pith. sign in

arxiv: 2605.18539 · v1 · pith:BRO4PYQPnew · submitted 2026-05-18 · 🪐 quant-ph

The QuaST Decision Tree: Achieving Automation With Data-Based Recommendations

Benedikt Poggel , Lena Tokuhiro , Georg Kruse , Jeanette Miriam Lorenz This is my paper

Pith reviewed 2026-05-20 10:31 UTC · model grok-4.3

classification 🪐 quant-ph
keywords QuaST Decision Treehybrid quantum algorithmsvariational algorithmsscalability analysisproblem classificationquantum software stackautomationalgorithm selection
0
0 comments X

The pith

The QuaST Decision Tree automates hybrid quantum algorithm selection through modular nodes that classify problem instances for variational feasibility via scalability analysis.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents the QuaST Decision Tree as a modular network that connects decisions on problem modeling, encoding, algorithm choice, and tuning to help users build effective hybrid classical-quantum solutions. It fills a gap in the quantum software stack by turning separate recommendation tools into one configurable system usable in industry solvers, HPC environments, or rapid development. Automation comes from individual modules, one of which performs a scalability analysis to classify whether variational algorithms are feasible for given problem instances. This classification reduces trial-and-error runs, improves overall solution performance, and allows better use of available quantum hardware.

Core claim

The QuaST Decision Tree delivers automation through its modular network structure of flexible computation nodes with data-based recommendations, and one such module judges the feasibility of variational algorithms by applying a robust scalability analysis together with classification of problem instances, which in turn improves end-to-end hybrid solutions and quantum device utilization.

What carries the argument

The QuaST Decision Tree, a modular network of computation nodes that supplies recommendations for preprocessing, algorithm selection, and hyperparameter choices.

If this is right

  • End-to-end hybrid solutions achieve higher performance with less manual tuning.
  • Expensive trial-and-error testing of quantum algorithms is reduced.
  • Quantum devices see improved utilization because only feasible algorithms are selected.
  • The framework can be reconfigured without code changes for industrial, HPC, or prototyping settings.
  • The benefit of the hybrid quantum approach becomes clearer to end users through automated guidance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same modular structure could be extended to recommend non-variational quantum algorithms once suitable scalability metrics are defined.
  • Integration with existing quantum programming libraries would let the decision tree act as an automatic front-end for current hardware.
  • Data collected from repeated classifications might reveal new patterns that refine future feasibility boundaries.
  • The approach could be tested on classical optimization benchmarks to see whether the same classification logic transfers outside quantum settings.

Load-bearing premise

The scalability analysis is robust and the classification of problem instances correctly identifies when variational algorithms will be feasible for practical cases.

What would settle it

A test case in which the module classifies a problem instance as suitable for a variational algorithm yet the algorithm fails to deliver the predicted scaling or performance benefit on real hardware.

Figures

Figures reproduced from arXiv: 2605.18539 by Benedikt Poggel, Georg Kruse, Jeanette Miriam Lorenz, Lena Tokuhiro.

Figure 1
Figure 1. Figure 1: Components of the quast-decisiontree package. core contains the framework, the DecisionTree base class and its building blocks. nodes provides a basic instance covering steps from problem loading to algorithm execution. algorithms and problems define templates for algorithms and problem classes, respectively. The core part comprises the following components, each realized as Python classes: • DecisionTree … view at source ↗
Figure 2
Figure 2. Figure 2: The algorithm selection part of a basic DecisionTree instance. Based on the selected algorithms, different choices follow: the definition of an ansatz (e.g., variational quantum eigensolver [49]), a depth and mixer (QAOA [23]), or skipping for a direct solver setup. Multiple nodes take part in the hyperparameter definitions. In the VQA case, the paths converge for the optimizer selection, which is not requ… view at source ↗
read the original abstract

Quantum computers are increasingly powerful. Software tools for the development of quantum-enhanced algorithms are maturing. However, the software stack still lacks the connection to applications that would enable hybrid algorithms combining classical and quantum computing steps. End users need to be assisted in choosing the best combination of preprocessing, postprocessing, classical and quantum algorithms options. The application-facing software stack is therefore required to cover problem modeling, encoding, algorithm selection and hyperparameter tuning. A variety of tools exist for specific recommendations. The QuaST Decision Tree reflects the complexity in combining individual decisions in its modular network structure, consisting of flexible computation nodes with modular recommendations. It can easily be configured to serve in an industrial solver, an HPC software stack, or for rapid prototyping in development. The key ingredient, automation, is delivered by modules. We present one such module judging the feasibility of variational algorithms based on a robust scalability analysis and classification of problem instances. The automation improves the performance of end-to-end solutions, highlights the benefit to be gained from the hybrid quantum solution, reduces expensive trial-and-error testing, and leads to an improved utilization of quantum devices for a practical benefit.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces the QuaST Decision Tree as a modular network structure for automating decisions in hybrid classical-quantum algorithm pipelines, covering problem modeling, encoding, algorithm selection, and hyperparameter tuning. A central module is presented that judges the feasibility of variational algorithms through a scalability analysis and classification of problem instances, with the goal of improving end-to-end performance, reducing trial-and-error, and enhancing quantum device utilization in industrial, HPC, or prototyping contexts.

Significance. If the scalability analysis and classification module can be shown to rest on explicit, externally validated criteria, the framework would address a genuine gap in application-facing quantum software by delivering data-driven automation. The modular design is a strength that could support flexible deployment, but the current description provides no quantitative validation results, scaling laws, or benchmark comparisons to establish practical impact.

major comments (1)
  1. [Abstract / Module description] Abstract and module description: the claim that the module performs a 'robust scalability analysis and classification of problem instances' to judge variational algorithm feasibility is load-bearing for the automation contribution, yet the text supplies no feature set, distance metric, decision boundary, noise model, or quantitative scaling law. Without these elements the mapping from instance properties to a feasibility verdict remains an internal modeling choice rather than a derived or tested result.
minor comments (1)
  1. [Abstract] The abstract refers to 'a variety of tools' for specific recommendations without citations; adding references would clarify the positioning of QuaST relative to existing work.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for highlighting the importance of substantiating the central module's claims. We address the major comment below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Abstract / Module description] Abstract and module description: the claim that the module performs a 'robust scalability analysis and classification of problem instances' to judge variational algorithm feasibility is load-bearing for the automation contribution, yet the text supplies no feature set, distance metric, decision boundary, noise model, or quantitative scaling law. Without these elements the mapping from instance properties to a feasibility verdict remains an internal modeling choice rather than a derived or tested result.

    Authors: We agree that the current manuscript text does not supply the explicit technical elements (feature set, distance metric, decision boundary, noise model, or quantitative scaling law) needed to fully support the robustness claim for the scalability analysis and classification module. This module is indeed central to the automation contribution. In the revised version we will add a dedicated subsection that defines the feature set extracted from problem instances, specifies the distance metric for similarity assessment, describes how decision boundaries are obtained from data-driven classification, incorporates the noise model used in the scalability analysis, and reports the quantitative scaling laws observed across benchmarked problem sizes. We will also include validation results that compare the module's feasibility predictions against measured performance on both simulators and quantum hardware. These additions will make clear that the verdicts are derived from tested, externally grounded criteria rather than purely internal modeling choices. revision: yes

Circularity Check

0 steps flagged

No circularity: descriptive framework for quantum decision automation

full rationale

The paper describes a modular decision tree (QuaST) for assisting end users in selecting hybrid quantum-classical algorithm components, with one module performing feasibility judgment for variational algorithms via scalability analysis and instance classification. No equations, fitted parameters presented as predictions, self-citations, or uniqueness theorems appear in the provided text that would reduce any central claim to its own inputs by construction. The automation benefit is stated as an outcome of the modular structure rather than derived from a self-referential loop or renamed empirical pattern. The derivation chain is therefore self-contained as an engineering description without load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Limited details available from abstract; the tool introduces a new structure but relies on assumptions about the effectiveness of its modules.

axioms (1)
  • domain assumption The scalability analysis provides a reliable measure of variational algorithm feasibility
    Invoked in the description of the module for judging feasibility.
invented entities (1)
  • QuaST Decision Tree no independent evidence
    purpose: Modular network for automated recommendations in quantum algorithm development
    The main contribution presented in the abstract.

pith-pipeline@v0.9.0 · 5733 in / 1363 out tokens · 70196 ms · 2026-05-20T10:31:35.079000+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

53 extracted references · 53 canonical work pages · 1 internal anchor

  1. [1]

    Research trends in combinatorial optimization,

    J. M. Weinand, K. Sörensen, P. San Segundo, M. Kleinebrahm, and R. McKenna, “Research trends in combinatorial optimization,”International Transactions in Operational Research, vol. 29, no. 2, pp. 667–705, 2022

    work page 2022

  2. [2]

    Reinforcement learning for combinatorial optimiza- tion: A survey,

    N. Mazyavkina, S. Sviridov, S. Ivanov, and E. Burnaev, “Reinforcement learning for combinatorial optimiza- tion: A survey,”Computers & Operations Research, vol. 134, p. 105 400, 2021

    work page 2021

  3. [3]

    Challenges and opportunities in quan- tum optimization,

    A. Abbas et al., “Challenges and opportunities in quan- tum optimization,”Nature Reviews Physics, vol. 6, no. 12, pp. 718–735, 2024

    work page 2024

  4. [4]

    Strengths and Weaknesses of Quantum Com- puting,

    C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazi- rani, “Strengths and Weaknesses of Quantum Com- puting,”SIAM Journal on Computing, vol. 26, no. 5, pp. 1510–1523, 1997

    work page 1997

  5. [5]

    Variational quantum algorithms,

    M. Cerezo et al., “Variational quantum algorithms,” Nature Reviews Physics, vol. 3, no. 9, pp. 625–644, 2021

    work page 2021

  6. [6]

    Quantum speedup of branch-and-bound algorithms,

    A. Montanaro, “Quantum speedup of branch-and-bound algorithms,”Phys. Rev. Res., vol. 2, no. 1, p. 013 056, 2020

    work page 2020

  7. [7]

    doi:10.48550/arxiv.2406.14792 , author =

    R. Seidel et al.,Qrisp: A Framework for Compil- able High-Level Programming of Gate-Based Quantum Computers, arXiv: 2406.14792, 2024

    work page arXiv 2024

  8. [8]

    Qiskit contributors,Qiskit: An Open-source Framework for Quantum Computing, Zenodo: 2573505, 2023

    work page 2023

  9. [9]

    OpenQASM 3: A Broader and Deeper Quantum Assembly Language,

    A. Cross et al., “OpenQASM 3: A Broader and Deeper Quantum Assembly Language,”ACM Transactions on Quantum Computing, vol. 3, no. 3, 12:1–12:50, 2022

    work page 2022

  10. [10]

    [Online]

    QIR Alliance,QIR Specification, 2021. [Online]. Avail- able: https://github.com/qir-alliance/qir-spec

    work page 2021

  11. [11]

    MQT Predictor: Automatic Device Selection with Device- Specific Circuit Compilation for Quantum Computing,

    N. Quetschlich, L. Burgholzer, and R. Wille, “MQT Predictor: Automatic Device Selection with Device- Specific Circuit Compilation for Quantum Computing,” ACM Transactions on Quantum Computing, vol. 6, no. 1, 2025

    work page 2025

  12. [12]

    Coelho, G

    R. Coelho, G. Kruse, and J. M. Lorenz,QAOA- Predictor: Forecasting Success Probabilities and Mini- mal Depths for Efficient Fixed-Parameter Optimization, arXiv:2603.02990 [quant-ph], 2026

    work page arXiv 2026

  13. [13]

    An Abstraction Hierarchy Toward Productive Quantum Programming,

    O. Di Matteo, S. Núñez-Corrales, M. St˛ echły, S. P. Reinhardt, and T. Mattson, “An Abstraction Hierarchy Toward Productive Quantum Programming,” in2024 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 01, 2024, pp. 979–989. [14]Iskay Quantum Optimizer – A Qiskit Function by Kipu Quantum. [Online]. Available: https://quantum....

    work page 2024

  14. [14]

    Poggel, X

    B. Poggel, X. Runge, A. Bärligea, and J. M. Lorenz, Creating Automated Quantum-Assisted Solutions for Optimization Problems, arXiv: 2409.20496, 2024

    work page arXiv 2024

  15. [15]

    Scala- bility challenges in variational quantum optimization under stochastic noise,

    A. Bärligea, B. Poggel, and J. M. Lorenz, “Scala- bility challenges in variational quantum optimization under stochastic noise,”Phys. Rev. A, vol. 112, no. 3, p. 032 407, 2025

    work page 2025

  16. [16]

    Van Rossum and F

    G. Van Rossum and F. L. Drake,Python 3 Reference Manual. CreateSpace, 2009

    work page 2009

  17. [17]

    Ising formulations of many NP problems,

    A. Lucas, “Ising formulations of many NP problems,” Frontiers in Physics, vol. 2, 2014

    work page 2014

  18. [18]

    Efficient Encodings of the Trav- elling Salesperson Problem for Variational Quantum Algorithms,

    M. Schnaus et al., “Efficient Encodings of the Trav- elling Salesperson Problem for Variational Quantum Algorithms,” in2024 IEEE International Conference on Quantum Software (QSW), 2024, pp. 81–87

    work page 2024

  19. [19]

    Highly efficient encoding for job-shop scheduling problems and its application on quantum computers,

    M. Schmid, S. Braun, R. Sollacher, and M. J. Hart- man, “Highly efficient encoding for job-shop scheduling problems and its application on quantum computers,” Quantum Science and Technology, vol. 10, no. 1, p. 015 051, 2025

    work page 2025

  20. [20]

    A Fast Quantum Mechanical Algorithm for Database Search,

    L. K. Grover, “A Fast Quantum Mechanical Algorithm for Database Search,” inProceedings of the Twenty- Eighth Annual ACM Symposium on Theory of Comput- ing, 1996, pp. 212–219

    work page 1996

  21. [21]

    A Quantum Approximate Optimization Algorithm

    E. Farhi, J. Goldstone, and S. Gutmann, “A quantum approximate optimization algorithm,”arXiv preprint arXiv:1411.4028, 2014

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  22. [22]

    A review on Quantum Approximate Optimization Algorithm and its variants,

    K. Blekos et al., “A review on Quantum Approximate Optimization Algorithm and its variants,”Physics Re- ports, vol. 1068, pp. 1–66, 2024

    work page 2024

  23. [23]

    Barren plateaus in quantum neural network training landscapes,

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

    work page 2018

  24. [24]

    E. R. Anschuetz and B. T. Kiani,Beyond Bar- ren Plateaus: Quantum Variational Algorithms Are Swamped With Traps, arXiv: 2205.05786, 2022

    work page arXiv 2022

  25. [25]

    [Online]

    IBM Quantum,IBM Quantum Roadmap. [Online]. Available: https://www.ibm.com/quantum/hardware# roadmap [28]IonQ | Roadmap. [Online]. Available: https://www.ionq. com/roadmap [29]Roadmap – IQM Quantum Computers, 2025. [Online]. Available: https://meetiqm.com/technology/roadmap/

    work page 2025

  26. [26]

    Grover Adaptive Search for Constrained Polynomial Binary Optimization,

    A. Gilliam, S. Woerner, and C. Gonciulea, “Grover Adaptive Search for Constrained Polynomial Binary Optimization,”Quantum, vol. 5, p. 428, 2021. [31]The Advantage™ Quantum Computer | D-Wave. [On- line]. Available: https://www.dwavesys.com/solutions- and-products/systems/ [32]Functions | IBM Quantum Platform. [Online]. Avail- able: https://quantum.cloud.ib...

    work page 2021

  27. [27]

    Towards Higher- Level Abstractions for Quantum Computing,

    A. Cobb, J.-G. Schneider, and K. Lee, “Towards Higher- Level Abstractions for Quantum Computing,” inPro- ceedings of the 2022 Australasian Computer Science Week, 2022, pp. 115–124. 11

    work page 2022

  28. [28]

    Towards Higher Abstraction Levels in Quantum Computing,

    H. Fürntratt, P. Schnabl, F. Krebs, R. Unterberger, and H. Zeiner, “Towards Higher Abstraction Levels in Quantum Computing,” inService-Oriented Computing – ICSOC 2023 Workshops, 2023, pp. 162–173

    work page 2023

  29. [29]

    The Art of Abstraction in Quantum Soft- ware,

    O. Di Matteo, “The Art of Abstraction in Quantum Soft- ware,” in2025 IEEE/ACM International Workshop on Quantum Software Engineering (Q-SE), 2025, pp. 25– 26

    work page 2025

  30. [30]

    Quantum programming languages,

    B. Heim et al., “Quantum programming languages,” Nature Reviews Physics, vol. 2, no. 12, pp. 709–722, 2020

    work page 2020

  31. [31]

    Zulehner and R

    A. Zulehner and R. Wille,Introducing Design Automa- tion for Quantum Computing. Springer, 2020

    work page 2020

  32. [32]

    Programming quantum computers using design automation,

    M. Soeken, T. Haener, and M. Roetteler, “Programming quantum computers using design automation,” in2018 Design, Automation & Test in Europe Conference & Exhibition (DATE), 2018, pp. 137–146

    work page 2018

  33. [33]

    The MQT Handbook: A Summary of Design Automation Tools and Software for Quantum Computing,

    R. Wille et al., “The MQT Handbook: A Summary of Design Automation Tools and Software for Quantum Computing,” in2024 IEEE International Conference on Quantum Software (QSW), 2024, pp. 1–8

    work page 2024

  34. [34]

    A Predictive Approach for Selecting the Best Quantum Solver for an Optimization Problem,

    D. V olpe, N. Quetschlich, M. Graziano, G. Turvani, and R. Wille, “A Predictive Approach for Selecting the Best Quantum Solver for an Optimization Problem,” in2024 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 01, 2024, pp. 1014–1025

    work page 2024

  35. [35]

    Towards an Automatic Framework for Solv- ing Optimization Problems with Quantum Computers,

    D. V olpe, N. Quetschlich, M. Graziano, G. Turvani, and R. Wille, “Towards an Automatic Framework for Solv- ing Optimization Problems with Quantum Computers,” in2024 IEEE International Conference on Quantum Software (QSW), 2024, pp. 46–57

    work page 2024

  36. [36]

    Hybrid Meta-Solving for Practical Quantum Computing,

    D. Eichhorn, M. Schweikart, N. Poser, F. Fiand, B. Poggel, and J. M. Lorenz, “Hybrid Meta-Solving for Practical Quantum Computing,” in2024 IEEE Interna- tional Conference on Quantum Computing and Engi- neering (QCE), vol. 01, 2024, pp. 421–431

    work page 2024

  37. [37]

    Recommending Solution Paths for Solv- ing Optimization Problems with Quantum Computing,

    B. Poggel, N. Quetschlich, L. Burgholzer, R. Wille, and J. M. Lorenz, “Recommending Solution Paths for Solv- ing Optimization Problems with Quantum Computing,” in2023 IEEE International Conference on Quantum Software (QSW), 2023

    work page 2023

  38. [38]

    N. Sachdeva et al.,Integrated error-suppressed pipeline for quantum optimization of nontrivial binary combina- torial optimization problems on gate-model hardware at the 156-qubit scale, arXiv:2406.01743 [quant-ph], 2026

    work page arXiv 2026

  39. [39]

    Digitized-counterdiabatic quan- tum approximate optimization algorithm,

    P. Chandarana et al., “Digitized-counterdiabatic quan- tum approximate optimization algorithm,”Physical Re- view Research, vol. 4, no. 1, p. 013 141, 2022

    work page 2022

  40. [40]

    Beyond the Buzz: Strategic Paths for Enabling Useful NISQ Applications,

    P. R. Hegde et al., “Beyond the Buzz: Strategic Paths for Enabling Useful NISQ Applications,” inProceedings of the 21st ACM International Conference on Computing Frontiers, 2024, pp. 310–313

    work page 2024

  41. [41]

    The Munich Quantum Soft- ware Stack: Connecting End Users, Integrating Diverse Quantum Technologies, Accelerating HPC,

    L. Burgholzer et al., “The Munich Quantum Soft- ware Stack: Connecting End Users, Integrating Diverse Quantum Technologies, Accelerating HPC,” inPro- ceedings of the Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region, 2026, pp. 55–67. [48]DecisionTree. [Online]. Available: https://www.quast- decisiontree.com/

    work page 2026

  42. [42]

    A variational eigenvalue solver on a photonic quantum processor,

    A. Peruzzo et al., “A variational eigenvalue solver on a photonic quantum processor,”Nature Communications, vol. 5, no. 1, p. 4213, 2014

    work page 2014

  43. [43]

    Toward a linear-ramp QAOA protocol: Evidence of a scaling advantage in solving some combinatorial optimization problems,

    J. A. Montañez-Barrera and K. Michielsen, “Toward a linear-ramp QAOA protocol: Evidence of a scaling advantage in solving some combinatorial optimization problems,”npj Quantum Information, vol. 11, no. 1, p. 131, 2025

    work page 2025

  44. [44]

    SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,

    P. Virtanen et al., “SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,”Nature Methods, vol. 17, pp. 261–272, 2020

    work page 2020

  45. [45]

    Warm-starting quantum optimization,

    D. J. Egger, J. Mare ˇcek, and S. Woerner, “Warm-starting quantum optimization,”Quantum, vol. 5, p. 479, 2021

    work page 2021

  46. [46]

    Multi-angle quantum approximate op- timization algorithm,

    R. Herrman, P. C. Lotshaw, J. Ostrowski, T. S. Humble, and G. Siopsis, “Multi-angle quantum approximate op- timization algorithm,”Scientific Reports, vol. 12, no. 1, p. 6781, 2022

    work page 2022

  47. [47]

    Chalupnik, H

    M. Chalupnik, H. Melo, Y . Alexeev, and A. Galda,Augmenting QAOA Ansatz with Multiparameter Problem-Independent Layer, 2022. arXiv: 2205.01192 [quant-ph]

    work page arXiv 2022

  48. [48]

    A uni- versal quantum algorithm for weighted maximum cut and ising problems,

    N. Kuete Meli, F. Mannel, and J. Lellmann, “A uni- versal quantum algorithm for weighted maximum cut and ising problems,”Quantum Information Processing, vol. 22, no. 7, p. 279, 2023

    work page 2023

  49. [49]

    A direct search optimization method that models the objective and constraint functions by linear interpolation,

    M. J. Powell, “A direct search optimization method that models the objective and constraint functions by linear interpolation,” inAdvances in Optimization and Numerical Analysis, Springer, 1994, pp. 51–67

    work page 1994

  50. [50]

    Multivariate stochastic approximation using a simultaneous perturbation gradient approximation,

    J. Spall, “Multivariate stochastic approximation using a simultaneous perturbation gradient approximation,” IEEE Transactions on Automatic Control, vol. 37, no. 3, pp. 332–341, 1992

    work page 1992

  51. [51]

    An efficient method for finding the minimum of a function of several variables without calculating derivatives,

    M. J. Powell, “An efficient method for finding the minimum of a function of several variables without calculating derivatives,”The Computer Journal, vol. 7, no. 2, pp. 155–162, 1964

    work page 1964

  52. [52]

    Sequential minimal optimization for quantum-classical hybrid al- gorithms,

    K. M. Nakanishi, K. Fujii, and S. Todo, “Sequential minimal optimization for quantum-classical hybrid al- gorithms,”Phys. Rev. Res., vol. 2, p. 043 158, 2020

    work page 2020

  53. [53]

    Experiments in quadratic 0–1 programming,

    F. Barahona, M. Jünger, and G. Reinelt, “Experiments in quadratic 0–1 programming,”Mathematical Pro- gramming, vol. 44, no. 1, pp. 127–137, 1989. 12

    work page 1989