Pith. sign in

REVIEW 4 major objections 5 minor 32 references

Quantum-Structured World Models (QSWMs) for Predictive Latent Dynamics

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read Complex-valued latent states sharpen next-step world-model prediction

desk verdict A careful empirical comparison, but the missing trivial rule-exact baseline and absent variance stats leave the central inductive-bias claim unproven. read the letter →

arxiv 2608.05371 v1 pith:CAA3JVIY submitted 2026-08-05 cs.LG

Hailong Jiang , Emran Hossain , Feng Yu , Jianfeng Zhu , Guilin Zhang , Wulan Guo This is my paper · ORCID
classification cs.LG
keywords Quantum-StructuredWorldModelslatentdynamicscomplex-valuedrepresentationsdensity-matrix-likestatesquantum-inspiredlearningelementarycellularautomatapredictivemodeling
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 introduces Quantum-Structured World Models (QSWMs), a framework for world models whose latent states carry mathematical structure borrowed from quantum theory—complex-valued amplitudes or density-matrix-like operators—while running on ordinary neural networks. It asks whether that structure is a useful inductive bias for predicting the next state of a dynamical system, and answers yes for the complex-valued instantiation. On elementary cellular automata (Rules 30, 90, and 110), ComplexQSWM achieves the lowest one-step prediction error and highest one-step accuracy among all models, beating classical baselines matched for parameter count, doubled real latent dimensions, and normalization. The paper also proves that classical probabilistic world models are a restricted diagonal case of QSWMs, that predictively sufficient latent states preserve future-relevant history information, and that tensor-structured latents can compactly represent certain correlated dynamics. The density-matrix variant and long-horizon rollout are weaker, so the claimed advantage is local and tied to the complex-valued representation.

What carries the argument

The load-bearing mechanism is the complex-valued latent state $\psi_t = u_t + i v_t$, with $u_t, v_t \in \mathbb{R}^d$ produced by the history encoder and normalized by $\|\psi_t\|_2 + \epsilon$. The transition is a learned complex linear map $A = A_r + i A_i$ acting through $u_{t+1} = A_r u_t - A_i v_t$ and $v_{t+1} = A_r v_t + A_i u_t$, and prediction is decoded from the concatenated real and imaginary parts. This construction isolates the representation change: compared with classical, parameter-matched, doubled-latent, and normalized baselines, the only systematic difference is the complex two-component structure and its norm-constrained evolution. The DensityQSWM variant instead builds a positive-semidefinite latent $\rho_t = v_t v_t^\top / (\operatorname{Tr}(v_t v_t^\top) + \epsilon)$ and evolves it as $A \rho A^\top$ with trace normalization; it does not reproduce the one-step advantage. The three formal theorems—classical inclusion, predictive sufficiency, and structured compactness—frame the latent representation, rather than the decoder alone, as the carrier of the predictive gain.

What would settle it

Train a classical baseline matched in parameter count but given a full hyperparameter sweep and per-seed error bars; if its best one-step BCE reaches or falls below ComplexQSWM's 0.4890, the claimed representation advantage is not established. Because the cellular automata are deterministic, a model that has actually learned the rule should achieve near-perfect next-state accuracy, so checking whether longer training closes the gap between all models and that floor would settle whether the difference is representational or merely optimization-level.

Watch

Extended reading notes

Core claim

The core discovery, on the paper's own terms, is that replacing a real-valued latent vector with a complex-valued latent state—normalized to unit norm and evolved through a learned complex linear transition—improves next-state prediction in a controlled world-model benchmark. Across elementary cellular automata, ComplexQSWM reports a binary cross-entropy of 0.4890 and a one-step accuracy of 0.7364, ahead of the classical world model (0.5935 BCE, 0.6654 Acc@1) and ahead of parameter-matched, doubled-latent, and normalized real baselines. The paper interprets this as evidence that complex-valued quantum-structured representation provides a genuine inductive bias for local predictive dynamics, not merely extra capacity or normalization. It also establishes three formal properties: classical inclusion (every finite classical probabilistic world model embeds as a diagonal QSWM), predictive sufficiency (optimal latents preserve the history's future-relevant information), and structured compactness (tensor-network latents use $O(n\chi^2)$ parameters where the unstructured table needs $O(2^n)$).

Load-bearing premise

The load-bearing premise is that the classical baselines are genuinely equal to ComplexQSWM in capacity and training effort, so the reported one-step gain comes from the complex-valued representation and not from underfitting or extra parameters.

Editorial extensions

If this is right

  • Complex-valued latent structure is a usable inductive bias: future world models for locally interacting dynamical systems can adopt normalized complex latents and expect better one-step prediction than capacity-matched real models.
  • The one-step benefit is not explained by parameter count, doubled real latent dimensions, or normalization, because each of those factors was controlled by a separate baseline.
  • The advantage is local: recursive rollout favors ComplexQSWM at short horizons and the gap narrows or disappears at longer horizons, so the claim should be scoped to one-step and short-horizon prediction.
  • Density-matrix-like latents, at least in this simple instantiation, do not share the advantage, so the positive result is tied to complex-valued structure rather than to quantum-structured representations in general.
  • Because classical probabilistic world models are diagonal QSWMs, the framework is an extension of classical world modeling rather than a replacement of it.

Reading between the lines

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

  • Editorial inference: if the complex-valued advantage is real, the relative phase between real and imaginary components may encode correlation structure among latent alternatives that a same-size real vector cannot express; testing on systems with known pairwise correlations would sharpen this hypothesis.
  • Editorial inference: on deterministic cellular automata, all reported one-step accuracies are far below the perfect-prediction floor, which suggests the models are underfit; giving the classical baselines a fuller training budget would provide the decisive control for separating representation effects from optimization effects.
  • Editorial inference: the structured-compactness theorem transfers directly to tensor-network world models, so a natural next experiment is a matrix-product-state QSWM on the same benchmarks, comparing its parameter-versus-accuracy trade-off against ComplexQSWM.
  • Editorial inference: classical inclusion gives the field a common language in which any future classical-versus-quantum-structured world-model comparison can be stated as movement along a single representation axis.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper introduces Quantum-Structured World Models (QSWMs), a framework in which latent world states are represented by quantum-inspired structures such as complex-valued vectors or density-matrix-like matrices. The authors define a QSWM as a tuple of encoder, latent transition, and measurement-inspired decoder, and claim three foundational properties: classical inclusion, predictive sufficiency, and structured compactness. They instantiate two variants, ComplexQSWM and DensityQSWM, and evaluate them on one-step prediction and recursive rollout for elementary cellular automata (Rules 30, 90, 110) against several classical baselines. The main empirical claim is that ComplexQSWM achieves the strongest one-step predictive performance (lowest BCE, highest Acc@1) and that this advantage persists under capacity-matched, doubled-latent, and normalized controls, suggesting a useful inductive bias from complex-valued latent structure. The paper also reports scaling and out-of-distribution density experiments, as well as latent probing.

Significance. If the central empirical claim were established, the paper would provide an interesting data point: that complex-valued latent representations can improve local predictive dynamics in world models. The formal framework, however, adds little new theory: classical inclusion is a standard diagonal embedding, predictive sufficiency is essentially a restatement of the definition, and structured compactness is a known property of tensor networks that is not instantiated in the experiments. The main value would lie in the controlled comparison, but the current evidence has serious gaps that prevent the claim from being accepted as stated.

major comments (4)
  1. [Section 6, Tables 1 and 2; Appendix B] The experiments omit a trivial rule-exact baseline, which is essential for interpreting results on deterministic elementary cellular automata. Given a history of H=4 states, the next state is a deterministic function of the local neighborhoods, so a model that simply applies the rule table to the last observed state should achieve near-perfect one-step accuracy. All learned models score far below this: aggregate Acc@1 is at most 0.7364, and on Rule 90 all models are near chance (Acc@1 ≈ 0.56, BCE ≈ 0.68). This indicates that every model substantially underfits the task. Under these conditions, the relative ordering among partially converged models does not isolate representational inductive bias; it may reflect optimization difficulty, initialization, or subtle capacity effects. The paper should include a rule-exact baseline and, if the learned models remain far below it, explicitly discuss what the comparison does and does not show about latent structure.
  2. [Section 6, Table 1; Appendix B.2] The paper reports no variance or significance information. All experiments use fixed random seeds, but no per-seed standard deviations, confidence intervals, or statistical tests are provided. The headline gap between ComplexQSWM (BCE 0.4890) and Matched-Complex (0.5738) is 0.0848, and the Acc@1 gap is 0.0558; without multiple-seed runs it is impossible to tell whether these differences are reproducible or within seed noise. The claim that ComplexQSWM 'consistently outperforms' baselines requires repeated runs and a statistical comparison, especially given the small absolute margins on some metrics.
  3. [Section 6; Appendix B] The capacity-matching and baseline architecture details are insufficient to support the claim that the advantage is due to complex structure rather than parameter count or optimization. Table 1 reports total parameter counts, but the architectures of ClassicalWM, Matched-Complex, Matched-Density, RealDoubled, and RealNorm are not described (e.g., layer types, widths, nonlinearities, use of normalization). Notably, Matched-Density has 55.5K parameters versus ComplexQSWM's 39.3K, so it is not parameter-matched. The paper also mentions 'doubled-latent' and 'normalized' controls in the text, but these do not appear in Table 1; they are only partially shown in Figure 2. To substantiate Finding 2, the paper must specify the exact construction of each baseline, the hyperparameter search budget, and the resulting optimization quality (e.g., training curves), so that the comparison can be assessed as capacity-matched and equally well optimized.
  4. [Section 4; Appendix A] The three foundational theorems are either standard, definitional, or disconnected from the experiments, and they do not support the empirical claim. Theorem 1 (classical inclusion) is a straightforward diagonal embedding of a probability vector into a density operator and a classical stochastic map; it is correct but not novel. Theorem 2 (predictive sufficiency) assumes that an optimal predictor exists and that the model class contains the true conditional distribution, then concludes p(yt|ht)=p(yt|ρt), which is exactly the definition of predictive sufficiency; the proof relies on an undefined notion of 'minimal optimal latent state' and does not establish that such a state exists. Theorem 3 (structured compactness) is a known parameter-counting fact about tensor networks and is not instantiated in the paper: ComplexQSWM uses a rank-1 vector latent and DensityQSWM uses a rank-1 outer product, neither of which is a tensor-network state with bond dimension χ. The authors should either reframe these as background observations or connect them directly to the evaluated architectures and the reported results.
minor comments (5)
  1. [Figures 3 and 5; Appendix B] There are several typos in model names: 'ComplexSEQWM' and 'DensitySEQWM' appear in Figure 3 and Figure 5, and should be 'ComplexQSWM' and 'DensityQSWM'.
  2. [Section 6; Table 1; Figure 2] The baseline naming is inconsistent: the text refers to 'RealDoubledMatched' and 'RealNormalizedMatched', Table 1 uses 'Matched-Complex' and 'Matched-Density', while Figure 3 uses 'ClassicalWorldModelMatchedComplex' and 'ClassicalWorldModelMatchedDensity'. The main table also does not list the doubled-latent and normalized baselines that the text claims are outperformed; please add these results to the main table or clearly state where they appear.
  3. [Appendix C, Table 2] For Rule 90, all models perform near chance (Acc@1 ≈ 0.56, BCE ≈ 0.68), yet the main text does not discuss this. The paper should explicitly address why the proposed method shows no benefit on Rule 90 and what this implies for the generality of the inductive-bias claim.
  4. [Sections 1 and 7] The phrases 'emergent world-modeling capabilities' and 'emergent abilities' are used in the introduction and conclusion, but the experiments do not measure any emergent phenomenon. Please either remove this framing or add a concrete definition and evaluation of emergence.
  5. [Appendix A.2] The proof of Theorem 2 uses the term 'minimal optimal latent state' without defining minimality. The assumption that the model class achieves the true conditional distribution p(yt|ht) is also not justified and should be stated explicitly as a condition.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor definitional restatement and one background self-citation; the central empirical claim is an external benchmark with no fitted-to-headline parameters.

  1. self definitional [Section 3, Definition 2 and Section 4, Theorem 2 (Appendix A.2)]
    "Definition 2: Predictive Sufficiency. A latent state ρt = Eθ(ht) is predictively sufficient for a future target yt if p(yt | h_t) = p(yt | ρ_t). ... Theorem 2: Predictive Sufficiency. If the encoder Eθ maps each interaction history h_t to a latent state ρt = Eθ(h_t) such that p(yt | h_t) = p(yt | ρ_t), then ρt is sufficient for predicting the future target yt from the history."

    The theorem's consequent is the definition's content verbatim: Definition 2 already defines predictive sufficiency as p(yt|h_t)=p(yt|ρ_t), and Theorem 2 merely asserts that if this equality holds then the latent state is sufficient for predicting yt. The proof adds assumptions of optimality and minimality, but the conclusion is a restatement of the definition, not a derived result. This is a tautological formal step. It does not feed into the empirical comparisons in Table 1 or the scaling/OOD experiments, so the paper's headline empirical claim does not reduce to this definition.

full rationale

The paper's central claim is the empirical comparison on elementary cellular automata: ComplexQSWM achieves the lowest BCE and highest Acc@1 against ClassicalWM, Matched-Complex, Matched-Density, and other controls. Those numbers come from trained models evaluated on held-out trajectories, not from parameters fitted to manufacture the headline result, so the main finding is not circular by construction. The only flagged circular element is Theorem 2, which restates Definition 2 rather than deriving a new property; it is presented as a foundational formal statement but is not used to generate the empirical predictions. The paper also cites its own prior work [31] (Zhang, Guo, Jiang) in a background sentence about QML and QRL, but that citation is motivational and non-load-bearing: the CA experiments and baseline comparisons do not depend on its validity. Concerns about classical baselines being underfit or not exactly capacity-matched would be correctness or robustness issues, not circularity, since no equation or fitted value forces ComplexQSWM's advantage. Overall, the derivation chain is largely self-contained: formal properties are either explicit constructions (classical inclusion), definitional restatements (predictive sufficiency), or standard tensor-network parameter counts (structured compactness), and the empirical contribution is an external controlled benchmark.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No physical entities are introduced; QSWMs are a classical representation framework. The derivation-style theorems are definitional or standard, and the empirical claim rests on the assumed adequacy of the ECA benchmark and matching of baselines, not on fitted physical constants.

free parameters (2)
  • latent dimension d = 32 (default)
    The main comparison uses d=32; scaling experiments sweep 16, 32, 64, 128 but no model-selection criterion is reported, so the central comparison depends on this hand-chosen capacity.
  • normalization constant epsilon = small (unspecified)
    Used in latent-state normalizations in Section 5 to avoid division by zero; arbitrary and not load-bearing.
assumptions (4)
  • domain assumption Finite-dimensional classical probabilistic world models are a faithful baseline class for the comparison.
    Theorems restrict to finite-dimensional classical latents and experiments use 32-bit CA states; the paper does not justify extension to high-dimensional or continuous world models.
  • standard math The trained models achieve optimality or near-optimality under a strictly proper predictive loss for Theorem 2.
    Theorem 2 assumes an optimal predictor; trained networks are not optimal, so the sufficiency result is conditional, not an empirical finding.
  • domain assumption Predictive state distributions of interest admit tensor-network representations with bond dimension at most chi.
    Theorem 3 applies only to distributions with bounded tensor-network structure; the paper does not show that CA world-model distributions satisfy this condition.
  • domain assumption The evaluated ECA rules are representative of predictive world-modeling dynamics.
    Generalization from three one-dimensional binary rules to world modeling is asserted, not demonstrated; Appendix G lists broader environments as future work.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum-Structured World Models (QSWMs) for Predictive Latent Dynamics." pith.science (2026). https://pith.science/paper/CAA3JVIY

@misc{pith2026260805371,
  author       = {Pith},
  title        = {Pith review of: Quantum-Structured World Models (QSWMs) for Predictive Latent Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CAA3JVIY}},
  note         = {Machine review of arXiv:2608.05371}
}
read the original abstract

World models learn latent states that summarize interaction histories, evolve over time, and support prediction, simulation, or planning. Most existing world models represent these states using classical vectors, probability distributions, recurrent hidden states, or transformer activations. In this paper, we introduce Quantum-Structured World Models (QSWMs), a quantum-inspired framework for predictive world modeling with structured latent states, latent transition operators, and measurement-inspired decoding maps. We study whether mathematical structures inspired by quantum theory, such as complex-valued representations and density-matrix-like latents, provide useful inductive biases for world modeling. We establish three foundational properties: classical inclusion, predictive sufficiency, and structured compactness. We then instantiate complex-valued and density-matrix-like QSWM variants and evaluate them on elementary cellular automata against strong classical baselines. Results show promising local predictive potential for complex-valued QSWMs, while also revealing limitations in long-horizon rollout, density-matrix variants

Figures

Figures reproduced from arXiv: 2608.05371 by the authors.

Figure 1
Figure 1. The overview of QSWM. Consider an agent interacting with an environment over discrete time. At time t, the agent receives an observation ot ∈ O, may take an action at ∈ A, and has access only to the interaction history ht = (o1, a1, o2, a2, . . . , ot−1, at−1, ot), rather than the true environment state st. A classical latent world model encodes this history into a latent vector, evolves it through learned dynamics,… view at source ↗
Figure 2
Figure 2. Scaling and out-of-distribution density evaluation. (a) One-step BCE under increasing latent dimension. (b) One-step accuracy under initial-density shifts from the training density p = 0.5. ization [17]. We further report scaling over latent dimensions d ∈ {16, 32, 64, 128} and latent probing with frozen world-model representations. Finding 1: ComplexQSWM improves local predictive dynamics [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 3
Figure 3. Recursive rollout accuracy (left) and Latent probing accuracy (right). quantum-structured latent representations provide a useful inductive bias across model capacity and data-distribution changes. Finding 4: Rollout and probing characterize learned dynamics [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Training and validation BCE curves for all evaluated models. ComplexQSWM achieves the lowest validation loss by the end of training [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: Linear probing accuracy of learned latent states [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references · 17 canonical work pages

  1. [1]

    arXiv preprint arXiv:2503.05788 (2025)

    Berti, L., Giorgi, F., Kasneci, G.: Emergent abilities in large language models: A survey. arXiv preprint arXiv:2503.05788 (2025)

    arXiv 2025

  2. [2]

    Nature549(7671), 195–202 (2017)

    Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quan- tum machine learning. Nature549(7671), 195–202 (2017)

    2017

  3. [3]

    In: Proceedings of the 2014 conference on empirical methods in natural language processing (EMNLP)

    Cho, K., Van Merriënboer, B., Gulçehre, Ç., Bahdanau, D., Bougares, F., Schwenk, H., Bengio, Y.: Learning phrase representations using rnn encoder–decoder for statistical machine translation. In: Proceedings of the 2014 conference on empirical methods in natural language processing (EMNLP). pp. 1724–1734 (2014)

    2014

  4. [4]

    arXiv preprint arXiv:2503.18938 (2025)

    Gao, S., Zhou, S., Du, Y., Zhang, J., Gan, C.: Adaworld: Learning adaptable world models with latent actions. arXiv preprint arXiv:2503.18938 (2025)

    arXiv 2025

  5. [5]

    arXiv preprint arXiv:1803.10122 (2018)

    Ha, D., Schmidhuber, J.: World models. arXiv preprint arXiv:1803.10122 (2018)

    arXiv 2018

  6. [6]

    In: International Conference on Learning Representations (2020)

    Hafner, D., Lillicrap, T., Ba, J., Norouzi, M.: Dream to control: Learning behaviors by latent imagination. In: International Conference on Learning Representations (2020)

    work page 2020

  7. [7]

    In: Proceedings of the Interna- tional Conference on Machine Learning

    Hafner, D., Lillicrap, T., Fischer, I., Villegas, R., Ha, D., Lee, H., Davidson, J.: Learning latent dynamics for planning from pixels. In: Proceedings of the Interna- tional Conference on Machine Learning. pp. 2555–2565 (2019)

    work page 2019

  8. [8]

    arXiv preprint arXiv:2010.02193 (2021)

    Hafner, D., Lillicrap, T., Norouzi, M., Ba, J.: Mastering atari with discrete world models. arXiv preprint arXiv:2010.02193 (2021)

    arXiv 2021

Show all 32 references
  1. [9]

    arXiv preprint arXiv:2301.04104 (2023)

    Hafner, D., Pasukonis, J., Ba, J., Lillicrap, T.: Mastering diverse domains through world models. arXiv preprint arXiv:2301.04104 (2023)

    2023 arXiv

  2. [10]

    arXiv preprint arXiv:2512.19410 (2025)

    Hazan, E., Shwartz, S.S., Srebro, N.: Research program: Theory of learning in dynamical systems. arXiv preprint arXiv:2512.19410 (2025)

    2025

  3. [11]

    Neural computation 9(8), 1735–1780 (1997)

    Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural computation 9(8), 1735–1780 (1997)

    1997

  4. [12]

    arXiv preprint arXiv:2505.11528 (2025)

    Huang, Y., Zhang, J., Zou, S., Liu, X., Hu, R., Xu, K.: Ladi-wm: A latent diffusion- based world model for predictive manipulation. arXiv preprint arXiv:2505.11528 (2025)

    2025 arXiv

  5. [13]

    Artificial intelligence101(1-2), 99–134 (1998)

    Kaelbling, L.P., Littman, M.L., Cassandra, A.R.: Planning and acting in partially observable stochastic domains. Artificial intelligence101(1-2), 99–134 (1998)

    1998

  6. [14]

    In: In- ternational Conference on Learning Representations (2020)

    Kaiser, L., Babaeizadeh, M., Milos, P., Osinski, B., Campbell, R.H., Czechowski, K., Erhan, D., Finn, C., Kozakowski, P., Levine, S., Mohiuddin, A., Sepassi, R., Tucker, G., Michalewski, H.: Model-based reinforcement learning for atari. In: In- ternational Conference on Learni...

    2020

  7. [15]

    arXiv preprint arXiv:2605.01694 (2026)

    Kim, K.W.: Latent state design for world models under sufficiency constraints. arXiv preprint arXiv:2605.01694 (2026)

    2026 arXiv

  8. [16]

    Encyclopedia5(2) (2025)

    Kyriazos, T., Poga, M.: Quantum-inspired statistical frameworks: Enhanc- ing traditional methods with quantum principles. Encyclopedia5(2) (2025). https://doi.org/10.3390/encyclopedia5020048, https://www.mdpi.com/2673- 8392/5/2/48

    2025 doi

  9. [17]

    arXiv preprint arXiv:2108.13624 (2021)

    Liu, J., Shen, Z., He, Y., Zhang, X., Xu, R., Yu, H., Cui, P.: Towards out-of- distribution generalization: A survey. arXiv preprint arXiv:2108.13624 (2021)

    2021 arXiv

  10. [18]

    arXiv preprint arXiv:2604.09430 (2026)

    Maio, D.: On the representational limits of quantum-inspired 1024-d document em- beddings: An experimental evaluation framework. arXiv preprint arXiv:2604.09430 (2026)

    2026 arXiv

  11. [19]

    Cambridge University Press (2010)

    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2010)

    2010

  12. [20]

    Annals of Physics349, 117–158 (2014)

    Orús, R.: A practical introduction to tensor networks: Matrix product states and projected entangled pair states. Annals of Physics349, 117–158 (2014)

    2014

  13. [21]

    Nature 588(7839), 604–609 (2020)

    Schrittwieser, J., Antonoglou, I., Hubert, T., Simonyan, K., Sifre, L., Schmitt, S., Guez, A., Lockhart, E., Hassabis, D., Graepel, T., Lillicrap, T., Silver, D.: Mastering atari, go, chess and shogi by planning with a learned model. Nature 588(7839), 604–609 (2020)

    2020

  14. [22]

    Springer (2018)

    Schuld, M., Petruccione, F.: Supervised Learning with Quantum Computers. Springer (2018)

    2018

  15. [23]

    Contemporary Physics56(2), 172–185 (2015)

    Schuld, M., Sinayskiy, I., Petruccione, F.: An introduction to quantum machine learning. Contemporary Physics56(2), 172–185 (2015)

    2015

  16. [24]

    IEEE Transactions on Knowledge and Data Engineering35(4), 4335–4345 (2021)

    Shi, J., Li, Z., Lai, W., Li, F., Shi, R., Feng, Y., Zhang, S.: Two end-to-end quantum-inspired deep neural networks for text classification. IEEE Transactions on Knowledge and Data Engineering35(4), 4335–4345 (2021)

    2021

  17. [25]

    In: Advances in Neural Information Processing Systems

    Sutskever, I., Hinton, G.E., Taylor, G.W.: The recurrent temporal restricted boltz- mann machine. In: Advances in Neural Information Processing Systems. vol. 21 (2008)

    2008

  18. [26]

    MIT Press (2018)

    Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press (2018)

    2018

  19. [27]

    Advances in neural information pro- cessing systems30(2017)

    Vaswani,A.,Shazeer,N.,Parmar,N.,Uszkoreit,J.,Jones,L.,Gomez,A.N.,Kaiser, Ł., Polosukhin, I.: Attention is all you need. Advances in neural information pro- cessing systems30(2017)

    2017

  20. [28]

    Yao, X., Gao, J., Xu, C.: Navmorph: A self-evolving world model for vision-and- languagenavigationincontinuousenvironments.In:ProceedingsoftheIEEE/CVF International Conference on Computer Vision. pp. 5536–5546 (2025)

    2025

  21. [29]

    In: GLOBECOM 2024 – 2024 IEEE Global Com- munications Conference

    Zeng, P., He, Y., Yu, F.R., Du, J.: A quantum temporal difference learning method based on quantum world model. In: GLOBECOM 2024 – 2024 IEEE Global Com- munications Conference. pp. 4010–4015 (2024)

    2024

  22. [30]

    In: GLOBECOM 2023 – 2023 IEEE Global Communica- tions Conference

    Zeng, P., He, Y., Yu, F.R., Leung, V.C.M.: Quantum reinforcement learning with quantum world model. In: GLOBECOM 2023 – 2023 IEEE Global Communica- tions Conference. pp. 1–6 (2023)

    2023

  23. [31]

    In: ICASSP 2026-2026 IEEE Inter- national Conference on Acoustics, Speech and Signal Processing (ICASSP)

    Zhang, G., Guo, W., Tan, Z., He, H., Guan, Q., Jiang, H.: Readout-side bypass for residual hybrid quantum-classical models. In: ICASSP 2026-2026 IEEE Inter- national Conference on Acoustics, Speech and Signal Processing (ICASSP). pp. 1841–1845. IEEE (2026)

    2026

  24. [32]

    Zhang, P., et al.: Complex-valued neural network-based quantum language model. ACM Transactions on Asian and Low-Resource Language Information Processing (2022) A Detailed Proofs A.1 Proof of Theorem 1: Classical Inclusion Theorem 1.Every finite-dimensional classical probabili...

    2022

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.