Pith. sign in

REVIEW 3 major objections 2 minor 33 references

Rethinking Expressibility-Trainability Trade-off in Hybrid Quantum Neural Networks

T0 review · 3 major / 2 minor · reviewed 2026-06-29 · grok-4.3

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

Pith's one-line read Hybrid quantum neural networks can eliminate the expressibility-trainability trade-off of pure quantum circuits.

desk verdict Full end-to-end hybrid training appears to weaken or remove the expressibility-trainability trade-off in these simulations, but the result tracks the chosen metrics and circuit families closely. read the letter →

arxiv 2605.25768 v1 pith:33PVJVPF submitted 2026-05-25 quant-ph

Muhammad Kashif , Muhammad Shafique This is my paper
classification quant-ph
keywords hybridquantumneuralnetworksexpressibilitytrainabilityparameterizedcircuitsbarrenplateausarchitecturesearchmachinelearningoptimizationlandscape
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 tests the widespread assumption that highly expressive parameterized quantum circuits suffer worse trainability due to barren plateaus, and checks whether this holds once those circuits sit inside larger hybrid classical-quantum models. It compares three regimes: training a pure quantum circuit alone, training only the quantum part inside a hybrid model, and training the entire hybrid model end-to-end. Pure circuits show only a weak, regime-dependent version of the expected trade-off, but full hybrid training increasingly removes the correlation, indicating that the classical layers change the loss landscape. This matters for model design because it suggests expressibility and trainability need not be traded off when classical and quantum components are optimized together. The authors also introduce a multi-objective search procedure that jointly tunes expressibility, trainability, and task accuracy over the combined design space.

What carries the argument

Systematic comparison of expressibility-trainability correlation across pure PQC training, quantum-only training inside hybrids, and full end-to-end hybrid training, performed over varying circuit depths, qubit counts, and entanglement topologies, plus a multi-objective neural architecture search that optimizes the three objectives jointly.

What would settle it

A persistent strong negative correlation between the expressibility and trainability metrics that remains even after full end-to-end training of the hybrid model on standard classification benchmarks would falsify the decoupling result.

Watch

Extended reading notes

Core claim

Pure parameterized quantum circuits exhibit only a weak and regime-dependent negative correlation between expressibility and trainability, while hybrid quantum neural networks increasingly disrupt and can eliminate this relationship once the full model is trained end-to-end; classical components reshape the optimization landscape and thereby decouple trainability from the expressibility of the embedded quantum circuit.

Load-bearing premise

The chosen numerical metrics for expressibility and trainability, together with the simulated circuit configurations and training procedures, accurately reflect the optimization behavior that would appear in practical hybrid quantum neural network applications.

Editorial extensions

If this is right

  • Designers of hybrid models can select more expressive parameterized quantum circuits without incurring the expected trainability penalty once classical layers participate in training.
  • The dominant factor controlling trainability shifts from the quantum circuit properties to the overall hybrid architecture and training mode.
  • Pareto fronts for expressibility, trainability, and task performance differ markedly between quantum-only and full end-to-end training regimes.
  • Standard guidelines that treat expressibility as a direct proxy for trainability apply only to isolated quantum circuits, not to embedded ones inside hybrids.

Reading between the lines

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

  • The result suggests that scaling quantum machine learning may benefit more from careful hybrid architecture choices than from further engineering of the quantum circuit alone.
  • Similar decoupling could appear in other hybrid quantum-classical settings whenever classical gradient steps dominate the loss surface.
  • A direct test would compare the same quantum circuit inside a hybrid model versus as a standalone circuit on identical data, measuring whether the correlation reappears when the classical layers are removed.
Share X Bluesky LinkedIn Reddit HN

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

3 major / 2 minor

Summary. The paper claims that pure parameterized quantum circuits (PQCs) exhibit only a weak, regime-dependent expressibility-trainability trade-off, whereas hybrid quantum neural networks (HQNNs) increasingly disrupt and can eliminate this relationship under full end-to-end training; classical components are said to reshape the optimization landscape and decouple trainability from PQC expressibility. The work also introduces a multi-objective neural architecture search (NAS) framework that jointly optimizes expressibility, trainability, and task performance, revealing different Pareto fronts for quantum-only versus full hybrid training.

Significance. If the empirical results are robust to metric choice and simulation details, the finding that hybridization can eliminate the conventional trade-off would be significant for quantum machine learning, as it suggests that classical layers can mitigate barren-plateau issues even for expressive PQCs and motivates architecture search over combined classical-quantum spaces. The consideration of multiple trainability definitions is a positive step toward generality.

major comments (3)
  1. [§4 (Results) and abstract] The central claim that full hybrid training eliminates the expressibility-trainability trade-off rests on the specific operational definitions of expressibility (likely a fidelity or covering-number measure on the isolated PQC unitary) and trainability (gradient variance or loss curvature). These definitions are not shown to remain valid once classical layers are inserted and trained end-to-end; if classical gradients dominate or if expressibility is never re-measured on the composite model, the decoupling conclusion does not follow for practical HQNNs.
  2. [§4 and Methods] No error bars, number of independent runs, or statistical tests are reported for the key figures or tables that demonstrate elimination of the trade-off under full hybrid training. Without these, it is impossible to determine whether the observed disruption is statistically reliable or sensitive to the chosen circuit depths, qubit counts, entanglement topologies, and random seeds.
  3. [§5 (NAS framework)] The multi-objective NAS framework is presented as revealing different Pareto-optimal solutions, yet the paper provides no ablation on the weighting of the three objectives or comparison against single-objective baselines or random search; this weakens the claim that the framework is practically useful for hybrid design.
minor comments (2)
  1. [Abstract / §1] The abstract states that 'different trainability definitions' are considered but does not list them explicitly; a short enumerated list in the introduction or methods would improve clarity.
  2. [§3 (Model definition)] Notation for the hybrid loss function and the interface between classical and quantum layers should be defined once in a dedicated subsection rather than introduced piecemeal.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript arXiv:2605.25768. We address each of the major comments point-by-point below, providing clarifications and indicating where revisions will be made to strengthen the paper.

read point-by-point responses

  1. Referee: [§4 (Results) and abstract] The central claim that full hybrid training eliminates the expressibility-trainability trade-off rests on the specific operational definitions of expressibility (likely a fidelity or covering-number measure on the isolated PQC unitary) and trainability (gradient variance or loss curvature). These definitions are not shown to remain valid once classical layers are inserted and trained end-to-end; if classical gradients dominate or if expressibility is never re-measured on the composite model, the decoupling conclusion does not follow for practical HQNNs.

    Authors: We appreciate the referee raising this point on the validity of the metrics in the hybrid setting. Expressibility is measured on the PQC in isolation using standard fidelity-based metrics, as is conventional. Trainability is evaluated through the gradient variance of the PQC parameters under the hybrid loss. Our results indicate that end-to-end training with classical layers modifies the loss landscape such that the gradient variances for PQC parameters do not follow the expected trade-off with expressibility. This decoupling is observed empirically across configurations. We will add a new paragraph in Section 4 to explicitly discuss the application of these metrics to HQNNs and address potential concerns about classical gradient dominance by showing that the PQC parameter gradients are indeed influenced but remain the focus of our analysis. revision: partial

  2. Referee: [§4 and Methods] No error bars, number of independent runs, or statistical tests are reported for the key figures or tables that demonstrate elimination of the trade-off under full hybrid training. Without these, it is impossible to determine whether the observed disruption is statistically reliable or sensitive to the chosen circuit depths, qubit counts, entanglement topologies, and random seeds.

    Authors: This is a valid observation. Although our simulations involved multiple independent runs with different random seeds to ensure reliability, these details and error bars were not included in the presented figures. We will revise the manuscript to report the number of runs (e.g., 20 per configuration), include error bars representing standard deviation in all plots, and add statistical analysis in the Methods section to confirm the significance of the observed differences. revision: yes

  3. Referee: [§5 (NAS framework)] The multi-objective NAS framework is presented as revealing different Pareto-optimal solutions, yet the paper provides no ablation on the weighting of the three objectives or comparison against single-objective baselines or random search; this weakens the claim that the framework is practically useful for hybrid design.

    Authors: We agree that additional experiments would enhance the NAS section. The primary goal was to show that different training regimes lead to distinct Pareto fronts. To address this, we will include ablations on objective weightings and comparisons with single-objective NAS and random search in the revised version, either in the main text or as supplementary material. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in empirical simulation study

full rationale

The paper reports results from systematic numerical simulations of expressibility and trainability metrics across circuit depths, qubit counts, topologies, and training regimes (pure PQC, quantum-only hybrid, full end-to-end hybrid). No derivation chain, fitted-parameter prediction, or uniqueness theorem is invoked; the central claim that hybridization can eliminate the trade-off is presented as an observed outcome of the simulations rather than a reduction to inputs by construction. The work is therefore self-contained against external benchmarks and receives the default non-circularity finding.

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

The study is an empirical simulation analysis of quantum circuits in hybrid settings. No free parameters, axioms, or invented entities are explicitly introduced or required based on the abstract.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Rethinking Expressibility-Trainability Trade-off in Hybrid Quantum Neural Networks." pith.science (2026). https://pith.science/paper/33PVJVPF

@misc{pith2026260525768,
  author       = {Pith},
  title        = {Pith review of: Rethinking Expressibility-Trainability Trade-off in Hybrid Quantum Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/33PVJVPF}},
  note         = {Machine review of arXiv:2605.25768}
}
read the original abstract

Hybrid quantum neural networks (HQNNs) integrate parameterized quantum circuits (PQCs) within classical networks, where the behavior of the underlying PQCs is often the primary focus of analysis. In this context, expressibility and trainability are widely used to characterize PQC's performance and are commonly assumed to exhibit a trade-off, where highly expressive circuits are more susceptible to barren plateaus. However, the validity of this relationship in HQNNs remains unclear. In this paper, we systematically analyze the expressibility--trainability relationship in HQNNs across varying circuit depths, qubit counts, entanglement topologies. We consider different training configurations, including pure PQCs, quantum-only training in hybrid setting, and full end-to-end training of hybrid models. Our results show that pure PQCs exhibit only a weak and regime-dependent trade-off, while hybrid architectures increasingly disrupt and can eliminate this relationship under full hybrid training. This indicates that classical components reshape the optimization landscape, decoupling trainability from PQC expressibility. We further propose a multi-objective neural architecture search (NAS) framework that jointly optimizes expressibility, trainability, and task performance over a combined classical--quantum design space, revealing different Pareto-optimal solutions under full end-to-end and quantum only training in hybrid setting. different trainability definitions. Our results suggest that hybridization is not just an implementation detail, but a defining factor in the performance of quantum machine learning models.

Figures

Figures reproduced from arXiv: 2605.25768 by the authors.

Figure 1
Figure 1. Overview of the our two-stage methodology. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Synthetic dataset used for Expressibility-Trainability analysis of HQNNs [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Stage I results across four architectural settings: (a) varying depth, (b) varying entanglement topology, (c) varying number of qubits, and (d) all parameters varied. Subplots (x1), (x2), and (x3) correspond to standalone PQCs, hybrid quantum-only training, and hybrid full-model training, respectively. −log10(gradvar) is based in Eq. 10, where smallers values means high gradiant variance (Better trainability) and vi… view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: NAS results for HQNN architectures under two trainability definitions. The blue panels correspond to full-model trainability (gradients computed with respect to all model [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

33 extracted references · 9 canonical work pages

  1. [1]

    Variational quantum algorithms,

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincioet al., “Variational quantum algorithms,”Nature Reviews Physics, vol. 3, no. 9, pp. 625–644, 2021

    2021

  2. [2]

    Filtering variational quantum algorithms for combinatorial optimization,

    D. Amaro, C. Modica, M. Rosenkranz, M. Fiorentini, M. Benedetti, and M. Lubasch, “Filtering variational quantum algorithms for combinatorial optimization,”Quantum Science & Technology, vol. 7, no. 1, p. 015021, 2022

    2022

  3. [3]

    Quav: Quantum-assisted path planning and optimization for uav navigation with obstacle avoidance,

    N. Innan, M. Kashif, A. Marchisio, Y .-S. Gan, F. Barbaresco, and M. Shafique, “Quav: Quantum-assisted path planning and optimization for uav navigation with obstacle avoidance,” in2025 IEEE International Conference on Quantum Artificial Intelligence (QAI). IEEE, 2025, pp. 208–215

    2025

  4. [4]

    Position paper: Quantum neural networks-a paradigm shift in ai or a theoretical promise?

    M. Kashif and M. Shafique, “Position paper: Quantum neural networks-a paradigm shift in ai or a theoretical promise?” in2025 International Joint Conference on Neural Networks (IJCNN). IEEE, 2025, pp. 1–10

    2025

  5. [5]

    An introduction to quantum machine learning,

    M. Schuld, I. Sinayskiy, and F. Petruccione, “An introduction to quantum machine learning,”Contemporary Physics, vol. 56, no. 2, pp. 172–185, 2015

    2015

  6. [6]

    Computational advantage in hybrid quantum neural networks: Myth or reality?

    M. Kashif, A. Marchisio, and M. Shafique, “Computational advantage in hybrid quantum neural networks: Myth or reality?” in2025 62nd ACM/IEEE Design Automation Conference (DAC). IEEE, 2025, pp. 1–7

    2025

  7. [7]

    doi: 10.1002/qute

    S. Sim, P. D. Johnson, and A. Aspuru-Guzik, “Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms,”Advanced Quantum Technologies, vol. 2, no. 12, Oct. 2019. [Online]. Available: http://dx.doi.org/10.1002/qute. 201900070

    work page doi:10.1002/qute 2019

  8. [8]

    Efficient estimation of trainability for variational quantum circuits,

    V . Heyraud, Z. Li, K. Donatella, A. Le Boit ´e, and C. Ciuti, “Efficient estimation of trainability for variational quantum circuits,”PRX Quantum, vol. 4, no. 4, p. 040335, 2023

    2023

Show all 33 references
  1. [9]

    Barren plateaus in quantum neural network training landscapes,

    J. R. McClean, S. Boixo, V . N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,”Nature communications, vol. 9, no. 1, p. 4812, 2018

    2018

  2. [10]

    Alleviating barren plateaus in parameterized quantum machine learning circuits: Investigating advanced parameter initialization strategies,

    M. Kashif, M. Rashid, S. Al-Kuwari, and M. Shafique, “Alleviating barren plateaus in parameterized quantum machine learning circuits: Investigating advanced parameter initialization strategies,” in2024 Design, Automation & Test in Europe Conference & Exhibition (DATE). IEEE, 2...

    2024

  3. [11]

    Connecting ansatz expressibility to gradient magnitudes and barren plateaus,

    Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, “Connecting ansatz expressibility to gradient magnitudes and barren plateaus,” PRX Quantum, vol. 3, no. 1, Jan. 2022. [Online]. Available: http://dx.doi.org/10.1103/PRXQuantum.3.010313

    2022 doi

  4. [12]

    Resqnets: a residual approach for mitigating barren plateaus in quantum neural networks,

    M. Kashif and S. Al-Kuwari, “Resqnets: a residual approach for mitigating barren plateaus in quantum neural networks,”EPJ Quantum Technology, vol. 11, no. 1, pp. 1–28, 2024

    2024

  5. [13]

    Expressibility and trainability of parametrized analog quantum systems for machine learning applications,

    J. Tangpanitanon, S. Thanasilp, N. Dangniam, M.-A. Lemonde, and D. G. Angelakis, “Expressibility and trainability of parametrized analog quantum systems for machine learning applications,”Physical Review Research, vol. 2, no. 4, p. 043364, 2020

    2020

  6. [14]

    How to find expressible and trainable parameterized quantum circuits?

    P. R ¨oseler, D. Willsch, and K. Michielsen, “How to find expressible and trainable parameterized quantum circuits?”arXiv preprint arXiv:2603.14451, 2026

    2026

  7. [15]

    High- expressibility quantum neural networks using only classical resources,

    M. Maronese, F. Ferrari, M. Vandelli, and D. Dragoni, “High- expressibility quantum neural networks using only classical resources,” Quantum Machine Intelligence, vol. 8, no. 1, p. 25, 2026

    2026

  8. [16]

    The unified effect of data encoding, ansatz expressibility and entanglement on the trainability of hqnns,

    M. Kashif and S. Al-Kuwari, “The unified effect of data encoding, ansatz expressibility and entanglement on the trainability of hqnns,” International Journal of Parallel, Emergent and Distributed Systems, vol. 38, no. 5, pp. 362–400, 2023

    2023

  9. [17]

    Efficiently architecting vqas: Expressibility–trainability–resources pareto- optimality,

    R. M. Sanz, A. Angles-Castillo, E. Alarcon, and C. G. Almudever, “Efficiently architecting vqas: Expressibility–trainability–resources pareto- optimality,”arXiv preprint arXiv:2603.22142, 2026

    2026

  10. [18]

    Analysis of parameterized quantum circuits: On the connection between expressibility and types of quantum gates,

    Y . Liu, K. Kaneko, K. Baba, J. Koyama, K. Kimura, and N. Takeda, “Analysis of parameterized quantum circuits: On the connection between expressibility and types of quantum gates,”IEEE Transactions on Quantum Engineering, vol. 6, pp. 1–12, 2025

    2025

  11. [19]

    Subtleties in the trainability of quantum machine learning models,

    S. Thanasilp, S. Wang, N. A. Nghiem, P. Coles, and M. Cerezo, “Subtleties in the trainability of quantum machine learning models,” Quantum Machine Intelligence, vol. 5, no. 1, p. 21, 2023

    2023

  12. [20]

    Design space exploration of hybrid quantum–classical neural networks,

    M. Kashif and S. Al-Kuwari, “Design space exploration of hybrid quantum–classical neural networks,”Electronics, vol. 10, no. 23, p. 2980, 2021

    2021

  13. [21]

    Quantumleap: Hybrid quantum neural network for financial predictions,

    E. Paquet and F. Soleymani, “Quantumleap: Hybrid quantum neural network for financial predictions,”Expert Systems with Applications, vol. 195, p. 116583, 2022

    2022

  14. [22]

    Hybrid quantum neural network for drug response prediction,

    A. Sagingalieva, M. Kordzanganeh, N. Kenbayev, D. Kosichkina, T. Tomashuk, and A. Melnikov, “Hybrid quantum neural network for drug response prediction,”Cancers, vol. 15, no. 10, p. 2705, 2023

    2023

  15. [23]

    Hybrid quantum-classical convolutional neural networks,

    J. Liu, K. H. Lim, K. L. Wood, W. Huang, C. Guo, and H.-L. Huang, “Hybrid quantum-classical convolutional neural networks,”Science China Physics, Mechanics & Astronomy, vol. 64, no. 9, p. 290311, 2021

    2021

  16. [24]

    Design space exploration of hybrid quantum neural networks for chronic kidney disease,

    M. Kashif, H. M. Siraj, N. Innan, A. Marchisio, and M. Shafique, “Design space exploration of hybrid quantum neural networks for chronic kidney disease,”arXiv preprint arXiv:2604.13608, 2026

    2026 arXiv

  17. [25]

    Faqnas: Flops-aware hybrid quantum neural architecture search using genetic algorithm,

    M. Kashif, S. Khalid, A. Marchisio, N. Innan, and M. Shafique, “Faqnas: Flops-aware hybrid quantum neural architecture search using genetic algorithm,”arXiv preprint arXiv:2511.10062, 2025

    2025

  18. [26]

    Hybrid quantum- classical neural architecture search,

    A. Marchisio, M. Kashif, N. Innan, and M. Shafique, “Hybrid quantum- classical neural architecture search,”arXiv preprint arXiv:2605.18345, 2026

    2026 arXiv

  19. [27]

    Closing the loop: Resource- aware hybrid nas guided by analytical and hardware-calibrated quantum cost modeling,

    M. Kashif, A. Marchisio, and M. Shafique, “Closing the loop: Resource- aware hybrid nas guided by analytical and hardware-calibrated quantum cost modeling,”arXiv preprint arXiv:2603.00625, 2026

    2026

  20. [28]

    The impact of cost function globality and locality in hybrid quantum neural networks on nisq devices,

    M. Kashif and S. Al-Kuwari, “The impact of cost function globality and locality in hybrid quantum neural networks on nisq devices,”Machine Learning: Science and Technology, vol. 4, no. 1, p. 015004, 2023

    2023

  21. [29]

    General parameter-shift rules for quantum gradients,

    D. Wierichs, J. Izaac, C. Wang, and C. Y .-Y . Lin, “General parameter-shift rules for quantum gradients,”Quantum, vol. 6, p. 677, 2022

    2022

  22. [30]

    Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility, and entangling capability,

    T. Hubregtsen, J. Pichlmeier, P. Stecher, and K. Bertels, “Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility, and entangling capability,”Quantum Machine Intelligence, vol. 3, no. 1, p. 9, 2021

    2021

  23. [31]

    Learning the expressibility of quantum circuit ansatz using transformer,

    F. Zhang, J. Li, Z. He, and H. Situ, “Learning the expressibility of quantum circuit ansatz using transformer,”Advanced Quantum Technologies, vol. 8, no. 6, p. 2400366, 2025

    2025

  24. [32]

    Eqnas: Evolutionary quantum neural architecture search for image classification,

    Y . Li, R. Liu, X. Hao, R. Shang, P. Zhao, and L. Jiao, “Eqnas: Evolutionary quantum neural architecture search for image classification,” Neural Networks, vol. 168, pp. 471–483, 2023

    2023

  25. [33]

    Quantum neural architecture search with quantum circuits metric and bayesian optimization,

    T. Duong, S. T. Truong, M. Tam, B. Bach, J.-Y . Ryu, and J.-K. K. Rhee, “Quantum neural architecture search with quantum circuits metric and bayesian optimization,”arXiv:2206.14115, 2022. [Online]. Available: https://arxiv.org/abs/2206.14115

    2022

Pith tools

Reviewed June 29, 2026 · model on record in the stance chip above.