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REVIEW 4 major objections 3 minor 32 references

Escaping Barren Plateau: Co-Exploration of Quantum Circuit Parameters and Architectures

T0 review · 4 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A co-exploration framework called AntiBP prunes quantum gates during training so VQE circuits can escape barren plateaus, with better noisy performance than fixed-ansatz baselines.

desk verdict Useful pruning heuristic for small VQEs, but the barren-plateau-escape claim is not supported because gradient variance is never measured. read the letter →

arxiv 2501.13275 v1 pith:OVOAD3DW submitted 2025-01-22 quant-ph

Yipei Liu , Yuhong Song , Jinyang Li , Qiang Guan , Cheng-chang Lu , Youzuo Lin , Weiwen Jiang This is my paper · ORCID
classification quant-ph
keywords barrenplateausvariationalquantumeigensolvercircuitarchitecturesearchgatepruningco-explorationdepolarizingnoiseNISQoptimization
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

Barren plateaus—regions of the loss landscape where gradients shrink exponentially and training stalls—are claimed not to be tied to a universal circuit depth: the same variational form can sit in a best-fit regime for one molecule and a barren-plateau regime for another, and device noise shrinks the workable region. To avoid hand-searching this region, AntiBP trains a binary-like activation weight for every gate together with the gate's rotation angle, prunes gates whose activations collapse to zero, and fine-tunes the survivors. In noise-free VQE simulations, AntiBP is reported to keep low expectation values at depths where random baseline circuits stagnate, provided the input circuit is not under-parameterized, and under depolarizing noise it reduces energy errors relative to vanilla VQE and the IdentityBlock baseline. If the claim holds, AntiBP gives an automated route from an overcomplete circuit to a compact, problem-specific one that is trainable and noise-tolerant.

What carries the argument

The load-bearing mechanism is the gated circuit representation of AntiBP Stage 1: a circuit becomes differentiable in its own architecture by replacing each parameterized gate with $G(\alpha_i\theta_i)$ and each non-parameterized controlled gate with $CR(\pi\beta_j)$, so activations and angles can be updated in one backpropagation loop. A steep sigmoid with slope 50 forces $\alpha_i$ and $\beta_j$ to act as near-binary switches; the search then keeps a gate when its switch is near 1 and prunes it when near 0. Stage 2 fixes the chosen architecture and fine-tunes only the surviving $\theta$, so the final circuit is both sparse and optimized.

What would settle it

Run the H2O, LiH, and NH3 VQE experiments across the depths used in Figures 1–3 and, at random initialization, compute $\mathrm{Var}_{\theta}[\partial E/\partial\theta]$ or cost concentration over many samples; if the depths labeled 'barren plateau' do not show exponentially decaying variance relative to shallower depths, the region classification is not established. As a companion check, run AntiBP while logging gradient variance after each pruning step and compare the final variance with a randomly pruned circuit of identical gate count; the framework's claim requires AntiBP's variance to recover where random pruning's does not.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a VQE's optimization landscape splits into four depth-dependent regimes—underfit, best-fit, barren-plateau, and BP-alleviated—and the boundaries of these regimes move between molecules and shrink under noise, so no fixed ansatz depth is safe across applications. AntiBP is the proposed way to find the right regime automatically: every rotation gate is rewritten as $G(\alpha_i\theta_i)$ and every fixed controlled gate as $CR(\pi\beta_j)$, where the $\alpha_i$ and $\beta_j$ are trainable architecture parameters steered toward 0 or 1 by a steep sigmoid while the gate angles $\theta$ are optimized. After convergence, gates with zeroed activations are pruned and the remaining angles are fine-tuned. The paper's experimental claim is that this targeted pruning, rather than simple gate-count reduction, keeps optimized circuits out of the barren-plateau regime at large depth and improves performance under depolarizing noise.

Load-bearing premise

The paper identifies the 'barren plateau region' from the final optimized energy at each circuit depth rather than from measured gradient variances, so the claim that AntiBP escapes barren plateaus rests on the assumption that energy stagnation at those depths is actually caused by exponentially vanishing gradients rather than by local minima or noise.

Editorial extensions

If this is right

  • A user can start from an overcomplete circuit and let AntiBP discover a compact architecture, replacing manual depth sweeps to locate the best-fit region.
  • Because AntiBP prunes both single-qubit rotations and two-qubit controlled gates, its circuits accumulate less depolarizing noise, which the paper reports as smaller energy gaps than vanilla VQE and IdentityBlock in noisy runs.
  • The same-pruning-ratio ablation implies that which gates are removed matters: randomly pruning the same number of gates leaves barren-plateau behavior intact, while AntiBP's targeted pruning does not.
  • If the four-region picture is right, architecture search becomes a necessary part of VQE deployment for each new molecule, rather than a one-time design choice.

Reading between the lines

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

  • The same gated-pruning idea could be carried over to other variational algorithms such as QAOA or quantum machine learning, where the paper offers no evidence but the mechanism is not VQE-specific.
  • The paper labels plateau regions using final optimized energies rather than gradient-variance measurements; if the stagnation at those depths were caused by local minima or noise rather than exponentially vanishing gradients, the BP-escape interpretation would need revision.
  • A direct test would be to record $\mathrm{Var}[\partial E/\partial\theta]$ during AntiBP Stage 1: the pruning should raise gradient variance in deep circuits, and the recovered variance should exceed that of randomly pruned circuits with the same gate count.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 3 minor

Summary. The paper proposes AntiBP, a two-stage framework that co-optimizes gate parameters and circuit architecture for VQE by associating each gate with a differentiable binary mask (α for parameterized gates, β for controlled gates, via a steep sigmoid), pruning gates with masks near zero, and then fine-tuning the remaining parameters. The paper first presents observations that VQE performance as a function of circuit depth exhibits four regions—underfit, best-fit, barren plateau, and BP alleviated—whose locations shift across molecules and shrink under noise. It then evaluates AntiBP on random circuits and H2/H2O molecules, comparing against vanilla VQE and identity-block circuits, and reports that AntiBP achieves lower expectation values, especially in noisy settings, and outperforms random pruning with the same gate count.

Significance. The idea of co-exploring architecture and parameters with differentiable gating is promising, and the random-pruning ablation (Figure 6) is a well-designed control that shows gate-count reduction alone does not explain the gains. If the method were shown to actually circumvent exponentially vanishing gradients, this would be a useful contribution to VQE architecture design. As it stands, the evidence supports a weaker claim: AntiBP finds lower-energy circuits than the tested baselines in the tested settings. The central BP-avoidance claim is not established because no direct BP diagnostic, such as gradient variance, is measured.

major comments (4)
  1. [Section III, Figures 1-3] The existence and location of the 'barren plateau region' and 'BP alleviated region' are inferred solely from the final optimized energy at each circuit depth, not from any measurement of gradient variance. Because BP is defined by exponentially vanishing gradients, and energy stagnation can also be caused by local minima, optimization hardness, or noise, the observation that these regions exist and shift is not sufficient to identify BP. In particular, the reported 'BP alleviated region' at large depths in Figure 1 is in tension with standard BP behavior, where increasing depth generally makes gradients exponentially smaller. The paper should either measure gradient variance (e.g., Var[∂E/∂θ] under random initialization) across depths, or rephrase the claims to be about optimization difficulty rather than BP. This is load-bearing because the abstract's central claim is that AntiBP avoids BP.
  2. [Section V, Table I] The noisy-environment evaluations are single-run comparisons against only vanilla VQE and identity-block circuits. To support the claim that AntiBP 'significantly outperforms baseline VQEs in noisy environments,' the paper needs statistical evidence (multiple independent runs with error bars) and comparison with relevant prior-art architecture-search or adaptive-pruning methods (e.g., Sim et al.'s adaptive pruning or Du et al.'s QCAS), not just the identity-block baseline. The current table reports one energy per configuration, so all reported differences could be within run-to-run variation.
  3. [Section IV-C] The use of a sigmoid with steepness 50 to approximate binary gates raises a gradient-saturation concern: for α or β values far from zero, the derivative of the sigmoid is exponentially small, so the architecture parameters may receive vanishing gradients precisely when gates are near their intended binary values. The paper asserts that the steep sigmoid 'ensures that the gradients with respect to α and β remain significant,' but this is not self-evident and needs either a derivation, a plot of gradient magnitudes during Stage 1, or an empirical check that α and β actually converge to 0/1 rather than becoming stuck at intermediate values. If the architecture parameters do not converge, the pruning step becomes arbitrary.
  4. [Section V, first paragraph and Figure 5] The benchmark in the noiseless depth-sweep is not fully specified. The text says the authors 'randomly generate single-qubit gates' and apply CZ gates, but it never states the Hamiltonian or observable whose expectation value is being minimized, nor how the reference energy (if any) is defined. Without this, the y-axis label 'expectation values' is not interpretable, and the claim that AntiBP 'consistently achieves the lowest expectation values' cannot be reproduced or compared to a ground-state energy. Please specify the Hamiltonian, the initial circuit distribution, and the number of random instances.
minor comments (3)
  1. [Table I] The header 'Vallina' should be 'Vanilla'; 'Improv.' should be defined as the percent improvement relative to the vanilla baseline, and the source of the reference energy (basis set or method) should be stated in the caption.
  2. [Figure 4] The notation in subfigure (b) is difficult to follow; the subscripts on α and β render ambiguously. Please redraw with clearer labels for gate-level indices and separate the preprocessing, Stage 1, and Stage 2 panels more explicitly.
  3. [Section V, noise model] The description of depolarizing noise as 'with a small probability p, the quantum state is replaced by a mixed state' is imprecise; specify whether the noise is applied after every gate, and give the exact p values used for the reported results rather than only the example p = 0.001.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the energy objective is externally defined and the random-pruning ablation gives the central claim independent content.

full rationale

The paper's derivation chain does not reduce to its own inputs. AntiBP's success is measured against the molecular ground-state energy, an external target defined by the Hamiltonian and independent of the pruning method. The architecture parameters alpha and beta are optimized to minimize this same energy, but the paper does not present that optimization as a prediction of a separate quantity; it is a direct benchmark. The ablation in Figure 6, which compares AntiBP with random pruning at the same gate count, breaks the identification between 'fewer gates' and 'better energy' and shows that the specific gate choices matter, so the central claim has independent empirical content. The self-citations in Refs. [11]-[14] appear in related-work context and are not used as a load-bearing theorem, uniqueness argument, or ansatz justification; they do not exclude alternatives or supply the sigmoid-pruning construction. A real limitation remains: the paper labels the 'barren plateau region' and 'BP alleviated region' from final optimized energies rather than from measured gradient variances, so the claim that AntiBP escapes exponentially vanishing gradients is not directly established. That is a construct-validity or evidence gap, not a circular equivalence: the paper does not define BP as low final energy, nor does it fit a parameter and then predict the same fitted quantity. Accordingly, no circular step can be exhibited.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central claim rests on one hand-chosen hyperparameter (sigmoid slope 50), two domain assumptions about how BP is diagnosed and how representative the random benchmark circuits are, and standard simulation assumptions. No new physical entities are introduced.

free parameters (1)
  • sigmoid steepness = 50
    Chosen by hand to force alpha/beta near binary; no sensitivity analysis given, and it directly controls whether architecture parameters have usable gradients.
assumptions (3)
  • domain assumption The four-region landscape (underfit/best-fit/BP/BP-alleviated) is read off from optimized energy versus depth curves, so energy stagnation is treated as equivalent to exponentially vanishing gradients.
    Central to Observation 1 and the motivation; no gradient variance is measured anywhere in the paper. Section III A.
  • domain assumption Randomly generated single-qubit rotations plus nearest-neighbor CZ gates are a representative benchmark for VQE ansatze.
    Used for Fig 5 and the noiseless benchmark; no chemistry structure is included in these circuits, so conclusions about VQE applicability are extrapolated. Section V.
  • standard math Backpropagation through the simulated quantum circuit yields correct gradients for alpha, beta, and theta.
    Standard in differentiable quantum circuit simulation, though the paper does not state whether parameter-shift or analytic simulation is used. Algorithm 1.

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Cite this review

Pith. "Pith review of Escaping Barren Plateau: Co-Exploration of Quantum Circuit Parameters and Architectures." pith.science (2026). https://pith.science/paper/OVOAD3DW

@misc{pith2026250113275,
  author       = {Pith},
  title        = {Pith review of: Escaping Barren Plateau: Co-Exploration of Quantum Circuit Parameters and Architectures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OVOAD3DW}},
  note         = {Machine review of arXiv:2501.13275}
}
read the original abstract

Barren plateaus (BP), characterized by exponentially vanishing gradients that hinder the training of variational quantum circuits (VQC), present a pervasive and critical challenge in applying variational quantum algorithms to real-world applications. It is widely recognized that the BP problem becomes more pronounced with an increase in the number of parameters. This work demonstrates that the BP problem manifests at different scales depending on the specific application, highlighting the absence of a universal VQC ansatz capable of resolving the BP issue across all applications. Consequently, there is an imminent need for an automated tool to design and optimize VQC architectures tailored to specific applications. To close the gap, this paper takes Variational Quantum Eigensolvers (VQEs) as a vehicle, and we propose a novel quantum circuit parameter and architecture co-exploration framework, namely AntiBP. Experimental results demonstrate that AntiBP effectively avoids the BP issue for circuits that are not under-parameterized in noise-free environments. Furthermore, AntiBP significantly outperforms baseline VQEs in noisy environments.

Figures

Figures reproduced from arXiv: 2501.13275 by the authors.

Figure 1
Figure 1. Performance of VQE on H2O molecule with different circuit depths, revealing four performance regions in the VQE optimization process inherently does not persist. To enable this, we use the VQE as a vehicle and analyze the optimization performance of backbone quantum circuit architectures as the circuit depth increases, which is proportional to the number of parameters [25]. Results, as shown in [PITH_FULL_IMAGE:fig… view at source ↗
Figure 2
Figure 2. Performance regions shift along with different applications, taking [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Performance of VQE with varying circuit depths for [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Overview of the proposed AntiBP framework: (a) AntiBP preprocessing: for encoding VQE with gate parameters only to VQE with both gate [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: AntiBP consistently achieves high performance when the original [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Works this paper leans on

32 extracted references · 25 canonical work pages

  1. [27]

    A semi-agnostic ansatz with variable structure for variational quantum algorithms,

    M. Bilkis, M. Cerezo, G. Verdon, P. J. Coles, and L. Cincio, “A semi-agnostic ansatz with variable structure for variational quantum algorithms,” Quantum Machine Intelligence , vol. 5, 2023

    work page 2023

  2. [29]

    Quantum circuit architecture search for variational quantum algorithms,

    Y . Du, T. Huang, S. You, M. H. Hsieh, and D. Tao, “Quantum circuit architecture search for variational quantum algorithms,” npj Quantum Information, vol. 8, 2022

    work page 2022

  3. [30]

    Adaptive pruning- based optimization of parameterized quantum circuits,

    S. Sim, J. Romero, J. F. Gonthier, and A. A. Kunitsa, “Adaptive pruning- based optimization of parameterized quantum circuits,” Quantum Science and Technology , vol. 6, no. 2, p. 025019, mar 2021. [Online]. Available: https://dx.doi.org/10.1088/2058-9565/abe107

    doi:10.1088/2058-9565/abe107 2021

  4. [1]

    Emerging quantum computing algorithms for quantum chemistry,

    M. Motta and J. E. Rice, “Emerging quantum computing algorithms for quantum chemistry,” Wiley Interdisciplinary Reviews: Computational Molecular Science, vol. 12, no. 3, p. e1580, 2022

    work page 2022

  5. [2]

    Overlap-adapt-vqe: Practical quantum chemistry on quantum computers via overlap-guided compact ansatze,

    C. Feniou, M. Hassan, D. Traor ´e, E. Giner, Y . Maday, and J.-P. Piquemal, “Overlap-adapt-vqe: Practical quantum chemistry on quantum computers via overlap-guided compact ansatze,” arXiv preprint arXiv:2301.10196 , 2023

    arXiv 2023

  6. [3]

    Quantum chemistry in the age of quantum computing,

    Y . Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferov ´a, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. Sawaya, S. Sim, L. Veis, and A. Aspuru-Guzik, “Quantum chemistry in the age of quantum computing,” Chemical reviews, vol. 119, no. 19, pp. 10 856– 10 915, 2019

    work page 2019

  7. [4]

    Unitary partitioning approach to the measurement problem in the variational quantum eigensolver method,

    A. F. Izmaylov, T.-C. Yen, R. A. Lang, and V . Verteletskyi, “Unitary partitioning approach to the measurement problem in the variational quantum eigensolver method,” Journal of chemical theory and compu- tation, vol. 16, no. 1, pp. 190–195, 2019

    work page 2019

  8. [5]

    Quantum computing in pharma: A multilayer embedding approach for near future applications,

    R. Izs ´ak, C. Riplinger, N. S. Blunt, B. de Souza, N. Holzmann, O. Crawford, J. Camps, F. Neese, and P. Schopf, “Quantum computing in pharma: A multilayer embedding approach for near future applications,” Journal of Computational Chemistry , vol. 44, no. 3, pp. 406–421, 2023

    work page 2023

Show all 32 references
  1. [6]

    Quantum algorithms for quantum chemistry and quantum materials science,

    B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, “Quantum algorithms for quantum chemistry and quantum materials science,” Chemical Re- views, vol. 120, no. 22, pp. 12 685–12 717, 2020

    2020

  2. [7]

    Quantum-centric supercomputing for materials science: A perspective on challenges and future directions,

    Y . Alexeev, M. Amsler, M. A. Barroca, S. Bassini, T. Battelle, D. Camps, D. Casanova, Y . J. Choi, F. T. Chong, C. Chunget al., “Quantum-centric supercomputing for materials science: A perspective on challenges and future directions,” Future Generation Computer Systems , vol....

    2024

  3. [8]

    Dft exchange: sharing perspectives on the workhorse of quantum chemistry and materials science,

    A. M. Teale, T. Helgaker, A. Savin, C. Adamo, B. Aradi, A. V . Arbuznikov, P. W. Ayers, E. J. Baerends, V . Barone, P. Calaminici et al., “Dft exchange: sharing perspectives on the workhorse of quantum chemistry and materials science,” Physical chemistry chemical physics , vol...

    2022

  4. [9]

    Graph neural networks for materials science and chemistry,

    P. Reiser, M. Neubert, A. Eberhard, L. Torresi, C. Zhou, C. Shao, H. Metni, C. van Hoesel, H. Schopmans, T. Sommer et al. , “Graph neural networks for materials science and chemistry,” Communications Materials, vol. 3, no. 1, p. 93, 2022

    2022

  5. [10]

    Perspec- tive on integrating machine learning into computational chemistry and materials science,

    J. Westermayr, M. Gastegger, K. T. Sch ¨utt, and R. J. Maurer, “Perspec- tive on integrating machine learning into computational chemistry and materials science,” The Journal of Chemical Physics , vol. 154, no. 23, 2021

    2021

  6. [11]

    A co-design framework of neural networks and quantum circuits towards quantum advantage,

    W. Jiang, J. Xiong, and Y . Shi, “A co-design framework of neural networks and quantum circuits towards quantum advantage,” Nature communications, vol. 12, no. 1, p. 579, 2021

    2021

  7. [12]

    Exploration of quantum neural architecture by mixing quantum neuron designs,

    Z. Wang, Z. Liang, S. Zhou, C. Ding, Y . Shi, and W. Jiang, “Exploration of quantum neural architecture by mixing quantum neuron designs,” in 2021 IEEE/ACM International Conference On Computer Aided Design (ICCAD). IEEE, 2021, pp. 1–7

    2021

  8. [13]

    When machine learning meets quantum computers: A case study,

    W. Jiang, J. Xiong, and Y . Shi, “When machine learning meets quantum computers: A case study,” in 2021 26th Asia and South Pacific Design Automation Conference (ASP-DAC). IEEE, 2021, pp. 593–598

    2021

  9. [14]

    Quclassi: A hybrid deep neural network architecture based on quantum state fidelity,

    S. A. Stein, B. Baheri, D. Chen, Y . Mao, Q. Guan, A. Li, S. Xu, and C. Ding, “Quclassi: A hybrid deep neural network architecture based on quantum state fidelity,” Proceedings of Machine Learning and Systems , vol. 4, 2022

    2022

  10. [15]

    Rgb image classification with quantum convolutional ansatz,

    Y . Jing, X. Li, Y . Yang, C. Wu, W. Fu, W. Hu, Y . Li, and H. Xu, “Rgb image classification with quantum convolutional ansatz,” Quantum Information Processing, vol. 21, no. 3, pp. 1–19, 2022

    2022

  11. [16]

    A multi-classification hybrid quantum neural network using an all-qubit multi-observable measurement strategy,

    Y . Zeng, H. Wang, J. He, Q. Huang, and S. Chang, “A multi-classification hybrid quantum neural network using an all-qubit multi-observable measurement strategy,” Entropy, vol. 24, no. 3, p. 394, 2022

    2022

  12. [17]

    Challenges and opportunities in quantum machine learning,

    M. Cerezo, G. Verdon, H.-Y . Huang, L. Cincio, and P. J. Coles, “Challenges and opportunities in quantum machine learning,” Nature Computational Science, vol. 2, no. 9, pp. 567–576, 2022

    2022

  13. [18]

    A variational eigenvalue solver on a photonic quantum processor,

    A. Peruzzo, J. McClean, P. Shadbolt, M. H. Yung, X. Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications, vol. 5, 2014

    2014

  14. [19]

    From the quantum approximate optimization algorithm to a quantum alternating operator ansatz,

    S. Hadfield, Z. Wang, B. O’Gorman, E. G. Rieffel, D. Venturelli, and R. Biswas, “From the quantum approximate optimization algorithm to a quantum alternating operator ansatz,” Algorithms, vol. 12, no. 2,

  15. [20]

    Equivalence of quantum barren plateaus to cost concentration and narrow gorges,

    A. Arrasmith, Z. Holmes, M. Cerezo, and P. J. Coles, “Equivalence of quantum barren plateaus to cost concentration and narrow gorges,” Quantum Science and Technology , vol. 7, no. 4, p. 045015, aug 2022. [Online]. Available: https://dx.doi.org/10.1088/2058-9565/ac7d06

    2022 doi

  16. [21]

    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

  17. [22]

    Beinit: Avoiding barren plateaus in variational quantum algorithms,

    A. Kulshrestha and I. Safro, “Beinit: Avoiding barren plateaus in variational quantum algorithms,” in 2022 IEEE international conference on quantum computing and engineering (QCE) . IEEE, 2022, pp. 197– 203

    2022

  18. [23]

    Limitations of optimization algo- rithms on noisy quantum devices,

    D. S. Franc ¸a and R. Garc ´ıa-Patr´on, “Limitations of optimization algo- rithms on noisy quantum devices,” Nature Physics, vol. 17, 2021

    2021

  19. [24]

    An initial- ization strategy for addressing barren plateaus in parametrized quantum circuits,

    E. Grant, L. Wossnig, M. Ostaszewski, and M. Benedetti, “An initial- ization strategy for addressing barren plateaus in parametrized quantum circuits,” Quantum, vol. 3, p. 214, 2019

    2019

  20. [25]

    Diagnosing barren plateaus with tools from quantum optimal control,

    M. Larocca, P. Czarnik, K. Sharma, G. Muraleedharan, P. J. Coles, and M. Cerezo, “Diagnosing barren plateaus with tools from quantum optimal control,” Quantum, vol. 6, 2022

    2022

  21. [26]

    The barren plateaus of quantum neural networks: review, taxonomy and trends,

    H. Qi, L. Wang, H. Zhu, A. Gani, and C. Gong, “The barren plateaus of quantum neural networks: review, taxonomy and trends,” 2023

    2023

  22. [28]

    Meta-variational quantum eigensolver: Learning energy profiles of parameterized hamiltonians for quantum simulation,

    A. Cervera-Lierta, J. S. Kottmann, and A. Aspuru-Guzik, “Meta-variational quantum eigensolver: Learning energy profiles of parameterized hamiltonians for quantum simulation,” PRX Quantum, vol. 2, p. 020329, May 2021. [Online]. Available: https://link.aps.org/doi/10.1103/PRXQua...

    2021 doi

  23. [31]

    Nature and measure of entanglement in quantum phase transitions,

    R. Somma, G. Ortiz, H. Barnum, E. Knill, and L. Viola, “Nature and measure of entanglement in quantum phase transitions,” 2004

    2004

  24. [2019]

    Available: https://www.mdpi.com/1999-4893/12/2/34

    [Online]. Available: https://www.mdpi.com/1999-4893/12/2/34

    1999

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