Pith. sign in

REVIEW 1 major objections 4 minor 7 cited by

This review maps the growing field of AI for quantum system characterization into three learning paradigms—machine learning, deep learning, and language models—and two core tasks, quantum property prediction and surrogate construction, argu

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 →

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

T0 review · deepseek-v4-flash

2026-08-05 05:45 UTC pith:CNO6B4PP

load-bearing objection A genuinely useful survey whose central three-paradigm framing does not hold up under close reading. the 1 major comments →

arxiv 2509.04923 v1 pith:CNO6B4PP submitted 2025-09-05 quant-ph cs.AIcs.LG

Artificial intelligence for representing and characterizing quantum systems

Yuxuan Du , Yan Zhu , Yuan-Hang Zhang , Min-Hsiu Hsieh , Patrick Rebentrost , Weibo Gao , Ya-Dong Wu , Jens Eisert
show 3 more authors
Giulio Chiribella Dacheng Tao Barry C. Sanders
This is my paper
classification quant-ph cs.AIcs.LG MSC 81P6868T0781-02
keywords quantum system characterizationquantum property predictionneural quantum stateslanguage models for quantum simulationclassical shadowsmachine learning for quantum many-body physicsfoundation models for quantum systemsquantum benchmarking
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.

This review argues that the many recent efforts to use artificial intelligence for understanding large quantum systems are best understood through a small map: three learning paradigms—machine learning, deep learning, and language models—applied to two core tasks, predicting quantum properties and building surrogates for quantum states. The authors assemble evidence from theoretical guarantees, numerical simulations, and experiments to show that each paradigm contributes differently: ML offers provably efficient prediction of linear properties; DL extends prediction to nonlinear properties and learns generative surrogates; language models pre-train on measurement statistics to become reusable foundation models. If this framing holds, it gives researchers a principled way to choose methods and clarifies where the open problems lie, such as whether advanced models really outperform classical ML under equal measurement budgets. The review's value is organizational and critical: it consolidates a rapidly growing literature and identifies benchmarks and theoretical questions that would settle the field's direction.

Core claim

The paper's central claim is that AI-based characterization of scalable quantum systems—states from analog simulators and digital quantum computers—can be systematically organized by AI methodology rather than by application. It identifies three learning paradigms: machine learning (linear-regression and kernel models with engineered feature maps), deep learning (neural networks that learn representations and generative models), and language models (GPT-style transformers pre-trained on measurement distributions and fine-tuned for downstream tasks). These paradigms address two core tasks: quantum property prediction (linear and nonlinear) and the construction of surrogates for quantum states

What carries the argument

The organizing machinery is a task-paradigm matrix. On one axis sit the learning paradigms: ML models built on engineered feature maps and kernels (e.g., truncated Dirichlet kernel, shadow-representation predictors), DL models that learn latent representations and act as generative models (e.g., autoregressive RNNs and transformers, energy-based RBMs), and GPT-style language models that pre-train on measurement outcome distributions and fine-tune for specific properties. On the other axis sit the tasks: linear property prediction (expectation values of observables), nonlinear property prediction (entropy, fidelity, phase classification), and implicit quantum state reconstruction (learning a

Load-bearing premise

The review's whole structure depends on the assumption that 'machine learning, deep learning, and language models' is a faithful and useful way to slice the field; since the paper itself notes deep learning is a subclass of machine learning and language models are a class of deep learning, the categories are not clean, and if the taxonomy is arbitrary the review's organizing value collapses to that of an annotated bibliography.

What would settle it

Run a pre-registered benchmark that fixes the total quantum measurement budget and training data for a canonical family (e.g., 2D random Heisenberg ground states) and compares kernel ML, a CNN/transformer DL model, and a GPT-style LM on identical property prediction tasks. If DL and LM models never outperform the kernel method under any fair budget, the paper's 'synergistic paradigms' framing would lose its practical justification, reducing to an annotated bibliography.

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

Share X Bluesky LinkedIn Reddit HN

If this is right

  • If the map is correct, researchers can select a paradigm by task: kernel ML when provable guarantees on linear properties are required; DL when nonlinear or multi-property predictions are needed; LMs when reusable, fine-tunable surrogates across state families are wanted.
  • The distinction between measurement-agnostic and measurement-based protocols becomes a primary design choice: it determines whether the trained model needs quantum measurement data at prediction time.
  • Open benchmarks under fixed measurement budgets would decide whether DL/LM advantages over ML are real; the review notes current comparisons are often unfair due to differing measurement strategies.
  • A general-purpose foundation model for quantum systems, pre-trained on diverse quantum data and fine-tuned to new tasks, is a concrete next target if the LM paradigm scales.
  • Provably efficient ML for nonlinear properties, such as entanglement or fidelity, remains the central open theoretical question, with topological phase classification as the only known nontrivial case.

Where Pith is reading between the lines

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

  • The taxonomy implies that the bottleneck for AI-driven characterization may shift from model architecture to data acquisition and measurement design; if so, investment in measurement protocols and open datasets could matter more than new neural architectures.
  • The convergence of classical shadows and learned latent representations suggests a possible unified 'learned shadow' formulation, where both serve as compressed summaries of quantum states; a testable extension would be comparing their sample-complexity trade-offs on the same tasks.
  • The review's emphasis on measurement-based protocols hints that future quantum advantage may be located in adaptive measurement strategies rather than in model expressivity—an inference the paper does not explicitly draw.
  • If foundation models trained on measurement statistics scale like language models, one might expect 'scaling laws' for quantum-state surrogates, where performance improves predictably with model size and training data—an untested but natural prediction from the LM paradigm.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 4 minor

Summary. This manuscript is a review of AI-based approaches to representing and characterizing scalable quantum systems. It organizes recent literature into three paradigms—machine learning, deep learning, and language models—applied to two core tasks: quantum property prediction and construction of quantum-state surrogates. The paper gives general workflows, representative algorithms, tables of methods, and a list of open questions. The ML sections emphasize provable sample-complexity results for linear property prediction; the DL sections cover property prediction, implicit state reconstruction, and applications to quantum computing; the LM section discusses GPT-style foundation models. The review also candidly notes that controlled comparisons of DL/LM versus classical ML are still lacking.

Significance. The manuscript is useful as a broad, reasonably careful survey: it assembles a large literature, is explicit about scope, and states sample-complexity results in Section III with care. It also deserves credit for openly flagging, in Section VI, that systematic benchmarking has not established a consistent advantage of deep learning or language models over classical ML, and for citing Ref. [299] in this context. If the organizing taxonomy were applied consistently, the review would be a valuable entry point for researchers choosing among ML, DL, and LM methods. However, the central three-paradigm claim is not supported consistently at the boundary between the deep-learning and language-model sections; this needs to be fixed before the paper's main organizing message is reliable.

major comments (1)
  1. [Sec. V.A–V.B (Eq. (12), 'Foundation model without quantum data')] The LM paradigm is defined in Section V.A by GPT-style pre-training/fine-tuning and an autoregressive negative log-likelihood objective over measurement outcomes (Eq. (12)). Yet the third concrete class in Section V.B, 'Foundation model without quantum data,' classifies Ref. [207] as an LM even though the displayed loss for that model is a variational energy ⟨ψ(θ;x)|H(x)|ψ(θ;x)⟩/⟨ψ(θ;x)|ψ(θ;x)⟩, with no autoregressive or language-modeling objective and no pre-training/fine-tuning protocol. This is not a boundary case: it is the variational neural-quantum-state approach already discussed under deep learning in Section IV.B.3, which the paper says is not its primary focus. Because the abstract's central claim is that AI-driven characterization is faithfully categorized into three paradigms, this inconsistent classification is load-bearing. Please reclassify Ref. [207], broaden the definiti
minor comments (4)
  1. [Sec. II] The introduction of Fig. 2 and the text state that DL is a subfield of ML and that LMs are a specific class of DL architectures. The abstract nonetheless advertises 'three synergistic paradigms.' Please clarify whether the taxonomy is a partition of the field or a methodological hierarchy; if the latter, define 'paradigm' accordingly so that readers do not expect disjoint categories.
  2. [Eq. (12)] The symbol T is overloaded: in Eq. (3) it is the number of measurement shots per state, while in Eq. (12) T(x^{(i)}) denotes the set of measurement outcomes and T also denotes the number of snapshots. Please use distinct notation, e.g., M(x^{(i)}) for the outcome set.
  3. [Table I and Sec. III.B.1] The runtime expression O(dO(C/ϵ)) is ambiguous and appears both in the text and in Table I. Please clarify the intended dependence (e.g., O(d · poly(C/ϵ)) or O(d · 2^{O(C/ϵ)})).
  4. [Sec. VI, Question 3] The review's own discussion concedes that DL does not consistently outperform classical ML and that random forest outperforms DL in error-mitigation benchmarks. This is honest, but it creates tension with the 'synergistic paradigms' framing. Please spell out what 'synergy' means concretely—e.g., different trade-offs in sample efficiency, measurement access, or transferability—so the central organizational claim is not merely a list of architectures.

Circularity Check

0 steps flagged

No circularity: the paper is an organizational literature review; its taxonomy is not a derived prediction and self-citations are illustrative, not load-bearing.

full rationale

This paper is a literature review, not a derivation. Its central claim is taxonomic: AI approaches for quantum system characterization can be organized into ML, DL, and LM paradigms applied to property prediction and state reconstruction. No quantity is derived from first principles, no fitted parameter is relabeled as a prediction, and no uniqueness theorem is invoked to force a choice. The cited works, including self-citations such as Refs. [81,199,282,283,302,303], serve as examples within the described taxonomy rather than as load-bearing evidence for a derived result. The review explicitly disclaims that any single categorization is definitive (Section II.C: 'no single and definitive categorization can encompass all models'), so the taxonomy is not presented as forced by prior results. The manuscript does contain a notable internal inconsistency: Section V.A defines the LM paradigm by GPT-style autoregressive pretraining (Eq. 12), yet Section V.B's 'Foundation model without quantum data' (describing Ref. [207]) is a variational energy-minimizing transformer ansatz, which the paper's own Section IV.B.3 classifies under variational NQS and which lacks a language-modeling objective. This is an organizational inconsistency and a potential correctness concern, but it is not circularity: no claim is reduced to its own input by construction. The review's value as an annotated map of the field may be questioned, but the circularity burden is not met. Score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

No free parameters, no derived equations, and no new physical entities; the ledger reflects the assumptions any reader must grant to trust the review.

axioms (3)
  • standard math The Hilbert space of an N-qubit system has dimension 2^N, so exact classical description is infeasible for large N.
    Invoked in the Introduction to motivate learning-based characterization.
  • ad hoc to paper The works surveyed since 2022 are representative of the field.
    Scope selection stated in the Introduction; not derived from any benchmark.
  • domain assumption Citations accurately reflect the methods and results being summarized.
    The review's reliability as a survey depends on faithful reporting of numerous cited theorems and experiments.

pith-pipeline@v1.4.0-alltime-deepseek-medium · 46132 in / 8545 out tokens · 81070 ms · 2026-08-05T05:45:57.115508+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of Artificial intelligence for representing and characterizing quantum systems." pith.science (2026). https://pith.science/paper/CNO6B4PP

@misc{pith2026250904923,
  author       = {Pith},
  title        = {Pith review of: Artificial intelligence for representing and characterizing quantum systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CNO6B4PP}},
  note         = {Machine review of arXiv:2509.04923}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Efficient characterization of large-scale quantum systems, especially those produced by quantum analog simulators and megaquop quantum computers, poses a central challenge in quantum science due to the exponential scaling of the Hilbert space with respect to system size. Recent advances in artificial intelligence (AI), with its aptitude for high-dimensional pattern recognition and function approximation, have emerged as a powerful tool to address this challenge. A growing body of research has leveraged AI to represent and characterize scalable quantum systems, spanning from theoretical foundations to experimental realizations. Depending on how prior knowledge and learning architectures are incorporated, the integration of AI into quantum system characterization can be categorized into three synergistic paradigms: machine learning, and, in particular, deep learning and language models. This review discusses how each of these AI paradigms contributes to two core tasks in quantum systems characterization: quantum property prediction and the construction of surrogates for quantum states. These tasks underlie diverse applications, from quantum certification and benchmarking to the enhancement of quantum algorithms and the understanding of strongly correlated phases of matter. Key challenges and open questions are also discussed, together with future prospects at the interface of AI and quantum science.

Figures

Figures reproduced from arXiv: 2509.04923 by Barry C. Sanders, Dacheng Tao, Giulio Chiribella, Jens Eisert, Min-Hsiu Hsieh, Patrick Rebentrost, WeiBo Gao, Ya-Dong Wu, Yan Zhu, Yuan-Hang Zhang, Yuxuan Du.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 7 Pith papers

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

  1. OmniQEC: discovering practical quantum error-correcting codes by an AI scientist

    quant-ph 2026-07 conditional novelty 6.0

    OmniQEC discovers qLDPC codes whose simulated circuit-level logical error rates beat the BB [[72,12,6]] and [[144,12,12]] baselines at 98- and 240-qubit budgets.

  2. Learning Topological Quantum Phases from Limited Subsystems

    quant-ph 2026-07 accept novelty 6.0

    Quantum kernels built from reduced density matrices of 1–4 sites classify the full phase diagrams of the generalized cluster-Ising and anisotropic Haldane chains, including SPT phases, and generalize across system sizes.

  3. Learning to Reconstruct Wigner Functions in Phase Space

    quant-ph 2026-07 conditional novelty 6.0

    Two machine learning models reconstruct continuous Wigner functions from sparse phase-space measurements: a provably efficient regression model for sparse states (O(s⁴ log d) samples) and a self-supervised neural netw...

  4. Comparing Classical Simulation and Sample-Based Learning of Quantum Systems

    quant-ph 2026-05 conditional novelty 6.0

    For random MPS and Clifford+T circuits, increases in entanglement or T-count correlate with sharper loss minima and worse reconstruction under constrained neural capacity.

  5. Comparing Classical Simulation and Sample-Based Learning of Quantum Systems

    quant-ph 2026-05 unverdicted novelty 5.0

    Empirical study finds neural-network learning difficulty (via Hessian eigenvalue and random subspace optimization) correlates with classical simulation hardness parameterized by MPS bond dimension and T-gate count.

  6. Spectral Decimation of Quantum Many-Body Hamiltonians

    cond-mat.stat-mech 2026-02 conditional novelty 5.0

    For a spectrum that is a statistical mixture of independent symmetry sectors, the correlated remainder after removing Poisson-distributed gaps has expected size equal to the size-biased average of the sector dimensions.

  7. Data-Driven Learnability Transition of Measurement-Induced Entanglement

    quant-ph 2025-12 conditional novelty 5.0

    A transformer trained only on measurement outcomes estimates measurement-induced entanglement with polynomial resources below a critical circuit depth; above it the estimate saturates at maximal uncertainty — a learna...

Reference graph

Works this paper leans on

300 extracted references · 32 canonical work pages · cited by 6 Pith papers · 18 internal anchors

  1. [1]

    Aaronson

    S. Aaronson. Shadow tomography of quantum states. InPro- ceedings of the 50th annual ACM SIGACT symposium on the- ory of computing, pages 325–338, 2018

    2018

  2. [2]

    Aaronson and D

    S. Aaronson and D. Gottesman. Improved simulation of sta- bilizer circuits.Physical Review A—Atomic, Molecular, and Optical Physics, 70:052328, 2004

    2004

  3. [3]

    Acampora et al

    G. Acampora et al. Quantum computing and artificial intelli- gence: status and perspectives.arXiv:2505.23860, 2025

    Pith/arXiv arXiv 2025

  4. [4]

    Agrawal, J

    U. Agrawal, J. Lopez-Piqueres, R. Vasseur, S. Gopalakrish- nan, and A. C. Potter. Observing quantum measurement collapse as a learnability phase transition.Phys. Rev. X, 14:041012, Oct 2024

    2024

  5. [5]

    Aharonov, X

    D. Aharonov, X. Gao, Z. Landau, Y . Liu, and U. Vazirani. A polynomial-time classical algorithm for noisy random circuit sampling. InProceedings of the 55th Annual ACM Symposium on Theory of Computing, pages 945–957, 2023

    2023

  6. [6]

    Ahmed, C

    S. Ahmed, C. S. Mu ˜noz, F. Nori, and A. F. Kockum. Quan- tum state tomography with conditional generative adversarial networks.Phys. Rev. Lett., 127:140502, 2021

    2021

  7. [7]

    G. Q. AI and Collaborators. Quantum error correction below the surface code threshold.Nature, 638:920–926, 2025

    2025

  8. [8]

    Ai and Y .-X

    H. Ai and Y .-X. Liu. Scalable parameter design for supercon- ducting quantum circuits with graph neural networks.Phys. Rev. Lett., 135:040601, 2025

    2025

  9. [9]

    A. A. Akhtar, H.-Y . Hu, and Y .-Z. You. Measurement- induced criticality is tomographically optimal.Phys. Rev. B, 109:094209, Mar 2024

    2024

  10. [10]

    Alexeev et al

    Y . Alexeev et al. Artificial intelligence for quantum comput- ing.arXiv:2411.09131, 2024

    arXiv 2024

  11. [11]

    Z. An, J. Wu, Z. Lin, X. Yang, K. Li, and B. Zeng. Dual- capability machine learning models for quantum hamiltonian parameter estimation and dynamics prediction.Phys. Rev. Lett., 134:120202, 2025

    2025

  12. [12]

    Z. An, J. Wu, M. Yang, D. L. Zhou, and B. Zeng. Uni- fied quantum state tomography and Hamiltonian learning: A language-translation-like approach for quantum systems. Phys. Rev. Appl., 21:014037, 2024

    2024

  13. [13]

    T. I. Andersen et al. Thermalization and criticality on an analogue–digital quantum simulator.Nature, 638:79–85, 2025

    2025

  14. [14]

    Anshu and S

    A. Anshu and S. Arunachalam. A survey on the complexity of learning quantum states.Nature Rev. Phys., 6:59–69, 2024

    2024

  15. [15]

    Arnold and F

    J. Arnold and F. Sch ¨afer. Replacing neural networks by opti- mal analytical predictors for the detection of phase transitions. Phys. Rev. X, 12:031044, 2022

    2022

  16. [16]

    Arnold, F

    J. Arnold, F. Sch ¨afer, M. ˇZonda, and A. U. J. Lode. Inter- pretable and unsupervised phase classification.Phys. Rev. Res., 3:033052, 2021

    2021

  17. [17]

    Arunachalam and R

    S. Arunachalam and R. de Wolf. Guest column: A survey of quantum learning theory.ACM Sigact News, 48:41–67, 2017

    2017

  18. [18]

    N. Asif, U. Khalid, A. Khan, T. Q. Duong, and H. Shin. En- tanglement detection with artificial neural networks.Sci. Rep., 13:1562, 2023

    2023

  19. [19]

    Baltru ˇsaitis, C

    T. Baltru ˇsaitis, C. Ahuja, and L.-P. Morency. Multimodal ma- chine learning: A survey and taxonomy.IEEE Trans. Patt. Ana. Mach. Int., 41:423–443, 2018

    2018

  20. [20]

    T. Bao, X. Ye, H. Ruan, C. Liu, W. Wu, and J. Yan. Beyond cir- cuit connections: A non-message passing graph transformer approach for quantum error mitigation. InThe Thirteenth In- ternational Conference on Learning Representations

  21. [21]

    Barratt, U

    F. Barratt, U. Agrawal, A. C. Potter, S. Gopalakrishnan, and R. Vasseur. Transitions in the learnability of global charges from local measurements.Phys. Rev. Lett., 129:200602, Nov 2022

    2022

  22. [22]

    Bausch et al

    J. Bausch et al. Learning high-accuracy error decoding for quantum processors.Nature, pages 1–7, 2024

    2024

  23. [23]

    Begu ˇsi´c, J

    T. Begu ˇsi´c, J. Gray, and G. K.-L. Chan. Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance.Sci. Adv., 10:eadk4321, 2024

    2024

  24. [24]

    Bengio, A

    Y . Bengio, A. Courville, and P. Vincent. Representation learn- ing: A review and new perspectives.IEEE Trans. Patt. Ana. Mach. Int., 35:1798–1828, 2013

    2013

  25. [25]

    E. R. Bennewitz, F. Hopfmueller, B. Kulchytskyy, J. Car- rasquilla, and P. Ronagh. Neural error mitigation of near-term quantum simulations.Nature Mach. Intell., 4:618–624, 2022

    2022

  26. [26]

    Bertoni, J

    C. Bertoni, J. Haferkamp, M. Hinsche, M. Ioannou, J. Eis- ert, and H. Pashayan. Shallow shadows: Expectation estima- tion using low-depth random clifford circuits.Phys. Rev. Lett., 133:020602, 2024

    2024

  27. [27]

    Bharti et al

    K. Bharti et al. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys., 94:015004, 2022

    2022

  28. [28]

    C. M. Bishop and N. M. Nasrabadi.Pattern recognition and machine learning, volume 4. Springer, 2006

    2006

  29. [29]

    Bluvstein et al

    D. Bluvstein et al. Logical quantum processor based on recon- figurable atom arrays.Nature, 626:58–65, 2024

    2024

  30. [30]

    Bohrdt, S

    A. Bohrdt, S. Kim, A. Lukin, M. Rispoli, R. Schittko, M. Knap, M. Greiner, and J. L ´eonard. Analyzing nonequilib- 26 rium quantum states through snapshots with artificial neural networks.Phys. Rev. Lett., 127:150504, 2021

    2021

  31. [31]

    D. A. Boiko, R. MacKnight, B. Kline, and G. Gomes. Au- tonomous chemical research with large language models.Na- ture, 624:570–578, 2023

    2023

  32. [32]

    Bouland, B

    A. Bouland, B. Fefferman, S. Ghosh, T. Metger, U. Vazirani, C. Zhang, and Z. Zhou. Public-key pseudoentanglement and the hardness of learning ground state entanglement structure. arXiv:2311.12017, 2023

    Pith/arXiv arXiv 2023

  33. [33]

    Bouland, C

    A. Bouland, C. Zhang, and Z. Zhou. On the hardness of learn- ing ground state entanglement of geometrically local Hamil- tonians.arXiv:2411.04353, 2024

    Pith/arXiv arXiv 2024

  34. [34]

    Bourgund et al

    D. Bourgund et al. Formation of individual stripes in a mixed-dimensional cold-atom Fermi–Hubbard system.Na- ture, 637:57–62, 2025

    2025

  35. [35]

    Bravyi and D

    S. Bravyi and D. Gosset. Improved classical simulation of quantum circuits dominated by Clifford gates.Phys. Rev. Lett., 116:250501, 2016

    2016

  36. [36]

    Brown et al

    T. Brown et al. Language models are few-shot learners.Adv. Neur. Inf. Proc. Sys., 33:1877–1901, 2020

    1901

  37. [37]

    Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Huggins, Y . Li, J. R. McClean, and T. E. O’Brien. Quantum error miti- gation.Rev. Mod. Phys., 95:045005, 2023

    2023

  38. [38]

    Campaioli, J

    F. Campaioli, J. H. Cole, and H. Hapuarachchi. Quantum mas- ter equations: Tips and tricks for quantum optics, quantum computing, and beyond.PRX Quantum, 5:020202, 2024

    2024

  39. [39]

    Campbell, H

    C. Campbell, H. M. Chen, W. Luk, and H. Fan. Enhancing LLM-based quantum code generation with multi-agent opti- mization and quantum error correction.arXiv:2504.14557, 2025

    Pith/arXiv arXiv 2025

  40. [40]

    H. Cao, F. Pan, Y . Wang, and P. Zhang. qecGPT: decoding quantum error-correcting codes with generative pre-trained transformers.arXiv:2307.09025, 2023

    Pith/arXiv arXiv 2023

  41. [41]

    S. Cao, Z. Zhang, M. Alghadeer, S. D. Fasciati, M. Piscitelli, M. Bakr, P. Leek, and A. Aspuru-Guzik. Agents for self-driving laboratories applied to quantum computing. arXiv:2412.07978, 2024

    arXiv 2024

  42. [42]

    Y . Cao, S. Li, Y . Liu, Z. Yan, Y . Dai, P. S. Yu, and L. Sun. A comprehensive survey of AI-generated content (AIGC): A history of generative AI from GAN to ChatGPT. arXiv:2303.04226, 2023

    Pith/arXiv arXiv 2023

  43. [43]

    Carleo, I

    G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. V ogt-Maranto, and L. Zdeborov ´a. Ma- chine learning and the physical sciences.Rev. Mod. Phys., 91:045002, 2019

    2019

  44. [44]

    Carleo and M

    G. Carleo and M. Troyer. Solving the quantum many-body problem with artificial neural networks.Science, 355:602– 606, 2017

    2017

  45. [45]

    Carrasco, A

    J. Carrasco, A. Elben, C. Kokail, B. Kraus, and P. Zoller. The- oretical and experimental perspectives of quantum verifica- tion.PRX Quantum, 2:010102, 2021

    2021

  46. [46]

    Carrasquilla

    J. Carrasquilla. Machine learning for quantum matter.Adv. Phys. X, 5:1797528, 2020

    2020

  47. [47]

    Carrasquilla and R

    J. Carrasquilla and R. G. Melko. Machine learning phases of matter.Nature Phys., 13:431, 2017

    2017

  48. [48]

    Carrasquilla and G

    J. Carrasquilla and G. Torlai. How to use neural networks to investigate quantum many-body physics.PRX Quantum, 2:040201, 2021

    2021

  49. [49]

    Carrasquilla, G

    J. Carrasquilla, G. Torlai, R. G. Melko, and L. Aolita. Re- constructing quantum states with generative models.Nature Mach. Intell., 1:155–161, 2019

    2019

  50. [50]

    Cerezo et al

    M. Cerezo et al. Variational quantum algorithms.Nature Rev. Phys., 3:625–644, 2021

    2021

  51. [51]

    Cerezo et al

    M. Cerezo et al. Does provable absence of barren plateaus imply classical simulability? or, why we need to rethink vari- ational quantum computing.arXiv:2312.09121, 2023

    Pith/arXiv arXiv 2023

  52. [52]

    Cerezo, M

    M. Cerezo, M. Larocca, D. Garc ´ıa-Mart´ın, N. L. Diaz, P. Braccia, E. Fontana, M. S. Rudolph, S. T. Pablo Bermejo, Aroosa Ijaz, E. R. Anschuetz, and Z. Holmes. Does provable absence of barren plateaus imply classical simulability.Nature Comm., 16:7907, 2025

    2025

  53. [53]

    Cervera-Lierta, J

    A. Cervera-Lierta, J. S. Kottmann, and A. Aspuru-Guzik. Meta-variational quantum eigensolver: Learning energy pro- files of parameterized Hamiltonians for quantum simulation. PRX Quantum, 2:020329, 2021

    2021

  54. [54]

    P. Cha, P. Ginsparg, F. Wu, J. Carrasquilla, P. L. McMahon, and E.-A. Kim. Attention-based quantum tomography.Mach. Learn. Sci. Technol., 3:01LT01, 2021

    2021

  55. [55]

    Chang et al

    Y . Chang et al. A survey on evaluation of large language mod- els.ACM transactions on intelligent systems and technology, 15:1–45, 2024

    2024

  56. [56]

    L. Che, C. Wei, Y . Huang, D. Zhao, S. Xue, X. Nie, J. Li, D. Lu, and T. Xin. Learning quantum Hamiltonians from single-qubit measurements.Phys. Rev. Res., 3:023246, 2021

    2021

  57. [57]

    Y . Che, C. Gneiting, and F. Nori. Exponentially improved efficient machine learning for quantum many-body states with provable guarantees.Phys. Rev. Res., 6:033035, 2024

    2024

  58. [58]

    Y . Che, C. Gneiting, X. Wang, and F. Nori. Quantum circuit complexity and unsupervised machine learning of topological order.arXiv preprint arXiv:2508.04486, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  59. [59]

    Chen and M

    A. Chen and M. Heyl. Empowering deep neural quantum states through efficient optimization.Nature Phys., 20:1476– 1481, 2024

    2024

  60. [60]

    C. Chen, C. Ren, H. Lin, and H. Lu. Entanglement struc- ture detection via machine learning.Quantum Sci. Tech., 6:035017, 2021

    2021

  61. [61]

    S. Chen, Y . Liu, M. Otten, A. Seif, B. Fefferman, and L. Jiang. The learnability of Pauli noise.Nature Comm., 14:52, 2023

    2023

  62. [62]

    S. Chen, J. d. D. Pont, J.-T. Hsieh, H.-Y . Huang, J. Lange, and J. Li. Predicting quantum channels over general product distributions.arXiv:2409.03684, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  63. [63]

    Y . Chen, Y . Pan, G. Zhang, and S. Cheng. Detecting quantum entanglement with unsupervised learning.Quantum Sci. Tech., 7:015005, 2021

    2021

  64. [64]

    Z. Chen, X. Lin, and Z. Wei. Certifying unknown genuine multipartite entanglement by neural networks.Quantum Sci. Tech., 8:035029, 2023

    2023

  65. [65]

    Cho and D

    G. Cho and D. Kim. Machine learning on quantum experimen- tal data toward solving quantum many-body problems.Nature Comm., 15:7552, 2024

    2024

  66. [66]

    M. Choi, D. Flam-Shepherd, T. H. Kyaw, and A. Aspuru- Guzik. Learning quantum dynamics with latent neural ordi- nary differential equations.Phys. Rev. A, 105:042403, 2022

    2022

  67. [67]

    Cimini, M

    V . Cimini, M. Barbieri, N. Treps, M. Walschaers, and V . Pa- rigi. Neural networks for detecting multimode Wigner nega- tivity.Phys. Rev. Lett., 125:160504, 2020

    2020

  68. [68]

    J. I. Cirac, D. P ´erez-Garc´ıa, N. Schuch, and F. Verstraete. Ma- trix product states and projected entangled pair states: Con- cepts, symmetries, theorems.Rev. Mod. Phys., 93:045003, 2021

    2021

  69. [69]

    Cirstoiu

    C. Cirstoiu. A Fourier analysis framework for approximate classical simulations of quantum circuits.arXiv:2410.13856, 2024

    Pith/arXiv arXiv 2024

  70. [70]

    Cramer, M

    M. Cramer, M. B. Plenio, S. T. Flammia, R. Somma, D. Gross, S. Bartlett, O. Landon-Cardinal, D. Poulin, and Y .-K. Liu. Efficient quantum state tomography.Nature Comm., 1:149, 2010. 27

    2010

  71. [71]

    Cybi ´nski, M

    K. Cybi ´nski, M. Płodzie ´n, M. Tomza, M. Lewenstein, A. Dauphin, and A. Dawid. Characterizing out-of-distribution generalization of neural networks: application to the disor- dered Su-Schrieffer-Heeger model.Mach. Learn. Sci. Tech- nol., 6:015014, 2025

    2025

  72. [72]

    Czarnik, A

    P. Czarnik, A. Arrasmith, P. J. Coles, and L. Cincio. Error mit- igation with clifford quantum-circuit data.Quantum, 5:592, 2021

    2021

  73. [73]

    Czarnik, M

    P. Czarnik, M. McKerns, A. T. Sornborger, and L. Cincio. Improving the efficiency of learning-based error mitigation. arXiv:2204.07109, 2022

    Pith/arXiv arXiv 2022

  74. [74]

    Czischek, M

    S. Czischek, M. S. Moss, M. Radzihovsky, E. Merali, and R. G. Melko. Data-enhanced variational Monte Carlo simu- lations for Rydberg atom arrays.Phys. Rev. B, 105:205108, 2022

    2022

  75. [75]

    Dawid, J

    A. Dawid, J. Arnold, B. Requena, A. Gresch, M. Płodzie ´n, K. Donatella, K. A. Nicoli, P. Stornati, R. Koch, M. B¨uttner, R. Okuła, G. Mu˜noz-Gil, R. A. Vargas-Hern´andez, A. Cervera-Lierta, J. Carrasquilla, V . Dunjko, M. Gabri ´e, P. H. E. van Nieuwenburg, F. Vicentini, L. Wang, S. J. Wetzel, G. Carleo, E. Greplov ´a, R. Krems, F. Marquardt, M. Tomza, M...

    2025

  76. [76]

    de Schoulepnikoff, G

    P. de Schoulepnikoff, G. Mu ˜noz-Gil, H. P. Nautrup, and H. J. Briegel. Interpretable representation learning of quan- tum data enabled by probabilistic variational autoencoders. arXiv:2506.11982, 2025

    arXiv 2025

  77. [77]

    DeCross et al

    M. DeCross et al. The computational power of random quan- tum circuits in arbitrary geometries.arXiv:2406.02501, 2024

    Pith/arXiv arXiv 2024

  78. [78]

    Dehghani, A

    H. Dehghani, A. Lavasani, M. Hafezi, and M. J. Gullans. Neural-network decoders for measurement induced phase transitions.Nature Comm., 14:2918, 2023

    2023

  79. [79]

    Denis, F

    J. Denis, F. Damanet, and J. Martin. Estimation of the geo- metric measure of entanglement with wehrl moments through artificial neural networks.SciPost Physics, 15:208, 2023

    2023

  80. [80]

    Du et al

    Y . Du et al. Quantum machine learning: A hands-on tutorial for machine learning practitioners and researchers. arXiv:2502.01146, 2025

    Pith/arXiv arXiv 2025

Showing first 80 references.