Pith. sign in

REVIEW 5 major objections 6 minor 1 cited by

Unraveling Quantum Environments: Transformer-Assisted Learning in Lindblad Dynamics

T0 review · 5 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read A Transformer can infer time-dependent dissipation rates in open quantum systems directly from time series of local observables, such as Pauli expectation values, without needing the initial quantum state or the Hamiltonian as input.

desk verdict A useful proof-of-concept for Transformer-based inference of Lindblad rates, undermined by an overclaiming abstract and unproven identifiability theorems. read the letter →

arxiv 2505.06928 v1 pith:LCLG5MW4 submitted 2025-05-11 quant-ph cs.LG

Chi-Sheng Chen , En-Jui Kuo This is my paper · ORCID
classification quant-phcs.LG
keywords openquantumsystemsLindbladmasterequationdissipationrateestimationTransformerBernsteinpolynomialsJaynes-Cummingsmodelenvironmentidentificationtime-seriesregression
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

The paper attempts to show that a Transformer-based sequence model can infer time-dependent dissipation rates in Lindblad master equations directly from time series of local observables, such as Pauli expectation values. The authors demonstrate this for single-qubit systems, two-qubit Heisenberg and transverse-field Ising models, and the Jaynes–Cummings light–matter model, reconstructing both constant and time-dependent rates with high $R^2$ scores. They also prove identifiability results: under the paper's assumptions, the jump rates in these models are uniquely fixed by a finite set of observable trajectories, without needing the initial quantum state. If true, this offers a data-driven alternative to analytic inversion for characterizing unknown quantum environments.

What carries the argument

The load-bearing mechanism is the composition of three pieces: identifiability, showing the rates are functions of the observed trajectories; a Bernstein-polynomial parameterization $\gamma(t)=\sum_{j=0}^2 a_j b_{j,2}(t)$ with non-negative coefficients, which guarantees non-negative rates and provides a fixed-dimensional regression target; and a Transformer encoder with multi-head self-attention that maps handcrafted time-series features of the observables to those coefficients. The Bernstein basis is what makes the target space smooth, non-negative, and easy to sample during supervised training.

What would settle it

Generate test trajectories whose true dissipation rates are exponential or sinusoidally varying profiles, outside the degree-2 Bernstein family, or contaminate the observable time series with realistic noise, then check whether the trained Transformer still recovers the rates with comparable accuracy.

Watch

Extended reading notes

Core claim

The central claim is that the map from observable time series to Lindblad dissipation rates is learnable and, in the models considered, well-posed. With the Hamiltonian and jump operators fixed and only the rates $\gamma_i(t)$ unknown, the paper shows that a Transformer encoder trained on statistically summarized Pauli, photon-number, and cross-observable trajectories predicts the Bernstein polynomial coefficients of the rates; reported $R^2$ values are above 0.99 for the single-qubit cases, at least 0.95 for the constant two-qubit rates, and above 0.9 for the Jaynes–Cummings coefficients. Accompanying analytic results give explicit inversion formulas in the single-qubit cases and argue via the Pauli-basis expansion of the Lindblad equation that multi-qubit rates are identifiable in principle, justifying the regression approach.

Load-bearing premise

The model is only demonstrated on decay-rate curves of the same quadratic Bernstein-polynomial form and the same sampling distributions used to generate its training set; how it behaves on other rate shapes or with measurement noise is not shown.

Editorial extensions

If this is right

  • Environment characterization for qubit-based devices can be reduced to training a sequence model on observable traces, bypassing difficult analytic inversion.
  • The same trained approach extends across interaction Hamiltonians, such as the Heisenberg and transverse-field Ising models, and to hybrid photonic-qubit systems, since the input does not contain the Hamiltonian parameters.
  • The identifiability proofs guarantee that high prediction accuracy reflects a genuine underlying map, rather than overfitting to noise, for the tested observable sets.
  • The paper argues the method transfers to other Markovian open-system frameworks, such as Redfield dynamics under the secular approximation, and to classical Fokker–Planck dynamics.

Reading between the lines

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

  • A critical boundary not tested in the paper: the model is trained and evaluated on dissipation profiles drawn from the same degree-2 Bernstein-coefficient distributions, so decay shapes outside this family, such as exponential, piecewise, or oscillatory rates, are not covered by the paper's evidence.
  • A direct stress test would be to train on one family of smooth profiles and evaluate on another, or to add realistic shot noise to the observables; failure there would show the method is interpolation within a function class rather than general rate inversion.
  • If the identifiability results and Transformer mapping hold beyond the tested regimes, a natural product is a real-time noise spectrometer that streams single-qubit Pauli traces and outputs instantaneous decay rates for feedback control.
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

5 major / 6 minor

Summary. The manuscript proposes a Transformer-based supervised regression framework for inferring time-dependent dissipation rates in Lindblad master equations from time series of local observables. The rates are parameterized as degree-2 Bernstein polynomials; the network inputs are observable trajectories and the outputs are Bernstein coefficients. Experiments cover single-qubit systems with H=sigma_z, two-qubit Heisenberg and transverse-field Ising models, and a Jaynes-Cummings model, with reported R^2 values mostly above 0.9. A supplement contains identifiability results: Theorem 1 for a single jump channel, Theorem 2 for two jump channels, and Theorem 3 for the Jaynes-Cummings model. The abstract and introduction claim that the framework infers dissipation rates 'without requiring knowledge of the initial quantum state and even Hamiltonian.'

Significance. If the claims held, the paper would offer a data-driven alternative to analytic inversion for environment identification in open quantum systems. The positive evidence is real but narrow: the numerical demonstrations are internally consistent in-distribution supervised regressions, and Theorem 1 is an elementary derivation that appears correct. The paper does not provide evidence for the abstract's broader claims of arbitrary time-dependent rates or Hamiltonian independence. The central contribution is better framed as a demonstration that a supervised sequence model can invert a specific low-dimensional parametric family of dissipation rates from observable trajectories, given a known Hamiltonian family during training. The reported R^2 scores, use of QuTiP for data generation, and detailed training hyperparameters are strengths that support reproducibility.

major comments (5)
  1. [Section II; Abstract] The abstract and introduction claim inference 'without requiring knowledge of the initial quantum state and even Hamiltonian,' but Section II explicitly states 'We assume that both the Hamiltonian H and jump operators {Li} are known.' Every experiment either fixes H (single-qubit H=sigma_z) or samples H from a narrow, known parametric family (Table I; Section III C). The observable-to-rate map depends on H, and Theorem 1 itself uses H=sigma_z. A model trained on H=sigma_z is not shown to transfer to H=0 or H=sigma_x. This overstatement is load-bearing for the paper's central claim; please restrict the claim to known Hamiltonian families or provide out-of-distribution experiments across Hamiltonian families.
  2. [Section II, Eq. (3); Table I; Supp Sections B-D] All time-dependent dissipation rates are degree-2 Bernstein polynomials with coefficients drawn from fixed bounded intervals, and the regression target is the coefficient vector. The experiments therefore only demonstrate interpolation within a six-parameter function class. The Weierstrass approximation remark in Supp Section A does not establish generalization to rates outside this class, since the training distribution is not dense in C[0,1] with n=2. The abstract's phrase 'time-dependent decay rates' and the broader claim of reconstructing arbitrary profiles are unsupported. Please qualify the claims and add tests with rates outside the Bernstein class, higher-degree or non-polynomial rates, coefficient ranges outside the training intervals, and measurement noise.
  3. [Supp Section E, Eq. (S22)] Equation (S22) is inconsistent with the preceding equations. From (S17), p0=(1+<sigma_z>)/2, and p1=(1-<sigma_z>)/2, the correct relation is (1/2) d<sigma_z>/dt = gamma_+(t)(1-<sigma_z>)/2 - gamma_-(t)(1+<sigma_z>)/2. The printed equation, (1/2) d<sigma_z>/dt = gamma_+(t) - gamma_-(t)(1+<sigma_z>)/2, has the wrong gamma_+ coefficient and sign structure. The closed-form expression for gamma_-(t) in Eq. (S24) is therefore unsupported. Please correct the derivation or explicitly mark the explicit formula as a numerical conjecture.
  4. [Supp Section E, Theorem 3] Theorem 3 is not proven as stated. The proof of Eqs. (S28)-(S31) invokes unmeasured correlations <(a^dagger-a)sigma_z>, <(a+a^dagger)sigma_z>, <a sigma_+>, and <a^dagger sigma_->, none of which are among the five observables listed in the theorem. The statement that these terms are 'fully determined by the state' and the condition 'provided the system is fully observed' assume exactly the identifiability claim at issue: for arbitrary rho, the unobserved two-time correlations are not functions of the five measured expectation values. Please provide a genuine observability argument for the listed observables, or downgrade Theorem 3 to a numerical observation.
  5. [Supp Section C; Fig. 5] The text states 'The final models achieve R2>=0.95 on all outputs for both systems,' but Fig. 5 reports R^2 = 0.8903, 0.8555, 0.8825, and 0.8593 for the transverse-field Ising model. This is an internal inconsistency in the reported results. Please correct the summary statement and adjust the main-text claim of 'strong generalization' to reflect the actually reported Ising performance.
minor comments (6)
  1. [Section I A] The word 'specilize' should be 'specialize.'
  2. [Fig. 2a caption] The example numbering in the caption is inconsistent with Section III A and Supp Section B: the caption describes 'Example 2' as including both gamma_+(t) and gamma_-(t), while the main text's Example 2 is a single time-dependent gamma_-(t). Please reconcile the numbering.
  3. [Section III C] 'dataset splited' should be 'dataset split.'
  4. [Section II / Table I] Table I lists the Hamiltonian in the 'Hamiltonian' column and the dissipation setup in later columns, but the header row is ambiguous about which initial-state and input columns apply to which example; please make the table self-contained.
  5. [General] No error bars, repeated-seed statistics, or ablations over random seeds are reported for the R^2 values; since the models are trained with early stopping and random initialization, a sensitivity check would strengthen the quantitative claims.
  6. [Section IV] The claim that the framework extends to Redfield equations and Fokker-Planck dynamics is speculative and not demonstrated; it would be helpful to mark it as a conjecture.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the supervised regressions are held-out tests and the identifiability theorems are independent analytic derivations; the main weaknesses are overclaims and a proof gap, not circular reasoning.

full rationale

The derivation chain is not circular. Section II defines a supervised regression task: observable trajectories generated by QuTiP from known Hamiltonians and jump operators with randomly sampled dissipation rates are the inputs, and the Bernstein coefficients of the dissipation profile are the regression labels (“The learning task is thus reduced to predicting the coefficient vector {a0,...,an} from time-series input features”). The reported R2 values are computed on held-out test samples drawn from the same distribution, so they are genuine predictions of unseen examples rather than fitted parameters renamed as predictions. The analytic identifiability results are independent of the Transformer and of the Bernstein ansatz: Theorem 1 explicitly derives gamma(t) = -(d/dt<sigma_z>)/(1+<sigma_z>) for H = sigma_z, and Theorem 2 gives algebraic reconstructions of gamma_+(t) and gamma_-(t) from Pauli expectation values. These derivations do not presuppose the ML output or the Bernstein coefficient vector. The paper's self-citations (refs. 26, 27, 36-39, 57) appear only as background context or as references for numerical methods and are not load-bearing. Two non-circular weaknesses should be flagged separately. First, the abstract's claim that the framework works “without requiring knowledge of the initial quantum state or even the system Hamiltonian” is contradicted by Section II's explicit assumption “We assume that both the Hamiltonian H and jump operators {Li} are known” and by Theorem 1, which relies on H = sigma_z; this is an overclaim, not a circular step. Second, Theorem 3's proof of identifiability in the Jaynes-Cummings model concludes that gamma and kappa “can be algebraically inferred from observable trajectories, provided the system is fully observed,” but the listed five observables do not determine the auxiliary terms <a sigma_+>, <a^dagger sigma_->, <(a^dagger - a) sigma_z>, and <(a + a^dagger) sigma_z> appearing in Eqs. (S28)-(S31); the theorem therefore has an unsupported observability assumption and an omitted proof step, but this is a logical gap rather than a reduction of the conclusion to its premises. Because no central claim reduces by construction to a fitted parameter, a self-citation chain, or a definition, the circularity score is 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The central claim rests on a set of domain assumptions about known Hamiltonians, restricted Bernstein representations, noiseless synthetic data, and a fixed initial-state distribution. The most fragile of these is the degree-2 Bernstein restriction, which is not justified as a general approximation of arbitrary dissipation profiles.

free parameters (1)
  • Bernstein polynomial degree n = 2
    All time-dependent dissipation profiles are represented as degree-2 Bernstein polynomials, chosen by hand in Eq. 3 and in all experiments. This limits the representable function class and is not learned.
assumptions (5)
  • domain assumption The Hamiltonian H and jump operators L_i are known to the learner (Section II, paragraph 2).
    The methods assume H and L_i are known, which contradicts the abstract's claim that the Hamiltonian is not required. The ML pipeline and identifiability theorems rely on this assumption.
  • ad hoc to paper Dissipation rates gamma(t) are exactly representable as degree-2 Bernstein polynomials with coefficients in bounded intervals (Section II, Eq. 3; Table I).
    All training and test profiles are drawn from this limited class; no tests on arbitrary or higher-degree rates are performed.
  • domain assumption Observable time series are noiseless and generated by exact Lindblad integration using QuTiP (Section III; Supplement Section C).
    No measurement noise or finite-sampling effects are modeled, so the method's behavior on realistic experimental data is untested.
  • domain assumption Initial states are drawn from Haar-random pure states or fixed |0>, matching the training distribution (Section III; Table I).
    The claim of initial-state independence is only proven for Theorem 1; ML generalization to unseen initial states is not tested.
  • ad hoc to paper For Theorem 3, unobserved correlations such as angle a sigma_plus and angle a_dagger sigma_minus are 'fully determined by the state' and need not be measured (Supplement Section E, proof of Theorem 3).
    This is an unproved observability assumption; the five listed observables do not determine these correlations in the provided equations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Unraveling Quantum Environments: Transformer-Assisted Learning in Lindblad Dynamics." pith.science (2026). https://pith.science/paper/LCLG5MW4

@misc{pith2026250506928,
  author       = {Pith},
  title        = {Pith review of: Unraveling Quantum Environments: Transformer-Assisted Learning in Lindblad Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LCLG5MW4}},
  note         = {Machine review of arXiv:2505.06928}
}
read the original abstract

Understanding dissipation in open quantum systems is crucial for the development of robust quantum technologies. In this work, we introduce a Transformer-based machine learning framework to infer time-dependent dissipation rates in quantum systems governed by the Lindblad master equation. Our approach uses time series of observable quantities, such as expectation values of single Pauli operators, as input to learn dissipation profiles without requiring knowledge of the initial quantum state or even the system Hamiltonian. We demonstrate the effectiveness of our approach on a hierarchy of open quantum models of increasing complexity, including single-qubit systems with time-independent or time-dependent jump rates, two-qubit interacting systems (e.g., Heisenberg and transverse Ising models), and the Jaynes--Cummings model involving light--matter interaction and cavity loss with time-dependent decay rates. Our method accurately reconstructs both fixed and time-dependent decay rates from observable time series. To support this, we prove that under reasonable assumptions, the jump rates in all these models are uniquely determined by a finite set of observables, such as qubit and photon measurements. In practice, we combine Transformer-based architectures with lightweight feature extraction techniques to efficiently learn these dynamics. Our results suggest that modern machine learning tools can serve as scalable and data-driven alternatives for identifying unknown environments in open quantum systems.

Figures

Figures reproduced from arXiv: 2505.06928 by the authors.

Figure 1
Figure 1. FIG. 1: Schematic illustration of the machine learning [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Predictions of dissipation rates for single- and [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Prediction of time-dependent dissipation rates in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Prediction results for Example 4 (Main Text) involving a single-qubit system with two quadratic time-dependent loss [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Prediction results for the transverse-field Ising model with four constant dissipation rates [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

Discussion (0). Continue with ORCID to comment.

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-Enhanced Channel Mixing in RWKV Models for Time Series Forecasting

    quant-ph 2025-05 conditional novelty 5.0 of 10

    A hybrid RWKV model with a four-qubit variational circuit in its channel-mixing layer beats the classical RWKV on six of ten synthetic forecasting tasks by mean error, though the differences are mostly within one stan...

Reference graph

Works this paper leans on

57 extracted references · 50 canonical work pages · cited by 1 Pith paper

  1. [1]

    Colloquium: Non-markovian dynamics in open quantum systems,

    Heinz-Peter Breuer, Elsi-Mari Laine, Jyrki Piilo, and Bas- sano Vacchini, “Colloquium: Non-markovian dynamics in open quantum systems,” Reviews of Modern Physics 88, 021002 (2016)

    work page 2016

  2. [2]

    10 (Springer, 2012)

    Angel Rivas and Susana F Huelga, Open quantum systems , V ol. 10 (Springer, 2012)

    work page 2012

  3. [3]

    Adiabatic quantum computation in open systems,

    MS Sarandy and DA Lidar, “Adiabatic quantum computation in open systems,” Physical review letters95, 250503 (2005)

    work page 2005

  4. [4]

    Modelling non-markovian quantum processes with recurrent neural networks,

    Leonardo Banchi, Edward Grant, Andrea Rocchetto, and Si- mone Severini, “Modelling non-markovian quantum processes with recurrent neural networks,” New Journal of Physics 20, 123030 (2018)

    work page 2018

  5. [5]

    Impact of dissipation on universal fluctuation dynamics in open quantum systems,

    Kazuya Fujimoto, Ryusuke Hamazaki, and Yuki Kawaguchi, “Impact of dissipation on universal fluctuation dynamics in open quantum systems,” Physical Review Letters 129, 110403 (2022)

    work page 2022

  6. [6]

    Nonequilibrium quan- tum criticality in open systems: The dissipation rate as an ad- ditional indispensable scaling variable,

    Shuai Yin, Peizhi Mai, and Fan Zhong, “Nonequilibrium quan- tum criticality in open systems: The dissipation rate as an ad- ditional indispensable scaling variable,” Physical Review B89, 094108 (2014)

    work page 2014

  7. [7]

    Controlling the dynamics of an open many-body quantum system with localized dissipation,

    Giovanni Barontini, R Labouvie, F Stubenrauch, A V ogler, V Guarrera, and H Ott, “Controlling the dynamics of an open many-body quantum system with localized dissipation,” Physi- cal review letters 110, 035302 (2013)

    work page 2013

  8. [8]

    Quantum sensing,

    Christian L Degen, Friedemann Reinhard, and Paola Cap- pellaro, “Quantum sensing,” Reviews of modern physics 89, 035002 (2017)

    work page 2017

Show all 57 references
  1. [9]

    Noise spec- troscopy through dynamical decoupling with a superconducting flux qubit,

    Jonas Bylander, Simon Gustavsson, Fei Yan, Fumiki Yoshi- hara, Khalil Harrabi, George Fitch, David G Cory, Yasunobu Nakamura, Jaw-Shen Tsai, and William D Oliver, “Noise spec- troscopy through dynamical decoupling with a superconducting flux qubit,” Nature Physics 7, 565–570 (2011)

    2011

  2. [10]

    Quantum sensing of open systems: Estimation of damp- ing constants and temperature,

    Jiaxuan Wang, Luiz Davidovich, and Girish Saran Agar- wal, “Quantum sensing of open systems: Estimation of damp- ing constants and temperature,” Physical Review Research 2, 033389 (2020)

    2020

  3. [11]

    Quantum sensing of oscil- lating electric fields with trapped ions,

    Fabian Wolf and Piet O Schmidt, “Quantum sensing of oscil- lating electric fields with trapped ions,” Measurement: Sensors 18, 100271 (2021)

    2021

  4. [12]

    Attention is all you need,

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polo- sukhin, “Attention is all you need,” Advances in Neural Infor- mation Processing Systems 30 (2017)

    2017

  5. [13]

    Enhancing the locality and breaking the memory bottleneck of transformer on time series forecast- ing,

    Shiyang Li, Xiyou Jin, Yao Xuan, Xiyou Zhou, Wenwu Chen, Yu Wang, and Xueqi Yan, “Enhancing the locality and breaking the memory bottleneck of transformer on time series forecast- ing,” Advances in Neural Information Processing Systems 32 (2019)

    2019

  6. [14]

    A transformer-based framework for multivariate time series representation learning,

    George Zerveas, Sercan Jayaraman, Dhaval Patel, Anastasios Bhamidipaty, and Carsten Eickhoff, “A transformer-based framework for multivariate time series representation learning,” Proceedings of the 27th ACM SIGKDD Conference on Knowl- edge Discovery and Data Mining (2021)

    2021

  7. [15]

    Temporal fusion transformers for interpretable multi-horizon time series forecasting,

    Bryan Lim and Stefan Zohren, “Temporal fusion transformers for interpretable multi-horizon time series forecasting,” Inter- 6 national Journal of Forecasting (2021)

    2021

  8. [16]

    Coherent multispin exchange coupling in a quantum-dot spin chain,

    Haifeng Qiao, Yadav P Kandel, Kuangyin Deng, Saeed Fal- lahi, Geoffrey C Gardner, Michael J Manfra, Edwin Barnes, and John M Nichol, “Coherent multispin exchange coupling in a quantum-dot spin chain,” Physical Review X 10, 031006 (2020)

    2020

  9. [17]

    The exchange interaction between neighboring quantum dots: physics and applications in quan- tum information processing,

    Zheng Zhou, Yixin Li, Zhiyuan Wu, Xinping Ma, Shichang Fan, and Shaoyun Huang, “The exchange interaction between neighboring quantum dots: physics and applications in quan- tum information processing,” Journal of Semiconductors 45, 101701 (2024)

    2024

  10. [18]

    Overview of spin-based quan- tum dot quantum computation,

    Xuedong Hu and S Das Sarma, “Overview of spin-based quan- tum dot quantum computation,” physica status solidi (b) 238, 360–365 (2003)

    2003

  11. [19]

    Ex- change coupling in a linear chain of three quantum-dot spin qubits in silicon,

    Kok Wai Chan, Harshad Sahasrabudhe, Wister Huang, Yu Wang, Henry C Yang, Menno Veldhorst, Jason CC Hwang, Fahd A Mohiyaddin, Fay E Hudson, Kohei M Itoh, et al., “Ex- change coupling in a linear chain of three quantum-dot spin qubits in silicon,” Nano Letters 21, 1517–1522 (2021)

    2021

  12. [20]

    Coherent spin-state transfer via heisenberg exchange,

    Yadav P Kandel, Haifeng Qiao, Saeed Fallahi, Geoffrey C Gardner, Michael J Manfra, and John M Nichol, “Coherent spin-state transfer via heisenberg exchange,” Nature 573, 553– 557 (2019)

    2019

  13. [21]

    The jaynes-cummings model,

    Bruce W Shore and Peter L Knight, “The jaynes-cummings model,” Journal of Modern Optics 40, 1195–1238 (1993)

    1993

  14. [22]

    See supplemental material,

    “See supplemental material,” (2024)

    2024

  15. [23]

    Machine learning and the physical sci- ences,

    Giuseppe Carleo, Ignacio Cirac, Kyle Cranmer, Laurent Daudet, Maria Schuld, Naftali Tishby, Leslie V ogt-Maranto, and Lenka Zdeborov´a, “Machine learning and the physical sci- ences,” arXiv preprint arXiv:1903.10563 (2019)

    2019 arXiv

  16. [24]

    Unsupervised learning of phase transi- tions: From principal component analysis to variational autoen- coders,

    Sebastian J Wetzel, “Unsupervised learning of phase transi- tions: From principal component analysis to variational autoen- coders,” Physical Review E96, 022140 (2017)

    2017

  17. [25]

    Learning phase transitions by confusion,

    Evert PL Van Nieuwenburg, Ye-Hua Liu, and Sebastian D Hu- ber, “Learning phase transitions by confusion,” Nature Physics 13, 435 (2017)

    2017

  18. [26]

    Decoding conformal field theories: From supervised to unsupervised learning,

    En-Jui Kuo, Alireza Seif, Rex Lundgren, Seth Whitsitt, and Mohammad Hafezi, “Decoding conformal field theories: From supervised to unsupervised learning,” Physical Review Re- search 4, 043031 (2022)

    2022

  19. [27]

    Unsupervised learning of interacting topological and symmetry-breaking phase transi- tions,

    En-Jui Kuo and Hossein Dehghani, “Unsupervised learning of interacting topological and symmetry-breaking phase transi- tions,” Physical Review B105, 235136 (2022)

    2022

  20. [28]

    Learn- ing phase transitions from dynamics,

    Evert van Nieuwenburg, Eyal Bairey, and Gil Refael, “Learn- ing phase transitions from dynamics,” Physical Review B 98, 060301 (2018)

    2018

  21. [29]

    Prob- ing many-body localization with neural networks,

    Frank Schindler, Nicolas Regnault, and Titus Neupert, “Prob- ing many-body localization with neural networks,” Physical Re- view B 95, 245134 (2017)

    2017

  22. [30]

    Machine learning in the string landscape,

    Jonathan Carifio, James Halverson, Dmitri Krioukov, and Brent D Nelson, “Machine learning in the string landscape,” Journal of High Energy Physics 2017, 157 (2017)

    2017

  23. [31]

    Deep learning and the AdS/CFT correspondence,

    Koji Hashimoto, Sotaro Sugishita, Akinori Tanaka, and Akio Tomiya, “Deep learning and the AdS/CFT correspondence,” Phys. Rev. D 98, 046019 (2018)

    2018

  24. [32]

    Solving the quantum many-body problem with artificial neural networks,

    Giuseppe Carleo and Matthias Troyer, “Solving the quantum many-body problem with artificial neural networks,” Science 355, 602–606 (2017)

    2017

  25. [33]

    Neural- network quantum state tomography,

    Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer, Roger Melko, and Giuseppe Carleo, “Neural- network quantum state tomography,” Nature Physics 14, 447 (2018)

    2018

  26. [34]

    Reconstructing quantum states with generative models,

    Juan Carrasquilla, Giacomo Torlai, Roger G Melko, and Le- andro Aolita, “Reconstructing quantum states with generative models,” Nature Machine Intelligence 1, 155 (2019)

    2019

  27. [35]

    Integrating neural networks with a quantum simula- tor for state reconstruction,

    Giacomo Torlai, Brian Timar, Evert PL van Nieuwenburg, Harry Levine, Ahmed Omran, Alexander Keesling, Hannes Bernien, Markus Greiner, Vladan Vuleti ´c, Mikhail D Lukin, et al. , “Integrating neural networks with a quantum simula- tor for state reconstruction,” arXiv preprint a...

    2019 arXiv

  28. [36]

    Training classical neural networks by quantum machine learning,

    Chen-Yu Liu, En-Jui Kuo, Chu-Hsuan Abraham Lin, Sean Chen, Jason Gemsun Young, Yeong-Jar Chang, and Min-Hsiu Hsieh, “Training classical neural networks by quantum machine learning,” arXiv preprint arXiv:2402.16465 (2024)

    2024 arXiv

  29. [37]

    Quantum-train: Rethinking hybrid quantum- classical machine learning in the model compression perspec- tive,

    Chen-Yu Liu, En-Jui Kuo, Chu-Hsuan Abraham Lin, Ja- son Gemsun Young, Yeong-Jar Chang, Min-Hsiu Hsieh, and Hsi-Sheng Goan, “Quantum-train: Rethinking hybrid quantum- classical machine learning in the model compression perspec- tive,” arXiv preprint arXiv:2405.11304 (2024)

    2024 arXiv

  30. [38]

    Learning molecular dynamics with simple language model built upon long short-term memory neural network,

    Sun-Ting Tsai, En-Jui Kuo, and Pratyush Tiwary, “Learning molecular dynamics with simple language model built upon long short-term memory neural network,” Nature communica- tions 11, 5115 (2020)

    2020

  31. [39]

    Path sampling of recurrent neural networks by in- corporating known physics,

    Sun-Ting Tsai, Eric Fields, Yijia Xu, En-Jui Kuo, and Pratyush Tiwary, “Path sampling of recurrent neural networks by in- corporating known physics,” Nature Communications 13, 7231 (2022)

    2022

  32. [40]

    Learning representations by back-propagating er- rors,

    David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams, “Learning representations by back-propagating er- rors,” Nature 323, 533–536 (1986)

    1986

  33. [41]

    Learning phrase representations using rnn encoder-decoder for statistical machine translation,

    Kyunghyun Cho, Bart van Merri ¨enboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio, “Learning phrase representations using rnn encoder-decoder for statistical machine translation,” arXiv preprint arXiv:1406.1078 (2014)

    2014 arXiv

  34. [42]

    Long short-term memory,

    Sepp Hochreiter and J ¨urgen Schmidhuber, “Long short-term memory,” Neural Computation9, 1735–1780 (1997)

    1997

  35. [43]

    Physicsformer: Modeling physical dy- namics with learnable differential equations and transformers,

    Xiaohan Huang et al., “Physicsformer: Modeling physical dy- namics with learnable differential equations and transformers,” arXiv preprint arXiv:2304.12259 (2023)

    2023 arXiv

  36. [44]

    Scaling laws for neural language models,

    Jared Kaplan, Sam McCandlish, Tom Henighan, et al. , “Scaling laws for neural language models,” arXiv preprint arXiv:2001.08361 (2021)

    2021 arXiv

  37. [45]

    Physics-informed transformer for solv- ing differential equations,

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar, “Physics-informed transformer for solv- ing differential equations,” arXiv preprint arXiv:2205.08853 (2022)

    2022 arXiv

  38. [46]

    Heinz-Peter Breuer, Francesco Petruccione, et al., The theory of open quantum systems (Oxford University Press on Demand, 2002)

    2002

  39. [47]

    Simple derivation of the lindblad equation,

    Philip Pearle, “Simple derivation of the lindblad equation,” Eu- ropean Journal of Physics 33, 805 (2012)

    2012

  40. [48]

    Quantum computation and quantum information,

    Michael A Nielsen and Isaac Chuang, “Quantum computation and quantum information,” (2002)

    2002

  41. [49]

    Qutip: An open-source python framework for the dynamics of open quantum systems,

    J Robert Johansson, Paul D Nation, and Franco Nori, “Qutip: An open-source python framework for the dynamics of open quantum systems,” Computer physics communications 183, 1760–1772 (2012)

    2012

  42. [50]

    Subir Sachdev, Quantum Phase Transitions (Cambridge Uni- versity Press, 2011)

    2011

  43. [51]

    Onset of a quantum phase transition with a trapped ion quan- tum simulator,

    Rajibul Islam, Erica E. Edwards, Kihwan Kim, Simcha Koren- blit, Chibum Noh, H. Carmichael, and Christopher Monroe, “Onset of a quantum phase transition with a trapped ion quan- tum simulator,” Nature Communications 2, 377 (2011)

    2011

  44. [52]

    Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,

    Jiehang Zhang, Guido Pagano, Paul W. Hess, Antonis Kyprian- idis, Peter Becker, Harvey Kaplan, Alexey V . Gorshkov, and 7 Christopher Monroe, “Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator,” Nature 551, 601–604 (2017)

    2017

  45. [53]

    The divincenzo criteria 20 years on,

    Iulia Georgescu, “The divincenzo criteria 20 years on,” Nature Reviews Physics 2, 666–666 (2020)

    2020

  46. [54]

    Solution of the redfield equation for the dissipative quantum dynamics of mul- tilevel systems,

    W Thomas Pollard and Richard A Friesner, “Solution of the redfield equation for the dissipative quantum dynamics of mul- tilevel systems,” The Journal of chemical physics 100, 5054– 5065 (1994)

    1994

  47. [55]

    The generalized weierstrass approximation theorem,

    Marshall H Stone, “The generalized weierstrass approximation theorem,” Mathematics Magazine 21, 237–254 (1948)

    1948

  48. [56]

    Efficient quantum tomog- raphy,

    Ryan O’Donnell and John Wright, “Efficient quantum tomog- raphy,” in Proceedings of the forty-eighth annual ACM sympo- sium on Theory of Computing (2016) pp. 899–912

    2016

  49. [57]

    Quantum state tomography via noncon- vex riemannian gradient descent,

    Ming-Chien Hsu, En-Jui Kuo, Wei-Hsuan Yu, Jian-Feng Cai, and Min-Hsiu Hsieh, “Quantum state tomography via noncon- vex riemannian gradient descent,” Physical Review Letters132, 240804 (2024). 8 Supplementary Material: Unraveling Quantum Environments: Transformer-Assisted Learn...

    2024

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.