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REVIEW 3 major objections 5 minor 35 references

QUBO-based training for VQAs on Quantum Annealers

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that the task of choosing a variational circuit's rotation angles can be formulated as a QUBO and minimized on a quantum annealer, with experiments on three datasets showing lower training time than classical and evolution

desk verdict The paper's central claim—that training a VQA reduces to minimizing a QUBO on an annealer—rests on a non-unitary substitution that changes the loss landscape, so the advertised equivalence is unsupported; the recursive search is a reasonable heuristic, but the core derivation does not hold up. read the letter →

arxiv 2509.01821 v1 pith:LQMAXXOS submitted 2025-09-01 quant-ph cs.LG

Ernesto Acosta , Guillermo Botella , Carlos Cano This is my paper · ORCID
classification quant-phcs.LG
keywords variationalquantumalgorithmsQUBOannealinggradient-freeoptimizationhybridquantum-classicalhierarchicalsearchparameterizedcircuitsadiabaticcomputing
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

This paper claims that choosing a variational circuit's rotation angles can be recast as a QUBO—an optimization over binary variables with a quadratic objective—and that a quantum annealer can then solve it. The authors build the QUBO directly from the ansatz's operator and the mean-squared-error loss, discretize every angle into allowed values, and wrap the search in a recursive refinement loop that narrows the angle range around the best candidate. On Iris, Heart Disease, and Diabetes classification experiments, they report that this annealer-based training matches or beats classical optimizers and evolutionary algorithms while using less wall-clock time. If true, the result matters because it offers a gradient-free training path for variational quantum algorithms, which often stall when gradients vanish or are corrupted by noise. The cost is that the QUBO is built from a non-unitary hyperbolic approximation of the circuit, so the objective being minimized is not exactly the circuit's true error.

What carries the argument

The central object is Equation (9), the QUBO loss: a sum over training records of squared differences between each expected amplitude and the corresponding amplitude produced by the ansatz operator Q, with the angle dependence entering through Q's entries. Those entries are rewritten using cosh and sinh identities so that products become sums of exponentials, making the whole loss quadratic in binary variables that represent one chosen discretized value per angle. The second mechanism is the hierarchical recursive optimization: partition each angle's search range, run the annealer on the QUBO for grouped validation points, take the best result as the new center, shrink the range, and repeat

What would settle it

Take a small fixed circuit, such as the two-qubit example in Appendix A, compute the true MSE loss over a dense grid of angles, then compute the QUBO surrogate loss over the same grid. If the annealer-selected angles do not land at or near a true local minimum of the real unitary circuit's cost—or if they perform no better than random angles on validation accuracy—the claimed equivalence between VQA training and QUBO minimization is refuted, because this test isolates exactly the unitarity-breaking substitution the whole construction rests on.

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Extended reading notes

Core claim

The paper's core claim is Equation (9): the mean-squared error between expected labels and the variational circuit's output state is expanded by writing the output state as Q applied to the input, with Q a parameterized operator whose entries are hyperbolic functions. This produces a cost that is quadratic in binary variables that select discretized angle values, so minimizing it becomes a QUBO problem solvable by an annealer. To make this concrete, the paper replaces the imaginary phase iθ in each rotation with a real angle θ—explicitly breaking unitarity—then expands products of cosh and sinh into sums of exponentials, discretizes each angle with a one-hot constraint, and wraps the QUBO in

Load-bearing premise

The QUBO objective is built from a simplified, non-unitary version of the circuit, replacing the complex phase iθ with a real angle θ; if the best angles under that simplified objective are not also good under the real circuit, the central mapping collapses.

Editorial extensions

If this is right

  • VQA training no longer needs gradients or a classical optimizer; the same QUBO construction can be reused for any ansatz whose operator can be represented in the required hyperbolic form.
  • Because the annealer performs the parameter search, training becomes insensitive to gradient noise and could continue where barren-plateau effects stop gradient descent.
  • Reported training time scales sublinearly with dataset size, so the method's relative advantage should grow as datasets grow.
  • The recursive scheme replaces one large, hardware-hungry QUBO with a sequence of small ones, easing qubit-count requirements at the price of more annealing runs.
  • The tunable parameters—levels, partitions, and validation points—give users a direct accuracy-versus-time control that classical optimizers do not offer.

Reading between the lines

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

  • Editorial inference: the unitarity-breaking substitution (iθ replaced by θ) changes not just the circuit but the loss landscape; a small-circuit comparison between the QUBO surrogate's optimum and the true unitary circuit's optimum would show whether reported accuracy gains come from the annealing search or from the surrogate being easier to minimize.
  • Editorial inference: the hyperbolic expansion makes QUBO entries grow exponentially with angle values, so the recursive range-shrinking step may be doing double duty—both refining precision and preventing runaway surrogate terms; testing the model with a fixed wide range across levels would separate the two effects.
  • Editorial inference: the same construction could be applied to problem-specific Hamiltonians, such as QAOA or chemistry ansätze, where diagonalization structure is known, which is a natural next step the paper does not experimentally cover.
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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

3 major / 5 minor

Summary. The paper proposes to train variational quantum algorithms (VQAs) by mapping the parameter optimization problem to a Quadratic Unconstrained Binary Optimization (QUBO) problem and solving it on a quantum annealer. The method defines a state-vector mean-squared-error loss, expresses the ansatz output as |φ> = Q(θ)|ψ>, and derives a formal quadratic expression in the operator matrix elements (Eq. 9). To make this expression QUBO-encodable, the paper replaces imaginary phases iθ with real angles, rewrites trigonometric functions as hyperbolic functions, and expands products of cosh into sums of exponentials. A recursive hierarchical search partitions the parameter space, uses the annealer on the QUBO, and validates the selected parameters by executing the actual VQA circuit. Experiments on Iris, Heart Disease, and Diabetes compare accuracy and runtime against classical optimizers (ADAM, COBYLA, SPSA) and an evolutionary algorithm, reporting favorable accuracy and reduced training time for the adiabatic approach.

Significance. If the reduction were mathematically sound, the idea of training a VQA by annealing a QUBO would be a genuinely interesting and potentially useful contribution to gradient-free variational optimization. The paper is also commendable for releasing public code, for the large parameter sweep in Appendix D, and for explicitly acknowledging in Appendix A that the iθ→θ substitution breaks unitarity. However, the central claim of the paper — that VQA training is mapped to QUBO minimization — is not established. The substitution changes the operator whose parameters the QUBO minimizes, and the exponential expansion in Eq. 12 is not turned into a quadratic binary polynomial. Because these two issues sit at the core of the method, the experimental results, while detailed, cannot validate the claimed equivalence.

major comments (3)
  1. [Section 3.1.2 and Appendix A] The QUBO objective is built from a non-unitary stand-in for the ansatz. Appendix A states: 'we apply a heuristic simplification that replaces the imaginary phase iθ with a real-valued angle θ. Although this substitution breaks unitarity.' This changes cos(θ/2) to cosh(θ/2) and similarly distorts sine terms. The actual VQA output is Q(θ)|ψ>, but the QUBO in Eq. 9 (as implemented) minimizes ∥|ψ> − Q̃(θ)|ψ>∥² with Q̃ the hyperbolic operator. Minimizing this does not generally minimize the true VQA loss: cos and cosh have opposite curvature at 0 and qualitatively different growth for large θ. No theorem, bound, or numerical comparison of the two landscapes is provided, and the experiments validate only the final circuit accuracy, not the QUBO objective's fidelity. This breaks the central equivalence claimed in the sentence after Eq. 9.
  2. [Section 3.1.2, Eq. 12] The expansion in Eq. 12 produces a sum of exponentials of the form exp(Σ_i (2b_i−1)x_i). Such expressions are not quadratic polynomials in the binary variables b_i; they are exponential functions. The paper states that they 'can be incorporated into a QUBO formulation,' but it does not provide a transformation to a finite quadratic form xᵀQx. Without an explicit encoding — e.g., a polynomial approximation with controlled error, auxiliary variables, or a derived QUBO matrix — the claim that the training task is a QUBO is unsupported. This is a load-bearing gap, not a technical detail.
  3. [Section 3.1.2, 'Generalization of the quantum operator expression'] The claimed generalizability to arbitrary Hamiltonians rests on 'if the ansatz operator is Hermitian, or can be symmetrized or approximated as such.' A general parameterized VQA circuit is unitary but not Hermitian; replacing it by a Hermitian or symmetrized operator is an additional approximation whose effect on the loss is not analyzed. The text gives no constructive procedure for performing this approximation for the TwoLocal or other standard ansätze, and any such approximation can reintroduce the non-unitarity problem from Appendix A. Thus the abstract's 'generalizable to arbitrary Hamiltonians' is not justified.
minor comments (5)
  1. [Section 3.2, Algorithm 2] The stopping criterion 'accuracy drop < τ' is not precisely defined. Does it compare the current level's best accuracy to the previous level's, or to the global best? The caption says 'current and best accuracy,' but the pseudocode does not specify how the drop is computed or what default τ is used.
  2. [Section 4.4 and Appendix B] The text uses both 'Lowest energy solution' and 'Accuracy' for the same selected parameters. Since the QUBO energy and the true VQA accuracy are different quantities, the reader needs to know which quantity selects the parameter configuration reported. The distinction is important for interpreting the recursive search.
  3. [Section 4.2, Figure 2] The figure comparing ADAM, COBYLA, and SPSA has no axis labels and no error bars. It would be clearer to report mean and standard deviation over the repeated runs, given that later tables average over runs.
  4. [Appendix A, Eq. A1–A2] The matrices A1 and A2 are hard to read because of missing delimiters and inconsistent typesetting. The exponential form in A2 is shown only for the first two columns, which makes the relation to the full matrix difficult to verify.
  5. [Section 4.5] The runtime comparison in Figure 5 is reported for different dataset sizes, but the classical and evolutionary baselines use fixed iteration budgets (100 iterations and 10 generations). Without scaling the baseline budgets or reporting convergence curves, the 'sublinear scaling' claim for the adiabatic method is not a controlled comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the QUBO objective is a direct reformulation of the training loss (under an admitted approximation), and the recursive search is validated against true VQA accuracy; the self-citation is background, not load-bearing.

full rationale

The paper's central derivation (Sec. 3.1) constructs the QUBO objective in Eq. 9 by substituting the ansatz operator into the MSE loss of Eq. 1. This is a mathematical reformulation, not a prediction derived from an input that already contains the result. The subsequent hyperbolic substitution (Appendix A) is explicitly admitted to break unitarity ('this substitution breaks unitarity'), so minimizing Eq. 9 is not shown to minimize the true VQA loss; however, that is an approximation/correctness concern, not circularity, because the paper does not define the true loss in terms of the QUBO or fit the QUBO to validation outcomes. The recursive search (Alg. 2) selects parameters by executing the actual VQA and measuring accuracy, so the final evaluation is independent of the QUBO energy. The only self-citation ([19], [20]) is used as prior work and motivation; the QUBO formulation is re-derived in this paper and the new contribution (recursive refinement, generalization, experiments) is tested against classical and evolutionary baselines. No step reduces by construction to its own inputs.

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

The central claim depends on a non-unitary heuristic approximation and an unproven QUBO encoding step, both introduced ad hoc. The algorithm's hyperparameters (d, w, L, rescaling factor, threshold) are set by exhaustive search over configurations, not derived from the problem structure.

free parameters (5)
  • d (partitions per angle) = varied 1-6 across runs (e.g., 2, 3, 4 in Tables D1-D3)
    Controls search discretization; different optimal values per dataset; no principled selection method given.
  • w (validation points per segment) = varied 1-6 (e.g., 1, 2, 3, 4, 5, 6 in Table D3)
    Controls the number of evaluations per level; best setting depends on the dataset.
  • L (maximum search levels) = varied 1-4 in Appendix D
    Controls recursion depth; accuracy gains saturate with depth (Fig. 6).
  • angle range rescaling factor = 0.5 in Appendix B example
    Hand-chosen; no sensitivity study provided.
  • accuracy threshold tau = Not specified numerically
    Used in Algorithm 2 to stop recursion; no value or selection criterion is given.
assumptions (5)
  • standard math Spectral Theorem
    Used in Sec 3.1.2 to claim that Hermitian ansatz operators admit a diagonal form simplifying QUBO construction.
  • ad hoc to paper Ansatz operator can be symmetrized or approximated as Hermitian
    Sec 3.1.2, Generalization paragraph: 'if the ansatz operator is Hermitian, or can be symmetrized or approximated as such'. This is an assumption about the ansatz that is not justified for the TwoLocal circuit used in experiments.
  • ad hoc to paper Replacement of iθ by θ in the ansatz matrix elements
    Appendix A: 'we apply a heuristic simplification that replaces the imaginary phase iθ with a real-valued angle θ. Although this substitution breaks unitarity...'. This is the key modeling assumption that changes the optimization objective.
  • ad hoc to paper Exponential sums over binary variables can be encoded as QUBO terms
    Sec 3.1.2: after Eq. 12, 'The resulting expression consists of sums of exponential terms that can be incorporated into a QUBO formulation'. No algebraic construction or coefficient matrix is given.
  • domain assumption Labels are representable as quantum state vectors
    Sec 3.1.1: the expected output |ψ> is 'derived from the label in the dataset'. This assumes a state encoding for labels exists and is fixed.

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Cite this review

Pith. "Pith review of QUBO-based training for VQAs on Quantum Annealers." pith.science (2026). https://pith.science/paper/LQMAXXOS

@misc{pith2026250901821,
  author       = {Pith},
  title        = {Pith review of: QUBO-based training for VQAs on Quantum Annealers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LQMAXXOS}},
  note         = {Machine review of arXiv:2509.01821}
}
read the original abstract

Quantum annealers provide an effective framework for solving large-scale combinatorial optimization problems. This work presents a novel methodology for training Variational Quantum Algorithms (VQAs) by reformulating the parameter optimization task as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Unlike traditional gradient-based methods, our approach directly leverages the Hamiltonian of the chosen VQA ansatz and employs an adaptive, metaheuristic optimization scheme. This optimization strategy provides a rich set of configurable parameters which enables the adaptation to specific problem characteristics and available computational resources. The proposed framework is generalizable to arbitrary Hamiltonians and integrates a recursive refinement strategy to progressively approximate high-quality solutions. Experimental evaluations demonstrate the feasibility of the method and its ability to significantly reduce computational overhead compared to classical and evolutionary optimizers, while achieving comparable or superior solution quality. These findings suggest that quantum annealers can serve as a scalable alternative to classical optimizers for VQA training, particularly in scenarios affected by barren plateaus and noisy gradient estimates, and open new possibilities for hybrid quantum gate - quantum annealing - classical optimization models in near-term quantum computing.

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Reference graph

Works this paper leans on

35 extracted references · 21 canonical work pages

  1. [1]

    Quantum Information Processing 23(1), 44 (2024) https://doi.org/10.1007/s11128-024-04438-2

    Cerezo, M., Arrasmith, A., Babbush, R., Benedetti, M., Cao, Y., Cincio, L., Head-Marsden, K., Larocca, M., Ostaszewski, M., Romero, J., Sim, S., Suba¸ sı, Y., Sze, K., Wang, L., Coles, P.J.: Variational quantum algorithms: Fundamental concepts, applications and challenges. Quantum Information Processing 23(1), 44 (2024) https://doi.org/10.1007/s11128-024-04438-2

    doi:10.1007/s11128-024-04438-2 2024

  2. [2]

    Limitations of optimization algorithms on noisy quantum devices

    Fran¸ ca, D.S., Garc ´ ıa-Patr´ on, R.: Limitations of optimization algorithms on noisy quantum devices. Nature Physics 18, 775–781 (2022) https://doi.org/10.1038/ s41567-022-01536-8 arXiv:2009.05532 [quant-ph]

    work page Pith review arXiv 2022

  3. [3]

    arXiv preprint arXiv:2111.13454 (2021)

    Bonet-Monroig, X., Finkel, F., Lizuain, I., Luis, A., Latorre, J.I.: Performance comparison of optimization methods on variational quantum algorithms. arXiv preprint arXiv:2111.13454 (2021)

    arXiv 2021

  4. [4]

    Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4

    McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9(1), 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4

    doi:10.1038/s41467-018-07090-4 2018

  5. [5]

    Nature communications 12(1), 6961 (2021)

    Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature communications 12(1), 6961 (2021)

    2021

  6. [6]

    Quantum Machine Intelligence 3(1), 5 (2021) https://doi.org/10.1007/s42484-021-00038-4 18

    Skolik, A., Jerbi, S., Elben, A., Seif, A., Dunjko, V., Briegel, H.J.: Layerwise learning for quantum neural networks. Quantum Machine Intelligence 3(1), 5 (2021) https://doi.org/10.1007/s42484-021-00038-4 18

    work page doi:10.1007/s42484-021-00038-4 2021

  7. [7]

    Physical Review A 98(6), 062324 (2018) https://doi.org/10.1103/PhysRevA.98

    Liu, J.-G., Wang, L.: Differentiable learning of quantum circuit born machines. Physical Review A 98(6), 062324 (2018) https://doi.org/10.1103/PhysRevA.98. 062324

    doi:10.1103/physreva.98 2018

  8. [8]

    Quantum 4, 269 (2020) https://doi.org/10.22331/q-2020-05-25-269

    Stokes, J., Izaac, J., Killoran, N., Carleo, G.: Quantum natural gradient. Quantum 4, 269 (2020) https://doi.org/10.22331/q-2020-05-25-269

    doi:10.22331/q-2020-05-25-269 2020

Show all 35 references
  1. [9]

    International Jour- nal of Quantum Information 12(1), 2041–2050 (2014) https://doi.org/10.1142/ S021974991450047X

    Schuld, M., Sinayskiy, I., Petruccione, F.: Parameterized quantum circuits for quantum state generation and variational algorithms. International Jour- nal of Quantum Information 12(1), 2041–2050 (2014) https://doi.org/10.1142/ S021974991450047X

  2. [10]

    Quantum 3, 149 (2019) https://doi

    Schuld, M., Schwab, P., Petruccione, F.: Gradient-free optimization of quantum circuits for variational quantum algorithms. Quantum 3, 149 (2019) https://doi. org/10.22331/q-2019-09-26-149

    2019 doi

  3. [11]

    The Computer Journal 13(3), 317–322 (1970) https://doi.org/10.1093/comjnl/13.3.317

    Fletcher, R.: A new approach to variable metric algorithms. The Computer Journal 13(3), 317–322 (1970) https://doi.org/10.1093/comjnl/13.3.317

    1970 doi

  4. [12]

    Mathematics of Computation 24(111), 647–656 (1970) https://doi.org/10.1090/ S0025-5718-1970-0274029-X

    Shanno, D.F.: Conditioning of quasi-newton methods for function minimization. Mathematics of Computation 24(111), 647–656 (1970) https://doi.org/10.1090/ S0025-5718-1970-0274029-X

    1970

  5. [13]

    CoRR (2022) https://doi.org/10.48550/arXiv.2202.01389

    Lockwood, O.: An empirical review of optimization techniques for quantum variational circuits. CoRR (2022) https://doi.org/10.48550/arXiv.2202.01389

    2022 doi arXiv

  6. [14]

    Naval Research Logistics Quarterly 3(1-2), 95–110 (1956) https://doi.org/10.1002/nav

    Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Research Logistics Quarterly 3(1-2), 95–110 (1956) https://doi.org/10.1002/nav. 3800030110

    1956 doi

  7. [15]

    SoftwareX 26, 101756 (2024) https://doi.org/10.1016/j.softx.2024.101756

    Acampora, G., Cano Guti´ errez, C., Chiatto, A., Soto Hidalgo, J.M., Vitiello, A.: Evovaq: Evolutionary algorithms-based toolbox for variational quantum circuits. SoftwareX 26, 101756 (2024) https://doi.org/10.1016/j.softx.2024.101756

    2024

  8. [16]

    Scientific Reports 11(1), 10029 (2021) https://doi.org/10.1038/ s41598-021-89461-4

    Date, P., Arthur, D., Pusey-Nazzaro, L.: QUBO formulations for training machine learning models. Scientific Reports 11(1), 10029 (2021) https://doi.org/10.1038/ s41598-021-89461-4

    2021

  9. [17]

    Frontiers in Artificial Intelligence 7 (2024) https: //doi.org/10.3389/frai.2024.1368569

    Abel, S., Criado, J.C., Spannowsky, M.: Training neural networks with universal adiabatic quantum computing. Frontiers in Artificial Intelligence 7 (2024) https: //doi.org/10.3389/frai.2024.1368569

    2024

  10. [18]

    In: NeurIPS 2024 Workshop Machine Learn- ing with New Compute Paradigms (2024)

    Pramanik, S., Goswami, K., Chatterjee, S., Chandra, M.G.: Training machine learning models with ising machines. In: NeurIPS 2024 Workshop Machine Learn- ing with New Compute Paradigms (2024). https://openreview.net/forum?id= Du5geIL4rM 19

    2024

  11. [19]

    https://arxiv.org/abs/2410.18618

    Acosta, E., Gutierrez, C.C., Botella, G., Campos, R.: Adiabatic training for Variational Quantum Algorithms (2024). https://arxiv.org/abs/2410.18618

    2024 arXiv

  12. [20]

    Conference held at the University of Melbourne, Melbourne, Australia

    8th International Conference on Quantum Techniques in Machine Learning (QTML 2024). Conference held at the University of Melbourne, Melbourne, Australia. https://qtml.org/ (2024)

    2024

  13. [21]

    Johns Hopkins University Press, Baltimore, MD (2013)

    Golub, G.H., Loan, C.F.V.: Matrix Computations, 4th edn. Johns Hopkins University Press, Baltimore, MD (2013)

    2013

  14. [22]

    Cambridge University Press, Cambridge, UK (2010)

    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Informa- tion, 10th anniversary edition edn. Cambridge University Press, Cambridge, UK (2010)

    2010

  15. [23]

    ACM Computing Surveys 54(2), 1–36 (2021) https://doi.org/10.1145/3388460

    Valejo, A., Ferreira, V.C., Fabbri, R., Oliveira, M.C.F., Andrade Lopes, A.: A critical survey of the multilevel method in complex networks. ACM Computing Surveys 54(2), 1–36 (2021) https://doi.org/10.1145/3388460

    2021 doi

  16. [24]

    Lulu, Durham, NC, USA (2013)

    Luke, S.: Essentials of Metaheuristics, 2nd edn. Lulu, Durham, NC, USA (2013). Available online at http://cs.gmu.edu/ ∼sean/book/metaheuristics/

    2013

  17. [25]

    Computers & Opera- tions Research 24(11), 1097–1100 (1997) https://doi.org/10.1016/S0305-0548(97) 00031-2

    Mladenovi´ c, N., Hansen, P.: Variable neighborhood search. Computers & Opera- tions Research 24(11), 1097–1100 (1997) https://doi.org/10.1016/S0305-0548(97) 00031-2

    1997 doi

  18. [26]

    American Jour- nal of Cardiology 64(5), 304–310 (1989) https://doi.org/10.1016/0002-9149(89) 90524-9

    Detrano, R., J´ anose, A., Steinbrunn, W., Pfisterer, M., Schmid, J.J., Sandhu, S., Guppy, K.H., Lee, S., Froelicher, V.: International application of a new probability algorithm for the diagnosis of coronary artery disease. American Jour- nal of Cardiology 64(5), 304–310 (198...

    1989 doi

  19. [27]

    In: Proceedings of the 12th Symposium on Computer Applications and Medical Care, pp

    Smith, J.W., Everhart, J.E., Dickson, W.C., Knowler, W.C., Johannes, R.S.: Using the adap learning algorithm to forecast the onset of diabetes mellitus. In: Proceedings of the 12th Symposium on Computer Applications and Medical Care, pp. 261–265. IEEE Computer Society, Orlando...

    1988

  20. [28]

    International Conference on Learning Representations (ICLR) (2015) arXiv:1412.6980 [cs.LG]

    Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. International Conference on Learning Representations (ICLR) (2015) arXiv:1412.6980 [cs.LG]

    2015 arXiv

  21. [29]

    IEEE Transactions on Automatic Control 37(3), 332–341 (1992) https://doi.org/10.1109/9.119632

    Spall, J.C.: Multivariate stochastic approximation using a simultaneous pertur- bation gradient approximation. IEEE Transactions on Automatic Control 37(3), 332–341 (1992) https://doi.org/10.1109/9.119632

    1992 doi

  22. [30]

    (eds.) A Direct Search Optimiza- tion Method That Models the Objective and Constraint Functions by Linear Interpolation, pp

    Powell, M.J.D.: In: Gomez, S., Hennart, J.-P. (eds.) A Direct Search Optimiza- tion Method That Models the Objective and Constraint Functions by Linear Interpolation, pp. 51–67. Springer, Dordrecht (1994). https://doi.org/10.1007/ 978-94-015-8330-5 4 . https://doi.org/10.1007/...

    1994 doi

  23. [31]

    Nature 549, 242–246 (2017) https://doi.org/ 10.1038/nature23879 arXiv:1704.05018 [quant-ph]

    Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017) https://doi.org/ 10.1038/nature23879 arXiv:1704.05018 [quant-ph]

    2017 arXiv

  24. [32]

    Technical Report 826, California Institute of Technology (1989)

    Moscato, P.: On evolution, search, optimization, genetic algorithms and martial arts: Towards memetic algorithms. Technical Report 826, California Institute of Technology (1989)

    1989

  25. [33]

    https://arxiv

    Bagaev, D.S., Gavreev, M.A., Mastiukova, A.S., Fedorov, A.K., Nemkov, N.A.: Regularizing quantum loss landscapes by noise injection (2025). https://arxiv. org/abs/2505.08759

    2025 arXiv

  26. [34]

    arXiv preprint arXiv:2402.08475 (2024)

    Kashif, M., Shafique, M.: HQNET: Harnessing quantum noise for effective train- ing of quantum neural networks in NISQ era. arXiv preprint arXiv:2402.08475 (2024). Version 3, last revised 15 Aug 2024 21 Appendix A Quantum Operator representation example A simple circuit of two ...

    2024 arXiv

  27. [35]

    (f) Training Level 2, execution 16

    (d) Training Level 1, execution 4. (f) Training Level 2, execution 16. (g) Training Level 3, execution 9. Based on circuit defined in Appendix A, composed by 2 qubits and 2 rotational gates (ie. 2 parameterizable angles: θ0, θ1), let us define the model metaheuristics paramete...

    2024

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