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REVIEW 3 major objections 5 minor 1 cited by

Digital-Analog Quantum Machine Learning

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A Perspective argues that mixing large analog evolution blocks with small digital gates can make quantum machine learning scale on near-term NISQ devices, and proposes the name DAQML for this research direction.

desk verdict A coherent but thin perspective whose central promise is extrapolated from subroutine resource gains and self-cited prior work; fine as a taxonomy, not as evidence of quantum machine learning advantage. read the letter →

arxiv 2411.10744 v1 pith:ZEYJC53D submitted 2024-11-16 quant-ph cs.AI

Lucas Lamata This is my paper · ORCID
classification quant-phcs.AI
keywords quantummachinelearningdigital-analogprotocolsNISQdevicesadvantagevariationalalgorithmsneutral-atomarraysFouriertransform
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 Perspective argues that a hybrid quantum computing recipe—large global analog evolution blocks stitched together by small single-qubit digital gates—can make machine learning calculations more scalable on today's noisy intermediate-scale quantum devices. The author proposes the name "digital-analog quantum machine learning" (DAQML) for this research avenue and reviews recent first instances: variational eigensolvers for molecules, a genetic algorithm, a quantum approximate optimization algorithm, quantum kernels for image classification, a digital-analog quantum Fourier transform, and neutral-atom learning algorithms. The combined evidence, in the author's reading, supports the idea that DAQML is fruitful and that better scalability of quantum machine learning may eventually yield a quantum advantage over classical machine learning. A reader should care because it offers a concrete path to useful quantum computation before fault-tolerant machines exist.

What carries the argument

The central object is the extreme digital-analog quantum protocol (EDAQP): a circuit made of global native-interaction blocks $U_k(t_k)$, each a unitary applied to all qubits by the platform's own Hamiltonian, separated by tiny single-qubit rotations $R_{i,j}$. This construction carries the argument because it concentrates the expensive work in large analog pieces that are natural to the hardware, while restricting the digital part to the operations a platform performs best. The result is a reduction in circuit depth and number of discrete gates, which is what the paper identifies as the route to scalability on NISQ devices.

What would settle it

A head-to-head experiment on a single platform—running a DAQML variational circuit and a purely digital variational circuit with the same expressibility on the same learning task—would falsify the central claim if the digital-analog version shows no reduction in circuit depth, gate count, or measured error.

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Extended reading notes

Core claim

The central claim is that the digital-analog quantum paradigm, previously developed for quantum simulation, carries over to machine learning and is already showing promise in proof-of-principle works. On the paper's terms, the extreme digital-analog quantum protocol (EDAQP) is the generic template: the largest possible analog blocks—global unitary gates generated by the platform's native Hamiltonian—are interleaved with the smallest possible digital operations, single-qubit gates, which have the best fidelities on most platforms. The reviewed works are taken as evidence that this combination is fruitful, and the paper's outlook states that combining large analog blocks with digital steps 'may represent a significant step forward' in quantum technologies, possibly the first approach to impact industry.

Load-bearing premise

The whole promise depends on the untested premise that NISQ devices with tens to hundreds of qubits can run digital-analog protocols with high enough fidelity and low enough overhead to beat classical machine learning, which the cited demonstrations do not yet establish.

Editorial extensions

If this is right

  • If DAQML is right, QML algorithms such as variational eigensolvers and quantum kernels can be implemented on NISQ hardware with fewer total gates than fully digital decompositions, because the global analog blocks replace sequences of two-qubit gates.
  • The digital-analog quantum Fourier transform, with its reported resource gains over the purely digital version, can be slotted into larger QML pipelines, cheapening a widely used primitive.
  • Neutral-atom arrays, with strong native interactions and recently demonstrated scalability, become a natural platform for DAQML and could be where a favourable machine-learning task first shows a practical quantum advantage.
  • Near-term industrial adoption may arrive through the co-design of algorithms with the native Hamiltonians of specific quantum platforms, before fault-tolerant error correction is available.

Reading between the lines

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

  • My inference: if DAQML matures, the hardware's native Hamiltonian effectively becomes a trainable layer, so choosing a platform becomes part of the learning model rather than a fixed constraint.
  • My inference: the resource gains claimed for individual primitives such as the quantum Fourier transform only become an end-to-end advantage if the analog blocks can be calibrated and controlled as reliably as digital gates; this is a testable assumption that the paper leaves open.
  • My inference: the same digital-analog trick might apply to quantum generative models, where global analog evolution could act as a fast mixer or sampler between digital readout and feedforward steps.
  • My inference: naming the area DAQML is a community-forming proposal, and its success will depend on whether independent groups adopt the term and build benchmarks around it.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This manuscript is a Perspective that proposes the name "Digital-Analog Quantum Machine Learning" (DAQML) for the combination of digital-analog quantum protocols with quantum machine learning algorithms. It reviews a small set of recent theoretical and experimental works (Refs. [3,4,6-10]) that employ large analog blocks of native Hamiltonian evolution together with single-qubit digital gates, and it argues that this combination may be fruitful and may enable better scalability of QML algorithms on NISQ devices. The paper also briefly surveys digital-analog quantum simulation experiments in trapped ions, superconducting circuits, and Rydberg atom arrays, and speculates that DAQML could become one of the first approaches to impact industry.

Significance. If the promise of DAQML materializes, the direction could provide a practical route toward near-term quantum advantage in machine learning by leveraging the scalability of analog simulation and the flexibility of digital gates. The paper is clearly written and serves as a concise entry point to a young subfield, and it performs the useful service of naming the area and collecting the relevant first-instance references. The author is appropriately cautious, using hedged language such as 'perhaps' and 'may'. However, the central claim of fruitfulness and potential advantage is not quantitatively anchored, and the evidence cited is mostly from first-instance proposals and simulation experiments rather than from demonstrations that DAQML outperforms classical baselines or reduces end-to-end resources in a learning task. The manuscript would be significantly strengthened by a more critical discussion of the conditions under which analog blocks could actually reduce the dominant costs of QML.

major comments (3)
  1. [Section 3, final paragraph] The central assertion that previous works 'show evidence that this combination can be fruitful' is supported only by citing first-instance proposals (Refs. [3,4,6,7,10]) and subroutine-level resource gains (Refs. [8,9]). None of these cited works is reported to outperform a classical machine learning baseline, and none provides an end-to-end resource count for a learning task that includes data loading, training, measurement overhead, and noise accumulation. Since this assertion is the main claim of the Perspective, it needs at least one quantitative anchor or a clearly stated condition under which DAQML would provably reduce the cost of a QML pipeline.
  2. [Section 3, Refs. [8] and [9]] The resource-gain evidence is drawn from the digital-analog quantum Fourier transform and from a co-design of the HHL algorithm, which are subroutines, not complete QML algorithms. The transfer of subroutine-level savings to the full QML setting is asserted rather than argued. For example, a faster QFT does not by itself imply faster training of a variational quantum classifier, because the training cost is dominated by repeated circuit evaluations and classical optimization. This is a load-bearing gap in the 'better scalability' claim.
  3. [Sections 4 and 5] The extrapolation from digital-analog quantum simulation experiments to quantum machine learning tasks ignores known obstacles to near-term QML advantage. The manuscript does not discuss barren plateaus in variational circuits, the possibility that circuits built from global low-depth native Hamiltonians are classically simulable, or the accumulation of errors in long analog blocks. Without addressing these issues, the Outlook's vision that DAQML 'may represent a significant step forward' remains an unsupported extrapolation. Adding a paragraph that either connects to known no-go results or explains why analog blocks circumvent them would substantially strengthen the Perspective.
minor comments (5)
  1. [Abstract] The word 'accesible' should be 'accessible' in the first paragraph of the abstract.
  2. [Figure 1] The figure contains a typographical artifact 'R1,,2' and the labels are not fully legible; please provide a cleaner version with consistent subscript formatting.
  3. [Section 1] The phrase 'which is significantly impacting society at large, by enabling a plethora of possibilities, as well as challenges' is a run-on sentence; consider splitting it for clarity.
  4. [Section 2] The term 'extreme digital-analog quantum protocol (EDAQP)' is introduced in the text and figure but is not defined elsewhere; a one-sentence explicit definition in the main text would help readers.
  5. [Section 5] The sentence 'This could, in turn, impact subsequently society at large, as well as the scientific enterprise as well' contains a redundant 'as well'; please revise.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the perspective's hedged promise is an extrapolation from cited first-instance works, including independent groups, not a reduction of the conclusion to its inputs.

full rationale

The paper is a short Perspective, not a derivation: its strongest claim is explicitly hedged, "show evidence that this combination can be fruitful, and perhaps, by enabling a better scalability of quantum machine learning algorithms, may provide a quantum advantage," and the supporting evidence is a set of cited first-instance implementations rather than an equation-level reduction. No parameter is fitted and later renamed as a prediction; no uniqueness theorem is imported from the authors' prior work to forbid alternatives; no ansatz is smuggled in via citation. The extensive self-citations, such as Refs. [2,4,8] and the Outlook phrase "the paradigm that we created more than 10 years ago," are normal attribution in a perspective and are not load-bearing: the fruitfulness/advantage claim rests on the existence of the cited works, including independent ones from PASQAL (Ref. [3]) and QuEra (Ref. [10]), and the author's own contributions are presented as first instances, not as proof of the general claim. The absence of a concrete end-to-end advantage argument is a weakness of the perspective, but that is a correctness/evidence gap, not circularity.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

No free parameters or invented entities appear because the paper presents no new computational result. The axioms are background assumptions about the viability of the digital-analog paradigm and the reliability of the cited literature. The proposed name 'DAQML' is a label, not an entity with independent evidence requirements.

assumptions (3)
  • domain assumption The digital-analog quantum paradigm can reduce resource overhead compared to purely digital quantum computing.
    Invoked in Sections 2 and 3 and used to argue that DAQML may enable NISQ advantage; based on the author's previous work (Ref. [2]) and Ref. [8].
  • domain assumption The cited theoretical and experimental works are correctly interpreted and reproducible.
    The perspective's positive assessment of DAQML rests entirely on the reliability of Refs [3,4,6,7,8,9,10].
  • domain assumption NISQ devices without fault tolerance can achieve practical machine learning tasks at scale.
    Stated in Sections 1 and 5 as the motivation; not demonstrated in the paper or, per the author's own caveats, in the cited literature.

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Cite this review

Pith. "Pith review of Digital-Analog Quantum Machine Learning." pith.science (2026). https://pith.science/paper/ZEYJC53D

@misc{pith2026241110744,
  author       = {Pith},
  title        = {Pith review of: Digital-Analog Quantum Machine Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZEYJC53D}},
  note         = {Machine review of arXiv:2411.10744}
}
read the original abstract

Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and therefore improve their performance in a certain context or environment. In this way, many useful possibilities have been made accessible. However, dealing with an increasing amount of data poses difficulties for classical devices. Quantum systems may offer a way forward, possibly enabling to scale up machine learning calculations in certain contexts. On the other hand, quantum systems themselves are also hard to scale up, due to decoherence and the fragility of quantum superpositions. In the short and mid term, it has been evidenced that a quantum paradigm that combines evolution under large analog blocks with discrete quantum gates, may be fruitful to achieve new knowledge of classical and quantum systems with no need of having a fault-tolerant quantum computer. In this Perspective, we review some recent works that employ this digital-analog quantum paradigm to carry out efficient machine learning calculations with current quantum devices.

Figures

Figures reproduced from arXiv: 2411.10744 by the authors.

Figure 1
Figure 1. scheme of a generic extreme digital-analog quantum protocol (EDAQP). This consists of a combination of the largest analog blocks possible, i.e., a set of global native interactions, namely, global unitary gates on all qubits based on the quantum platform native Hamiltonian, U1(t1), U2(t2),...,Uk(tk),..., and the smallest digital gates possible, i.e., single￾qubit gates, which can be done with the best fidelities in … view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum memristors for neuromorphic quantum machine learning

    quant-ph 2024-12 unverdicted

    A perspective asserting that quantum memristors are a promising modular hardware route for neuromorphic quantum machine learning, without presenting new results.

Reference graph

Works this paper leans on

3 extracted references · 1 canonical work pages · cited by 1 Pith paper

  1. [3]

    Yelin, and Sheng-Tao Wang, Digital-analog quantum learning on Rydberg atom arrays, arXiv:2401.02940 (2024)

    Liu, Susanne F. Yelin, and Sheng-Tao Wang, Digital-analog quantum learning on Rydberg atom arrays, arXiv:2401.02940 (2024). 11 Andrew J. Daley, Immanuel Bloch, Christian Kokail, Stuart Flannigan, Natalie Pearson, Matthias Troyer and Peter Zoller, Practical quantum advantage in quantum simulation, Nature 607, 667 (2022). 12 www.pasqal.com 13 www.quera.com 4

    arXiv 2024

  2. [1]

    1 Yunfei Wang and Junyu Liu, A comprehensive review of quantum machine learning: from NISQ to fault tolerance, Rep. Prog. Phys. 87 116402 (2024). 2 L Lamata, A Parra-Rodriguez, M Sanz, and E Solano, Digital-Analog Quantum Simulations with Su- perconducting Circuits, Adv. Phys.: X 3 (1), 1457981 (2018). 3 Antoine Michel, Sebastian Grijalva, Lo ¨ ıc Henriet...

    work page 2024

  3. [2]

    de Groot, G

    Quelle, C. de Groot, G. V. Velikova, V. E. Elfving, and M. Dagrada, Qadence: a differentiable interface for digital-analog programs, arXiv:2401.09915 (2024). 6 David Headley, Thorge M¨ uller, Ana Martin, Enrique Solano, Mikel Sanz, and Frank K. Wilhelm, Ap- proximating the quantum approximate optimization algorithm with digital-analog interactions, Phys. ...

    arXiv 2024

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Reviewed August 12, 2026 · model on record in the stance chip above.