]

Understanding the dif- ficulty of training deep feedforward neural net- works,

X. Glorot and Y . Bengio, “Understanding the dif- ficulty of training deep feedforward neural net- works,” inProceedings of the thirteenth inter- national conference on artificial intelligence and statistics. JMLR Workshop and Conference Pro- ceedings, 2010, pp. 249–256

2010
[15]

Rethinking the inception architecture for computer vision,

C. Szegedy, V . Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna, “Rethinking the inception architecture for computer vision,” inProceedings of the IEEE conference on computer vision and pattern recog- nition, 2016, pp. 2818–2826

2016
[16]

Decoupled weight decay regularization,

I. Loshchilov and F. Hutter, “Decoupled weight decay regularization,”arXiv preprint arXiv:1711.05101, 2017

2017 arXiv
[17]

Multi- column deep neural networks for image classifica- tion,

D. Ciregan, U. Meier, and J. Schmidhuber, “Multi- column deep neural networks for image classifica- tion,” in2012 IEEE conference on computer vision and pattern recognition. IEEE, 2012, pp. 3642– 3649. 9

2012

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Gradient-based learning applied to document recognition,

Y . LeCun, L. Bottou, Y . Bengio, and P. Haffner, “Gradient-based learning applied to document recognition,”Proceedings of the IEEE, vol. 86, no. 11, pp. 2278–2324, 2002

2002

[2] [2]

Deep learning based large scale handwritten devanagari character recognition,

S. Acharya, A. K. Pant, and P. K. Gyawali, “Deep learning based large scale handwritten devanagari character recognition,” in2015 9th International Conference on Software, Knowledge, Information Management and Applications (SKIMA). IEEE, 2015, pp. 1–6

work page 2015

[3] [3]

Quantum machine learn- ing,

J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learn- ing,”Nature, vol. 549, no. 7671, pp. 195–202, 2017

work page 2017

[4] [4]

Quantum computing in the nisq era and beyond,

J. Preskill, “Quantum computing in the nisq era and beyond,”Quantum, vol. 2, p. 79, 2018

2018

[5] [5]

Hybrid quantum-classical neural network for calculating ground state ener- gies of molecules,

R. Xia and S. Kais, “Hybrid quantum-classical neural network for calculating ground state ener- gies of molecules,”Entropy, vol. 22, no. 8, p. 828, 2020

work page 2020

[6] [6]

Imagenet classification with deep convolutional neural networks,

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,”Communications of the ACM, vol. 60, no. 6, pp. 84–90, 2017

2017

[7] [7]

Transfer learning using cnn for handwritten devanagari character recognition,

A. Vidwans and S. Aneja, “Transfer learning using cnn for handwritten devanagari character recognition,” in2019 1st International Conference on Advances in Information Technology (ICAIT). IEEE, 2019, pp. 293–296

work page 2019

[8] [8]

Variational quan- tum algorithms,

M. Cerezo, A. Arrasmith, R. Babbush, S. C. Ben- jamin, S. Endo, K. Fujii, J. R. McClean, K. Mi- tarai, X. Yuan, L. Cincioet al., “Variational quan- tum algorithms,”Nature Reviews Physics, vol. 3, no. 9, pp. 625–644, 2021

work page 2021