Pith. sign in

REVIEW 6 minor 2 cited by

Advances in Machine Learning: Where Can Quantum Techniques Help?

T0 review · 0 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Quantum machine learning will only pay off for quantum-native data and specialist tasks like chemistry and sensing, because classical-data encoding consumes the theoretical speedup.

desk verdict A solid, skeptical QML survey whose conditional thesis survives close reading; the real problems are local citation and encoding-quantification slips, not the argument. read the letter →

arxiv 2507.08379 v1 pith:4IG7SSDE submitted 2025-07-11 cs.LG quant-ph

Samarth Kashyap , Rohit K Ramakrishnan , Kumari Jyoti , Apoorva D Patel This is my paper · ORCID
classification cs.LGquant-ph
keywords QuantumMachineLearningAdvantageDataEncodingNISQdevicesTheoryPrincipalComponentAnalysisNeuralNetworksHybridQuantum-ClassicalModels
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

Quantum machine learning promises to speed up data-driven tasks, but this review argues the promise is heavily conditional: theoretical speedups survive only when the data is already quantum or cheap to prepare, and generic classical datasets pay an encoding cost that erases the gain. The paper is a structured review, not a new experiment; it pairs classical learning theory with a taxonomy of data type (classical versus quantum) and hardware type (classical, hybrid, quantum) to decide where quantum techniques could still help. It evaluates flagship proposals—quantum principal component analysis, quantum-enhanced sensing, variational quantum eigensolvers—and finds that each advantage depends on assumptions about state preparation or error rates that current hardware does not satisfy. The bottom line, stated in the outlook, is that QML's broad real-world utility remains unproven, while its niche value in quantum chemistry and sensing is concrete.

What carries the argument

The argument is carried by two interacting cost-accounting devices. The first is the encoding bottleneck: amplitude encoding of arbitrary classical feature vectors requires $\Omega(2^n/n)$ two-qubit gates, so any claimed speedup must be quoted net of state-preparation cost. The second is the learning-theoretic sample-complexity framework (agnostic PAC learnability, VC dimension), which fixes how many samples any learner, quantum or classical, needs; the paper's taxonomy of data and hardware combinations then forces each QML proposal to show its end-to-end price, including encoding and error mitigation, before advantage is claimed.

What would settle it

A definitive test would be an end-to-end comparison on a standard large-scale classical dataset of the kind the review itself cites (MNIST or CIFAR-10): raw data to final prediction, with state-preparation time and error mitigation included in the runtime. If a quantum learner consistently beats the best classical model on wall-clock time and accuracy, the claim that encoding erases speedups is falsified.

Watch

Extended reading notes

Core claim

The central claim is a negative one, argued systematically: across the main routes to quantum machine learning, complexity-theoretic gains are real but do not translate into end-to-end practical advantage for ordinary classical data. The paper shows that the leading results—the sample-complexity guarantees of agnostic PAC learning, the exponential copy advantage of quantum principal component analysis, the time-complexity separations from quantum learning theory—all carry a hidden precondition: either the input arrives as a quantum state, or the classical-to-quantum encoding must be cheap. Because arbitrary amplitude encoding is expensive (bounded below by $\Omega(2^n/n)$ two-qubit gates), and because NISQ noise and barren plateaus cap trainable circuit depth, the review concludes that near-term QML is viable mainly for quantum data (sensor outputs, simulation states) and for specialized physics and chemistry tasks, not as a general replacement for classical machine learning.

Load-bearing premise

The review's skeptical outlook rests on the premise that encoding classical data into quantum states is expensive enough to cancel quantum speedups, and that cheap encoding or abundant quantum data will not become routine.

Editorial extensions

If this is right

  • Near-term QML deployments should target quantum-native inputs—measurement records from sensors, states produced by simulators, error-correction syndromes—where the encoding step is effectively free.
  • Benchmarking QML against classical baselines must include the full pipeline (encoding, training, error mitigation) and wall-clock runtime; circuit-level complexity alone overstates the gain.
  • Algorithms translated from classical ML are unlikely to be the winning designs; the observation that removing entangling gates leaves several QML models' performance unchanged indicates current architectures are not exploiting quantum resources.
  • QPCA-style exponential advantages should be treated as conditional on state preparation; without a quantum data source or an efficient encoding route, they offer no end-to-end speedup over classical PCA.
  • For classical data, the expected quantum advantage is in time complexity, not sample complexity: quantum learners match classical PAC guarantees but do not get a generic sample-efficiency lift.

Reading between the lines

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

  • Editorial extension: if cheap structured state preparation (sparse or almost-uniform amplitude encoding) becomes practical, the review's negative conclusion for classical data would narrow to dense, unstructured datasets; a benchmark of end-to-end cost on sparse high-dimensional data would test this boundary.
  • Editorial extension: the paper treats quantum data as scarce today, but if quantum sensing scales commercially, the volume of quantum-native data could grow quickly and turn the paper's 'niche' into a mainstream input class sooner than the NISQ framing suggests.
  • Editorial extension: the review's taxonomy implies a measurable 'dequantization rate'—how often quantum-inspired classical algorithms reproduce a proposed quantum speedup; tracking that rate would convert the paper's qualitative concern about translated algorithms into a quantitative risk.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 6 minor

Summary. This manuscript is a review of quantum machine learning (QML) that surveys classical learning theory, quantum data encodings, quantum learning theory, a taxonomy of QML approaches by data/hardware type, specific developments (QPCA, quantum sensing, the discrete-log dataset, materials science), NISQ-era challenges, and future directions. The central thesis, stated in the abstract and Section 8, is that QML offers real but niche advantages—e.g., in quantum chemistry, sensing, and settings with quantum data—while broader real-world utility remains contingent on overcoming encoding overhead, hardware noise, and benchmarking gaps. The paper argues that encoding classical data into quantum states often negates theoretical speedups and that many current QML algorithms are de facto classical translations that do not exploit quantum resources.

Significance. If taken as a survey, the paper is a useful and balanced synthesis: it gives a careful account of learning-theoretic results (sample versus time complexity, agnostic PAC learnability, noise robustness), distinguishes quantum versus classical data sources, and keeps the central claim explicitly conditional rather than overclaiming. The authors deserve credit for including discussions of dequantized algorithms, the QAEX oracle, and the subtlety that sample-complexity advantages are not generally available. The review does not introduce new theorems or experiments, so its value lies in its breadth and its reasonably sober assessment of the field. Its conclusions are consistent with a large part of the QML literature, though a few citation-level and presentational inaccuracies, detailed below, should be corrected before publication.

minor comments (6)
  1. [3.1.2] The amplitude-encoding cost statement 'lower-bounded by 2^n/n two-qubit gates' should be clarified: the lower bound from Ref. [10] applies to preparing an arbitrary state on a logarithmic number of qubits, i.e., n features require ⌈log2 n⌉ qubits, and the complexity is exponential in the number of qubits, not in the number of features as the current phrasing suggests. Please rephrase to avoid conflating feature count with qubit count.
  2. [5.1] The sentence 'Quantum PCA can approximately predict the expectation values of observables ... with only O(1) copies of ρ' misattributes a result that is due to Huang et al. [52] (and related shadow-tomography results), not to the QPCA algorithm of Lloyd, Mohseni, and Rebentrost [51]. Please correct the attribution and the surrounding comparison with the classical lower bound.
  3. [5.4] The claim that 'classical approximations like density functional theory (DFT) remain more practical for most material science problems' is cited to Ref. [19] (Cross, Smith, and Smolin), which is a paper on quantum learning robust against noise and does not discuss DFT or material-science practicality. Please replace this citation with an appropriate reference or remove it.
  4. [3.3.1] There is a duplicated phrase in the sentence beginning 'Since a QAEX oracle can be used to sample classical data...'—the text repeats 'to Since a QAEX oracle...'—which should be corrected.
  5. [6.2.1] The use of Ref. [52] to support the statement that 'data encodings require significant quantum memory and coherence time' and to describe Sycamore experiments is imprecise: Ref. [52] does discuss learning from experiments on Sycamore, but the specific encoding-cost claim would be better supported by Refs. [51,53] or a dedicated encoding reference.
  6. [References] Several references are duplicated (e.g., Refs. [1] and [4] are the same book by Shalev-Shwartz and Ben-David); please consolidate the bibliography to avoid duplicate entries.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: survey's conditional conclusion is self-contained; the sole self-citation is a non-load-bearing example.

full rationale

This is a review article, not a derivation-based paper. The central claim in Section 8, that QML's broader utility 'remains contingent on overcoming technological and methodological hurdles', is a conditional assessment supported by external literature (encoding lower bounds [10], learning-theory results [14,17,18], hardware studies [28,55,59]), not by any fitted parameter or construction-by-definition. No equation in the paper is defined in terms of a quantity it is supposed to predict; no parameter is fitted to a subset of data and then renamed a prediction; no uniqueness theorem from the authors' own prior work is invoked to force a choice; and no ansatz is smuggled in via self-citation. The only self-citation is [41] (Kashyap and Garani) in Section 4.3, where QCNNs are listed as one attempted scenario among several; it is an example, not load-bearing evidence for the review's skeptical outlook. Even if the cited QCNN were flawed, the conclusion would be unchanged, because the conclusion is conditional and drawn from the broader cited literature. The duplicated sentence at the end of Section 3.3.1 is a typographical error and does not create a circular dependence. Consistent with the hard rules, a non-finding is appropriate: the central claim has independent content and no circular reduction is exhibited.

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

The review rests entirely on cited results; it adds no free parameters or new entities. The axioms listed are the background theorems and assumptions it invokes.

assumptions (6)
  • standard math Agnostic PAC learnability and sample complexity bounds for finite hypothesis classes (Section 2.1.3)
    The review's comparison of classical and quantum learning relies on these standard bounds from Shalev-Shwartz and Ben-David [1].
  • standard math No-free-lunch theorem (Theorem 1, Section 2.1.5)
    Used to justify that no universal learner exists, framing the search for problem-specific quantum advantages.
  • standard math VC dimension characterizes learnability (Section 2.1.6)
    Used as the metric to compare classical and quantum learnability.
  • domain assumption Quantum agnostic PAC learning framework with QAEX oracle (Section 3.3.1, ref [14])
    Assumes the validity of Arunachalam and de Wolf's quantum sample complexity model.
  • domain assumption Quantum state preparation lower bound of Omega(2^n/n) two-qubit gates (Section 3.1.2, ref [10])
    Underpins the claim that amplitude encoding is a bottleneck.
  • domain assumption NISQ hardware constraints as described by Preskill (Section 6.1, ref [55])
    The review's practical pessimism depends on these extrapolated hardware limitations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Advances in Machine Learning: Where Can Quantum Techniques Help?." pith.science (2026). https://pith.science/paper/4IG7SSDE

@misc{pith2026250708379,
  author       = {Pith},
  title        = {Pith review of: Advances in Machine Learning: Where Can Quantum Techniques Help?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4IG7SSDE}},
  note         = {Machine review of arXiv:2507.08379}
}
read the original abstract

Quantum Machine Learning (QML) represents a promising frontier at the intersection of quantum computing and artificial intelligence, aiming to leverage quantum computational advantages to enhance data-driven tasks. This review explores the potential of QML to address the computational bottlenecks of classical machine learning, particularly in processing complex datasets. We introduce the theoretical foundations of QML, including quantum data encoding, quantum learning theory and optimization techniques, while categorizing QML approaches based on data type and computational architecture. It is well-established that quantum computational advantages are problem-dependent, and so potentially useful directions for QML need to be systematically identified. Key developments, such as Quantum Principal Component Analysis, quantum-enhanced sensing and applications in material science, are critically evaluated for their theoretical speed-ups and practical limitations. The challenges posed by Noisy Intermediate-Scale Quantum (NISQ) devices, including hardware noise, scalability constraints and data encoding overheads, are discussed in detail. We also outline future directions, emphasizing the need for quantum-native algorithms, improved error correction, and realistic benchmarks to bridge the gap between theoretical promise and practical deployment. This comprehensive analysis underscores that while QML has significant potential for specific applications such as quantum chemistry and sensing, its broader utility in real-world scenarios remains contingent on overcoming technological and methodological hurdles.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

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

    cs.LG 2026-07 conditional novelty 5.0 of 10

    Joint multi-expert unitary convolution plus stabilizer-syndrome features roughly halves MNIST/Fashion-MNIST failure rates versus classical diffusion pooling, at moderate GPU overhead.

  2. Quantum kernel and HHL-based support vector machines for multi-class classification

    quant-ph 2025-09 conditional novelty 4.0 of 10

    On a reduced SDSS dataset, quantum-kernel QSVM outperforms HHL LS-SVM, classical SVMs are slightly ahead, and the HHL method's constant scaling stems from using only two class-average representatives.

Reference graph

Works this paper leans on

65 extracted references · 22 canonical work pages · cited by 2 Pith papers

  1. [52]

    Science 376(6598), 1182–1186 (2022) https://doi.org/ 10.1126/science.abn7293

    Huang, H.-Y., Broughton, M., Cotler, J., Chen, S., Li, J., Mohseni, M., Neven, H., Babbush, R., McClean, J., Kueng, R., Preskill, J.: Quantum advantage in learning from experiments. Science 376(6598), 1182–1186 (2022) https://doi.org/ 10.1126/science.abn7293

    doi:10.1126/science.abn7293 2022

  2. [19]

    Physical Review A - Atomic, Molecular, and Optical Physics 92 (2015) https: //doi.org/10.1103/PhysRevA.92.012327

    Cross, A.W., Smith, G., Smolin, J.A.: Quantum learning robust against noise. Physical Review A - Atomic, Molecular, and Optical Physics 92 (2015) https: //doi.org/10.1103/PhysRevA.92.012327

    work page doi:10.1103/physreva.92.012327 2015

  3. [41]

    In: Proceedings of the International Joint Conference on Neural Networks, vol

    Kashyap, S., Garani, S.S.: Quantum convolutional neural network architecture for multi-class classification. In: Proceedings of the International Joint Conference on Neural Networks, vol. 2023-June (2023). https://doi.org/10.1109/IJCNN54540. 2023.10191561

    work page arXiv 2023

  4. [2]

    Communications of the ACM 27, 1134– 1142 (1984) https://doi.org/10.1145/1968.1972

    Valiant, L.G.: A theory of the learnable. Communications of the ACM 27, 1134– 1142 (1984) https://doi.org/10.1145/1968.1972

    arXiv 1984

  5. [3]

    IEEE Transactions on Neural Networks 10 (1999) https://doi.org/10.1109/72.788640

    Vapnik, V.N.: An overview of statistical learning theory. IEEE Transactions on Neural Networks 10 (1999) https://doi.org/10.1109/72.788640

    doi:10.1109/72.788640 1999

  6. [4]

    9781107057135, (2013)

    Shalev-Shwartz, S., Ben-David, S.: Understanding Machine Learning: From Theory to Algorithms vol. 9781107057135, (2013). https://doi.org/10.1017/ CBO9781107298019

    work page 2013

  7. [5]

    Machine Learning 4, 67–97 (1989) https://doi.org/10.1007/BF00114804

    Natarajan, B.K.: On learning sets and functions. Machine Learning 4, 67–97 (1989) https://doi.org/10.1007/BF00114804

    doi:10.1007/bf00114804 1989

  8. [6]

    Cambridge University Press, Cambridge (1999)

    Anthony, M., Bartlett, P.L.: Neural Network Learning. Cambridge University Press, Cambridge (1999). https://doi.org/10.1017/CBO9780511624216

    doi:10.1017/cbo9780511624216 1999

Show all 65 references
  1. [7]

    Theory of Probability & Its Applications 16, 264–280 (1971) https://doi.org/10.1137/1116025

    Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative fre- quencies of events to their probabilities. Theory of Probability & Its Applications 16, 264–280 (1971) https://doi.org/10.1137/1116025

    1971 doi

  2. [8]

    Journal of the ACM (JACM) 36 (1989) https: //doi.org/10.1145/76359.76371 22

    Blumer, A., Ehrenfeucht, A., Haussler, D., Warmuth, M.K.: Learnability and the vapnik-chervonenkis dimension. Journal of the ACM (JACM) 36 (1989) https: //doi.org/10.1145/76359.76371 22

    1989

  3. [9]

    Springer, Cham (2021)

    Schuld, M., Petruccione, F.: Machine Learning with Quantum Computers. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-83098-4

    2021 doi

  4. [10]

    Physical Review A - Atomic, Molecular, and Optical Physics 83 (2011) https://doi.org/10.1103/PhysRevA.83.032302

    Plesch, M., Brukner: Quantum-state preparation with universal gate decompo- sitions. Physical Review A - Atomic, Molecular, and Optical Physics 83 (2011) https://doi.org/10.1103/PhysRevA.83.032302

    2011 doi

  5. [11]

    https://arxiv.org/ abs/2405.20273

    Gonzales, A., Herrman, R., Campbell, C., Gaidai, I., Liu, J., Tomesh, T., Saleem, Z.H.: Arbitrary State Preparation via Quantum Walks (2024). https://arxiv.org/ abs/2405.20273

    2024

  6. [12]

    IEEE Access12, 46118–46137 (2024) https://doi.org/10.1109/ACCESS.2024.3382150

    Khan, M.A., Aman, M.N., Sikdar, B.: Beyond bits: A review of quantum embed- ding techniques for efficient information processing. IEEE Access12, 46118–46137 (2024) https://doi.org/10.1109/ACCESS.2024.3382150

    2024

  7. [13]

    Nature Physics 15, 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8

    Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics 15, 1273–1278 (2019) https://doi.org/10.1038/s41567-019-0648-8

    2019 doi

  8. [14]

    Accessed via ACM Digital Library (2018)

    Arunachalam, S., Wolf, R.D.: Optimal quantum sample complexity of learning algorithms. Accessed via ACM Digital Library (2018). https://dl.acm.org/doi/ abs/10.5555/3291125.3309633

    2018

  9. [15]

    SIAM Journal on Computing 28 (1999) https://doi

    Bshouty, N.H., Jackson, J.C.: Learning dnf over the uniform distribution using a quantum example oracle. SIAM Journal on Computing 28 (1999) https://doi. org/10.1137/s0097539795293123

    1999 doi

  10. [16]

    Machine Learning 2 (1988) https: //doi.org/10.1023/A:1022821128753

    Angluin, D.: Queries and concept learning. Machine Learning 2 (1988) https: //doi.org/10.1023/A:1022821128753

    1988 doi

  11. [17]

    SIAM Journal on Computing33(5), 1067–1092 (2004) https: //doi.org/10.1137/S0097539704412910

    Servedio, R.A., Gortler, S.J.: Equivalences and separations between quantum and classical learnability. SIAM Journal on Computing33(5), 1067–1092 (2004) https: //doi.org/10.1137/S0097539704412910

    2004 doi

  12. [18]

    Quantum Information and Computation 12, 575–588 (2012) https: //doi.org/10.26421/QIC12.7-8-3

    Gavinsky, D.: Quantum predictive learning and communication complexity with single input. Quantum Information and Computation 12, 575–588 (2012) https: //doi.org/10.26421/QIC12.7-8-3

    2012 doi

  13. [20]

    Quantum Information Processing 6(5), 323–348 (2007) https://doi.org/10.1007/ s11128-007-0061-6

    Atıcı, A., Servedio, R.A.: Quantum algorithms for learning and testing juntas. Quantum Information Processing 6(5), 323–348 (2007) https://doi.org/10.1007/ s11128-007-0061-6

    2007

  14. [21]

    In: ACM International Conference Proceeding Series, vol

    A ¨ ımeur, E., Brassard, G., Gambs, S.: Quantum clustering algorithms. In: ACM International Conference Proceeding Series, vol. 227 (2007). https://doi.org/10. 23 1145/1273496.1273497

    2007

  15. [22]

    Physical Review Letters 117 (2016) https://doi.org/10.1103/PhysRevLett.117

    Dunjko, V., Taylor, J.M., Briegel, H.J.: Quantum-enhanced machine learning. Physical Review Letters 117 (2016) https://doi.org/10.1103/PhysRevLett.117. 130501

    2016 doi

  16. [23]

    Physical Review A 99 (2019) https://doi.org/ 10.1103/PhysRevA.99.032331

    Schuld, M., Bergholm, V., Gogolin, C., Izaac, J., Killoran, N.: Evaluating analytic gradients on quantum hardware. Physical Review A 99 (2019) https://doi.org/ 10.1103/PhysRevA.99.032331

    2019 doi

  17. [24]

    https://arxiv.org/abs/1811.04968

    Bergholm, V., Izaac, J., Schuld, M., Gogolin, C., Ahmed, S., Ajith, V., Alam, M.S., Alonso-Linaje, G., AkashNarayanan, B., Asadi, A., Arrazola, J.M., Azad, U., Banning, S., Blank, C., Bromley, T.R., Cordier, B.A., Ceroni, J., Delgado, A., Matteo, O.D., Dusko, A., Garg, T., Gua...

    2022 arXiv

  18. [25]

    Frontiers of Physics19 (2024) https://doi.org/10.1007/s11467-023-1346-7

    Chen, R., Guang, Z., Guo, C., Feng, G., Hou, S.Y.: Pure quantum gradient descent algorithm and full quantum variational eigensolver. Frontiers of Physics19 (2024) https://doi.org/10.1007/s11467-023-1346-7

    2024 doi

  19. [26]

    The Computer Journal 7 (1965) https://doi.org/10.1093/comjnl/7.4.308

    Nelder, J.A., Mead, R.: A simplex method for function minimization. The Computer Journal 7 (1965) https://doi.org/10.1093/comjnl/7.4.308

    1965 doi

  20. [27]

    Physical Review Research 2 (2020) https: //doi.org/10.1103/PhysRevResearch.2.043158

    Nakanishi, K.M., Fujii, K., Todo, S.: Sequential minimal optimization for quantum-classical hybrid algorithms. Physical Review Research 2 (2020) https: //doi.org/10.1103/PhysRevResearch.2.043158

    2020 doi

  21. [28]

    Nature Communications 9 (2018) https://doi.org/10.1038/s41467-018-07090-4

    McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9 (2018) https://doi.org/10.1038/s41467-018-07090-4

    2018 doi

  22. [29]

    Physical Review Letters 69 (1992) https://doi.org/10.1103/PhysRevLett.69

    White, S.R.: Density matrix formulation for quantum renormalization groups. Physical Review Letters 69 (1992) https://doi.org/10.1103/PhysRevLett.69. 2863

    1992 doi

  23. [30]

    In: Welsh, D.J.A

    Penrose, R.: Applications of negative dimensional tensors. In: Welsh, D.J.A. (ed.) Combinatorial Mathematics and Its Applications, pp. 221–244. Academic Press, Burlington (1971) 24

    1971

  24. [31]

    Physical Review A - Atomic, Molecular, and Optical Physics 65 (2002) https://doi.org/10.1103/ PhysRevA.65.032314

    Vidal, G., Werner, R.F.: Computable measure of entanglement. Physical Review A - Atomic, Molecular, and Optical Physics 65 (2002) https://doi.org/10.1103/ PhysRevA.65.032314

    2002

  25. [32]

    In: Proceedings of the 30th International Conference on Neural Information Process- ing Systems

    Stoudenmire, E.M., Schwab, D.J.: Supervised learning with tensor networks. In: Proceedings of the 30th International Conference on Neural Information Process- ing Systems. NIPS’16, pp. 4806–4814. Curran Associates Inc., Red Hook, NY, USA (2016). https://dl.acm.org/doi/10.5555/...

    2016

  26. [33]

    https://arxiv.org/abs/ 1806.05964

    Glasser, I., Pancotti, N., Cirac, J.I.: From probabilistic graphical models to gen- eralized tensor networks for supervised learning (2019). https://arxiv.org/abs/ 1806.05964

    2019 arXiv

  27. [34]

    In: Journal of the ACM, vol

    Chia, N.H., Lin, H.H., Gily´ en, A., Tang, E., Li, T., Wang, C.: Sampling- based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning. In: Journal of the ACM, vol. 69 (2022). https://doi.org/10. 1145/3549524

    2022

  28. [35]

    Physical Review A 96 (2017) https://doi.org/10.1103/PhysRevA.96.022329

    Chakhmakhchyan, L., Cerf, N.J., Garcia-Patron, R.: Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices. Physical Review A 96 (2017) https://doi.org/10.1103/PhysRevA.96.022329

    2017 doi

  29. [36]

    Quantum 4 (2020) https://doi.org/10.22331/ Q-2020-08-13-307

    Arrazola, J.M., Delgado, A., Bardhan, B.R., Lloyd, S.: Quantum-inspired algorithms in practice. Quantum 4 (2020) https://doi.org/10.22331/ Q-2020-08-13-307

    2020

  30. [37]

    In: Proceedings of the Annual ACM Symposium on Theory of Computing (2019)

    Tang, E.: A quantum-inspired classical algorithm for recommendation systems. In: Proceedings of the Annual ACM Symposium on Theory of Computing (2019). https://doi.org/10.1145/3313276.3316310

    2019

  31. [38]

    Nature Physics 14 (2018) https: //doi.org/10.1038/s41567-018-0048-5

    Torlai, G., Mazzola, G., Carrasquilla, J., Troyer, M., Melko, R., Carleo, G.: Neural-network quantum state tomography. Nature Physics 14 (2018) https: //doi.org/10.1038/s41567-018-0048-5

    2018 doi

  32. [39]

    Nature Physics 13 (2017) https://doi.org/10.1038/nphys4035

    Carrasquilla, J., Melko, R.G.: Machine learning phases of matter. Nature Physics 13 (2017) https://doi.org/10.1038/nphys4035

    2017 doi

  33. [40]

    Physical Review B 94 (2016) https://doi.org/10.1103/PhysRevB.94.195105

    Wang, L.: Discovering phase transitions with unsupervised learning. Physical Review B 94 (2016) https://doi.org/10.1103/PhysRevB.94.195105

    2016 doi

  34. [42]

    Quantum Machine 25 Intelligence 2 (2020) https://doi.org/10.1007/s42484-020-00012-y

    Henderson, M., Shakya, S., Pradhan, S., Cook, T.: Quanvolutional neural net- works: powering image recognition with quantum circuits. Quantum Machine 25 Intelligence 2 (2020) https://doi.org/10.1007/s42484-020-00012-y

    2020 doi

  35. [43]

    In: Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M.F., Lin, H

    Bausch, J.: Recurrent quantum neural networks. In: Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M.F., Lin, H. (eds.) Advances in Neural Information Processing Systems, vol. 33, pp. 1368–1379 (2020). https://proceedings.neurips. cc/paper files/paper/2020/file/0ec96be397dd6...

    2020

  36. [44]

    Nature 567 (2019) https://doi.org/10.1038/s41586-019-0980-2

    Havl ´ ıˇ cek, V., C´ orcoles, A.D., Temme, K., Harrow, A.W., Kandala, A., Chow, J.M., Gambetta, J.M.: Supervised learning with quantum-enhanced feature spaces. Nature 567 (2019) https://doi.org/10.1038/s41586-019-0980-2

    2019 doi

  37. [45]

    Quantum Machine Intelligence 4 (2022) https://doi.org/10

    Hur, T., Kim, L., Park, D.K.: Quantum convolutional neural network for classical data classification. Quantum Machine Intelligence 4 (2022) https://doi.org/10. 1007/s42484-021-00061-x

    2022

  38. [46]

    Nature Physics 17 (2021) https://doi.org/10

    Liu, Y., Arunachalam, S., Temme, K.: A rigorous and robust quantum speed- up in supervised machine learning. Nature Physics 17 (2021) https://doi.org/10. 1038/s41567-021-01287-z

    2021

  39. [47]

    Quantum Science and Technology 7 (2022) https://doi.org/10.1088/2058-9565/ac4f2f

    Casares, P.A.M., Campos, R., Martin-Delgado, M.A.: Qfold: Quantum walks and deep learning to solve protein folding. Quantum Science and Technology 7 (2022) https://doi.org/10.1088/2058-9565/ac4f2f

    2022 doi

  40. [48]

    Physical Review X 8 (2018) https://doi.org/10.1103/PhysRevX

    Amin, M.H., Andriyash, E., Rolfe, J., Kulchytskyy, B., Melko, R.: Quantum boltz- mann machine. Physical Review X 8 (2018) https://doi.org/10.1103/PhysRevX. 8.021050

    2018 doi

  41. [49]

    https://arxiv.org/abs/1411.4028

    Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014). https://arxiv.org/abs/1411.4028

    2014 arXiv

  42. [50]

    https://arxiv.org/abs/2403

    Bowles, J., Ahmed, S., Schuld, M.: Better than classical? The subtle art of bench- marking quantum machine learning models (2024). https://arxiv.org/abs/2403. 07059

    2024

  43. [51]

    Nature Physics 10 (2014) https://doi.org/10.1038/NPHYS3029

    Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nature Physics 10 (2014) https://doi.org/10.1038/NPHYS3029

    2014 doi

  44. [53]

    Tang, E.: Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions. Phys. Rev. Lett. 127, 060503 (2021) https://doi.org/10.1103/PhysRevLett.127.060503

    2021 doi

  45. [54]

    : Variational quantum algorithms

    Cerezo, M., et al. : Variational quantum algorithms. Nature Reviews Physics 3, 26 625–644 (2021) https://doi.org/10.1038/s42254-021-00348-9

    2021 doi

  46. [55]

    Quantum 2, 79 (2018) https://doi.org/10.22331/q-2018-08-06-79

    Preskill, J.: Quantum computing in the nisq era and beyond. Quantum 2, 79 (2018) https://doi.org/10.22331/q-2018-08-06-79

    2018 doi

  47. [56]

    Reviews of Modern Physics 84, 621 (2012) https://doi.org/10.1103/RevModPhys.84.621

    Weedbrook, C., et al.: Gaussian quantum information. Reviews of Modern Physics 84, 621 (2012) https://doi.org/10.1103/RevModPhys.84.621

    2012 doi

  48. [57]

    Science 355, 602–606 (2017) https://doi.org/10.1126/science

    Carleo, G., Troyer, M.: Solving the quantum many-body problem with artificial neural networks. Science 355, 602–606 (2017) https://doi.org/10.1126/science. aag2302

    2017 doi

  49. [58]

    Machine Learning 113, 1189–1217 (2024) https://doi.org/10.1007/ s10994-023-06490-y

    Heese, R., Wolter, M., M¨ ucke, S., Franken, L., Piatkowski, N.: On the effects of biased quantum random numbers on the initialization of artificial neural networks. Machine Learning 113, 1189–1217 (2024) https://doi.org/10.1007/ s10994-023-06490-y

    2024

  50. [59]

    Nature Computational Science 2, 567–576 (2022) https://doi.org/10.1038/s43588-022-00311-3

    Cerezo, M., Verdon, G., Huang, H.-Y., Cincio, L., Coles, P.J.: Challenges and opportunities in quantum machine learning. Nature Computational Science 2, 567–576 (2022) https://doi.org/10.1038/s43588-022-00311-3

    2022 doi

  51. [60]

    Physical Review A 86, 032324 (2012) https://doi.org/10.1103/PhysRevA.86.032324

    Fowler, A.G., Mariantoni, M., Martinis, J.M., Cleland, A.N.: Surface codes: Towards practical large-scale quantum computation. Physical Review A 86, 032324 (2012) https://doi.org/10.1103/PhysRevA.86.032324

    2012 doi

  52. [61]

    Nature 574, 505–510 (2019) https://doi.org/10.1038/s41586-019-1666-5

    Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G.S.L., Buell, D.A., Burkett, B., Chen, Y., Chen, Z., Chiaro, B., Collins, R., Courtney, W., Dunsworth, A., Farhi, E., Foxen, B., Fowler, A., Gidney, C., Giustina, M., Gra...

    2019

  53. [62]

    Nature Communications 9, 4195 (2018) https://doi.org/10.1038/ s41467-018-06598-z

    Xia, R., Kais, S.: Quantum machine learning for electronic structure cal- culations. Nature Communications 9, 4195 (2018) https://doi.org/10.1038/ s41467-018-06598-z

    2018

  54. [63]

    Physical Review Letters 27 81, 5932–5935 (1998) https://doi.org/10.1103/PhysRevLett.81.5932

    Briegel, H.-J., D¨ ur, W., Cirac, J.I., Zoller, P.: Quantum repeaters: The role of imperfect local operations in quantum communication. Physical Review Letters 27 81, 5932–5935 (1998) https://doi.org/10.1103/PhysRevLett.81.5932

    1998 doi

  55. [64]

    Physical Review Letters 121, 040502 (2018) https://doi.org/10.1103/PhysRevLett.121

    Lloyd, S., Weedbrook, C.: Quantum generative adversarial learning. Physical Review Letters 121, 040502 (2018) https://doi.org/10.1103/PhysRevLett.121. 040502

    2018 doi

  56. [65]

    Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisci- plinary Topics 58 (1998) https://doi.org/10.1103/PhysRevE.58.5355

    Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse ising model. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisci- plinary Topics 58 (1998) https://doi.org/10.1103/PhysRevE.58.5355

    1998 doi

  57. [66]

    Quantum Science and Technology 4, 043001 (2019) https://doi.org/10.1088/2058-9565/ab4eb5 28

    Benedetti, M., Lloyd, E., Sack, S., Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quantum Science and Technology 4, 043001 (2019) https://doi.org/10.1088/2058-9565/ab4eb5 28

    2019 doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.