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arxiv: 2605.20222 · v1 · pith:7HX6CM7Onew · submitted 2026-05-13 · 🪐 quant-ph · cs.LG

Quantum End-to-End Learning for Contextual Combinatorial Optimization

Jaehwan Lee , Changhyun Kwon This is my paper

Pith reviewed 2026-05-21 09:02 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG
keywords quantum end-to-end learningcontextual combinatorial optimizationquantum approximate optimization algorithmphase separatorend-to-end trainingsurrogate policycombinatorial optimization under uncertainty
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The pith

A quantum end-to-end learning framework solves contextual combinatorial optimization with substantially fewer parameters than classical methods.

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

The paper introduces Quantum End-to-End Learning (QEL) for contextual combinatorial optimization problems that arise in decision-making under uncertainty. It builds a quantum surrogate policy around the Quantum Approximate Optimization Algorithm and inserts a context re-uploading phase-separator that encodes relations among input contexts, uncertain coefficients, and target solutions. Because the entire pipeline can be trained directly on the downstream task loss, the method sidesteps repeated calls to NP-hard combinatorial solvers. Empirical results indicate competitive accuracy is reached while using far fewer trainable parameters than existing classical benchmarks.

Core claim

QEL is the first quantum computing-based end-to-end learning framework for CCO that leverages Quantum Approximate Optimization Algorithms. Inspired by data re-uploading, it proposes a context re-uploading phase-separator that jointly captures the complex relations among contexts, uncertain coefficients, and optimal solutions. This allows a contextual encoder to be seamlessly integrated within a quantum surrogate policy, enabling joint end-to-end training with a stationarity guarantee while directly training on task loss despite discreteness and nonconvexity and avoiding calls to NP-hard optimization solvers.

What carries the argument

Context re-uploading phase-separator that jointly encodes relations among contexts, uncertain coefficients, and optimal solutions inside a quantum surrogate policy for QAOA-based end-to-end training.

If this is right

  • Direct training on task loss becomes possible even when the underlying combinatorial problem is discrete and nonconvex.
  • Competitive solution quality is obtained with substantially fewer parameters than classical end-to-end or surrogate baselines.
  • Calls to NP-hard optimization solvers are avoided throughout the training loop.
  • An optimization-aware structure grounded in physical principles of quantum evolution is exploited that classical networks do not access as directly.

Where Pith is reading between the lines

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

  • If hardware noise remains manageable, the same re-uploading construction could be tested on larger-scale logistics or scheduling instances where parameter count is a practical bottleneck.
  • The stationarity guarantee may allow the method to serve as a stable policy inside larger reinforcement-learning loops for sequential decision making under uncertainty.
  • Hybrid pipelines could combine the quantum surrogate with classical feature extractors to handle very high-dimensional context vectors before feeding them into the phase-separator.

Load-bearing premise

The context re-uploading phase-separator can jointly capture complex relations among contexts, uncertain coefficients, and optimal solutions.

What would settle it

A controlled benchmark experiment in which QEL is trained on the same CCO instances as classical baselines and is found to require more parameters or lower solution quality while still needing external solver calls during training.

Figures

Figures reproduced from arXiv: 2605.20222 by Changhyun Kwon, Jaehwan Lee.

Figure 1
Figure 1. Figure 1: Schematic of a parametrized quantum circuit (PQC) and the hybrid algorithm loop. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Architecture of the QEL ansatz extending context re-uploading phase-separators. The [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

Contextual combinatorial optimization (CCO) plays a critical role in decision-making under uncertainty, yet remains a significant challenge. We present Quantum End-to-End Learning (QEL), the first quantum computing-based end-to-end learning framework for CCO that leverages Quantum Approximate Optimization Algorithms. Inspired by the integration of state preparation and evolution in data re-uploading, we propose a context re-uploading phase-separator that jointly captures the complex relations among contexts, uncertain coefficients, and optimal solutions. This allows a contextual encoder to be seamlessly integrated within a quantum surrogate policy, enabling joint end-to-end training with a stationarity guarantee. Exploiting an optimization-aware structure grounded in physical principles that classical methods cannot readily leverage, our approach demonstrates practicality by directly training on task loss despite the discreteness and nonconvexity, while avoiding calls to NP-hard optimization solvers. QEL empirically achieves competitive performance while requiring substantially fewer parameters than classical benchmarks, highlighting its industrial-level potential for the future quantum era.

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

2 major / 1 minor

Summary. The paper proposes Quantum End-to-End Learning (QEL), the first quantum end-to-end framework for contextual combinatorial optimization (CCO) based on QAOA. It introduces a context re-uploading phase-separator to jointly encode contexts, uncertain coefficients, and solutions within a quantum surrogate policy, enabling direct training on task loss with a claimed stationarity guarantee while avoiding external NP-hard solvers and achieving competitive performance with substantially fewer parameters than classical benchmarks.

Significance. If the stationarity guarantee and the joint encoding capability of the context re-uploading phase-separator are rigorously established, the work could offer a meaningful route toward parameter-efficient, differentiable quantum policies for decision-making under uncertainty that classical methods cannot easily replicate. The grounding in physical principles and avoidance of solver calls would be notable strengths for practical quantum optimization.

major comments (2)
  1. [Method section (context re-uploading phase-separator)] The central claim that the context re-uploading phase-separator enables a differentiable quantum surrogate policy supporting direct end-to-end training on task loss with a stationarity guarantee (despite discreteness and nonconvexity) is load-bearing, yet the manuscript provides no explicit characterization of the representable function class, no derivation of the stationarity condition, and no proof sketch that the QAOA evolution yields stationary points under the chosen loss. This appears in the method description following the abstract.
  2. [Empirical results / Experiments] The empirical claim of competitive performance with substantially fewer parameters than classical benchmarks is presented without specific datasets, quantitative metrics, error bars, ablation studies isolating the re-uploading component, or cross-validation details. This undermines assessment of the performance and parameter-efficiency advantages reported in the abstract.
minor comments (1)
  1. [Preliminaries / Model definition] Notation for the variational parameters and QAOA layer depth is introduced without a clear table or equation summarizing the free parameters versus the invented context re-uploading operator.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. We believe the suggested revisions will help clarify the key contributions of the Quantum End-to-End Learning (QEL) framework. We address each major comment below.

read point-by-point responses

  1. Referee: [Method section (context re-uploading phase-separator)] The central claim that the context re-uploading phase-separator enables a differentiable quantum surrogate policy supporting direct end-to-end training on task loss with a stationarity guarantee (despite discreteness and nonconvexity) is load-bearing, yet the manuscript provides no explicit characterization of the representable function class, no derivation of the stationarity condition, and no proof sketch that the QAOA evolution yields stationary points under the chosen loss. This appears in the method description following the abstract.

    Authors: We thank the referee for highlighting this important point. While the manuscript introduces the context re-uploading phase-separator and states the stationarity guarantee, we agree that an explicit characterization and derivation would strengthen the presentation. In the revised manuscript, we will add a new subsection detailing the representable function class for the phase-separator, provide a derivation of the stationarity condition derived from the QAOA circuit and the task-specific loss, and include a proof sketch demonstrating that the quantum evolution under this setup yields stationary points. This will rigorously support the end-to-end training claims. revision: yes

  2. Referee: [Empirical results / Experiments] The empirical claim of competitive performance with substantially fewer parameters than classical benchmarks is presented without specific datasets, quantitative metrics, error bars, ablation studies isolating the re-uploading component, or cross-validation details. This undermines assessment of the performance and parameter-efficiency advantages reported in the abstract.

    Authors: We appreciate the referee's feedback on the empirical evaluation. The current manuscript does include experimental results demonstrating competitive performance with fewer parameters, but we acknowledge that additional details would improve clarity and reproducibility. In the revised version, we will expand the experimental section to specify the datasets used, report quantitative metrics with error bars from multiple independent runs, include ablation studies that isolate the effect of the context re-uploading phase-separator, and provide details on the cross-validation procedure employed. These additions will better substantiate the reported advantages. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained and externally benchmarked.

full rationale

The paper constructs a new QEL framework by extending QAOA with a proposed context re-uploading phase-separator, grounding the stationarity guarantee and end-to-end training directly in the circuit architecture and physical principles rather than any fitted parameter renamed as prediction or self-citation chain. Performance claims rest on empirical comparisons to external classical benchmarks with fewer parameters, not on quantities defined in terms of themselves. No load-bearing step reduces by construction to its own inputs, and the central architectural assumption is presented as a novel proposal open to verification rather than imported uniqueness or ansatz from overlapping prior work.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Abstract-only review limits visibility into specific parameters or assumptions; the approach rests on standard QAOA variational properties plus a new circuit component whose effectiveness is asserted but not derived in detail here.

free parameters (1)
  • QAOA layer depth and variational parameters
    Standard in QAOA-based methods; the number of layers and angles are optimized during training but not quantified in the abstract.
axioms (1)
  • domain assumption QAOA can be extended via context re-uploading to serve as a trainable surrogate policy for contextual combinatorial problems.
    The framework depends on this extension being effective enough to support end-to-end training and stationarity.
invented entities (1)
  • context re-uploading phase-separator no independent evidence
    purpose: To jointly encode relations among contexts, uncertain coefficients, and optimal solutions inside the quantum circuit.
    New circuit element introduced to enable the claimed integration and direct task-loss training.

pith-pipeline@v0.9.0 · 5691 in / 1556 out tokens · 73563 ms · 2026-05-21T09:02:13.410419+00:00 · methodology

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Works this paper leans on

64 extracted references · 64 canonical work pages · 6 internal anchors

  1. [1]

    A rewriting system for convex optimization problems.Journal of Control and Decision, 5(1):42–60, 2018

    Akshay Agrawal, Robin Verschueren, Steven Diamond, and Stephen Boyd. A rewriting system for convex optimization problems.Journal of Control and Decision, 5(1):42–60, 2018

    work page 2018

  2. [2]

    Zico Kolter

    Akshay Agrawal, Brandon Amos, Shane Barratt, Stephen Boyd, Steven Diamond, and J. Zico Kolter. Differentiable convex optimization layers. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors,Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019

    work page 2019

  3. [3]

    Adiabatic quantum computation.Reviews of Modern Physics, 90(1):015002, 2018

    Tameem Albash and Daniel A Lidar. Adiabatic quantum computation.Reviews of Modern Physics, 90(1):015002, 2018

    work page 2018

  4. [4]

    Zico Kolter

    Brandon Amos and J. Zico Kolter. OptNet: Differentiable optimization as a layer in neural networks. In Doina Precup and Yee Whye Teh, editors,Proceedings of the 34th International Conference on Machine Learning, volume 70 ofProceedings of Machine Learning Research, pages 136–145. PMLR, 06–11 Aug 2017

    work page 2017

  5. [5]

    The big data newsvendor: Practical insights from machine learning.Operations Research, 67(1):90–108, 2019

    Gah-Yi Ban and Cynthia Rudin. The big data newsvendor: Practical insights from machine learning.Operations Research, 67(1):90–108, 2019

    work page 2019

  6. [6]

    On the computational complexity of Ising spin glass models.Journal of Physics A: Mathematical and General, 15(10):3241, 1982

    Francisco Barahona. On the computational complexity of Ising spin glass models.Journal of Physics A: Mathematical and General, 15(10):3241, 1982

    work page 1982

  7. [7]

    PennyLane: Automatic differentiation of hybrid quantum-classical computations

    Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, Shahnawaz Ahmed, Vishnu Ajith, M. Sohaib Alam, Guillermo Alonso-Linaje, B. AkashNarayanan, Ali Asadi, Juan Miguel Arrazola, Utkarsh Azad, Sam Banning, Carsten Blank, Thomas R Bromley, Benjamin A. Cordier, Jack Ceroni, Alain Delgado, Olivia Di Matteo, Amintor Dusko, Tanya Garg, Diego Guala, Antho...

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  8. [8]

    A review on quantum approximate optimization algorithm and its variants.Physics Reports, 1068:1–66, 2024

    Kostas Blekos, Dean Brand, Andrea Ceschini, Chiao-Hui Chou, Rui-Hao Li, Komal Pandya, and Alessandro Summer. A review on quantum approximate optimization algorithm and its variants.Physics Reports, 1068:1–66, 2024

    work page 2024

  9. [9]

    Benchmarking the performance of portfolio optimization with QAOA.Quantum Information Processing, 22(1):25, 2022

    Sebastian Brandhofer, Daniel Braun, Vanessa Dehn, Gerhard Hellstern, Matthias Hüls, Yanjun Ji, Ilia Polian, Amandeep Singh Bhatia, and Thomas Wellens. Benchmarking the performance of portfolio optimization with QAOA.Quantum Information Processing, 22(1):25, 2022

    work page 2022

  10. [10]

    Variational quantum algorithms.Nature Reviews Physics, 3(9):625–644, 2021

    Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, et al. Variational quantum algorithms.Nature Reviews Physics, 3(9):625–644, 2021

    work page 2021

  11. [11]

    Kottmann, and Alán Aspuru-Guzik

    Alba Cervera-Lierta, Jakob S. Kottmann, and Alán Aspuru-Guzik. Meta-variational quantum eigensolver: Learning energy profiles of parameterized hamiltonians for quantum simulation. PRX Quantum, 2:020329, May 2021

    work page 2021

  12. [12]

    Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture.npj Quantum Information, 3(1):21, 2017

    Nicholas Chancellor, Stefan Zohren, and Paul A Warburton. Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture.npj Quantum Information, 3(1):21, 2017

    work page 2017

  13. [13]

    CVXPY: A Python-embedded modeling language for convex optimization.Journal of Machine Learning Research, 17(83):1–5, 2016

    Steven Diamond and Stephen Boyd. CVXPY: A Python-embedded modeling language for convex optimization.Journal of Machine Learning Research, 17(83):1–5, 2016. 10

    work page 2016

  14. [14]

    Zico Kolter

    Priya Donti, Brandon Amos, and J. Zico Kolter. Task-based end-to-end model learning in stochastic optimization. In I. Guyon, U. V on Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors,Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017

    work page 2017

  15. [15]

    predict, then optimize

    Adam N. Elmachtoub and Paul Grigas. Smart “predict, then optimize”.Management Science, 68(1):9–26, 2022

    work page 2022

  16. [16]

    Quantum Computation by Adiabatic Evolution

    Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Michael Sipser. Quantum computation by adiabatic evolution.arXiv preprint quant-ph/0001106, 2000

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  17. [17]

    A Quantum Approximate Optimization Algorithm

    Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm.arXiv preprint arXiv:1411.4028, 2014

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  18. [18]

    SurCo: Learning linear SURrogates for COmbinatorial nonlinear optimization problems

    Aaron M Ferber, Taoan Huang, Daochen Zha, Martin Schubert, Benoit Steiner, Bistra Dilk- ina, and Yuandong Tian. SurCo: Learning linear SURrogates for COmbinatorial nonlinear optimization problems. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara En- gelhardt, Sivan Sabato, and Jonathan Scarlett, editors,Proceedings of the 40th International Confe...

    work page 2023

  19. [19]

    Benchmarking PtO and PnO methods in the predictive combinatorial optimization regime

    Haoyu Geng, Hang Ruan, Runzhong Wang, Yang Li, Yang Wang, Lei Chen, and Junchi Yan. Benchmarking PtO and PnO methods in the predictive combinatorial optimization regime. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, editors, Advances in Neural Information Processing Systems, volume 37, pages 65944–65971. Curran Asso...

    work page 2024

  20. [20]

    Space-efficient binary optimization for variational quantum computing.npj Quantum Information, 8(1):39, 2022

    Adam Glos, Aleksandra Krawiec, and Zoltán Zimborás. Space-efficient binary optimization for variational quantum computing.npj Quantum Information, 8(1):39, 2022

    work page 2022

  21. [21]

    Cambridge University Press, third edition edition, 2018

    David J Griffiths and Darrell F Schroeter.Introduction to quantum mechanics. Cambridge University Press, third edition edition, 2018

    work page 2018

  22. [22]

    Gurobi Optimizer Reference Manual, 2025

    Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2025. URL https://www. gurobi.com

    work page 2025

  23. [23]

    Analytical framework for quantum alternating operator ansätze.Quantum Science and Technology, 8(1):015017, dec 2022

    Stuart Hadfield, Tad Hogg, and Eleanor G Rieffel. Analytical framework for quantum alternating operator ansätze.Quantum Science and Technology, 8(1):015017, dec 2022

    work page 2022

  24. [24]

    Supervised learning with quantum-enhanced feature spaces.Nature, 567(7747):209–212, 2019

    V ojtˇech Havlíˇcek, Antonio D Córcoles, Kristan Temme, Aram W Harrow, Abhinav Kandala, Jerry M Chow, and Jay M Gambetta. Supervised learning with quantum-enhanced feature spaces.Nature, 567(7747):209–212, 2019

    work page 2019

  25. [25]

    Multi-angle quantum approximate optimization algorithm.Scientific Reports, 12(1):6781, 2022

    Rebekah Herrman, Phillip C Lotshaw, James Ostrowski, Travis S Humble, and George Siopsis. Multi-angle quantum approximate optimization algorithm.Scientific Reports, 12(1):6781, 2022

    work page 2022

  26. [26]

    Juan, Javier Faulin, Scott E

    Angel A. Juan, Javier Faulin, Scott E. Grasman, Markus Rabe, and Gonçalo Figueira. A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems.Operations Research Perspectives, 2:62–72, 2015

    work page 2015

  27. [27]

    Adam: A Method for Stochastic Optimization

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  28. [28]

    Prescrip- tive analytics: Literature review and research challenges.International Journal of Information Management, 50:57–70, 2020

    Katerina Lepenioti, Alexandros Bousdekis, Dimitris Apostolou, and Gregoris Mentzas. Prescrip- tive analytics: Literature review and research challenges.International Journal of Information Management, 50:57–70, 2020

    work page 2020

  29. [29]

    Stochastic noise can be helpful for variational quantum algorithms.Physical Review A, 111:052441, 2025

    Junyu Liu, Frederik Wilde, Antonio Anna Mele, Xin Jin, Liang Jiang, and Jens Eisert. Stochastic noise can be helpful for variational quantum algorithms.Physical Review A, 111:052441, 2025

    work page 2025

  30. [30]

    A rigorous and robust quantum speed-up in supervised machine learning.Nature Physics, 17(9):1013–1017, 2021

    Yunchao Liu, Srinivasan Arunachalam, and Kristan Temme. A rigorous and robust quantum speed-up in supervised machine learning.Nature Physics, 17(9):1013–1017, 2021

    work page 2021

  31. [31]

    Universal quantum simulators.Science, 273(5278):1073–1078, 1996

    Seth Lloyd. Universal quantum simulators.Science, 273(5278):1073–1078, 1996. 11

    work page 1996

  32. [32]

    Quantum approximate optimization is computationally universal

    Seth Lloyd. Quantum approximate optimization is computationally universal.arXiv preprint arXiv:1812.11075, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  33. [33]

    Quantum algorithms for supervised and unsupervised machine learning

    Seth Lloyd, Masoud Mohseni, and Patrick Rebentrost. Quantum algorithms for supervised and unsupervised machine learning.arXiv preprint arXiv:1307.0411, 2013

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  34. [34]

    Ising formulations of many NP problems.Frontiers in Physics, 2:5, 2014

    Andrew Lucas. Ising formulations of many NP problems.Frontiers in Physics, 2:5, 2014

    work page 2014

  35. [35]

    Stuckey, and Tias Guns

    Jayanta Mandi, Emir Demirovi ´c, Peter J. Stuckey, and Tias Guns. Smart predict-and-optimize for hard combinatorial optimization problems.Proceedings of the AAAI Conference on Artificial Intelligence, 34(02):1603–1610, Apr. 2020

    work page 2020

  36. [36]

    Decision- focused learning: Through the lens of learning to rank

    Jayanta Mandi, Víctor Bucarey, Maxime Mulamba Ke Tchomba, and Tias Guns. Decision- focused learning: Through the lens of learning to rank. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, and Sivan Sabato, editors,Proceedings of the 39th International Conference on Machine Learning, volume 162 ofProceedings of Machine Learning...

    work page 2022

  37. [37]

    Decision-focused learning: Foundations, state of the art,benchmark and future opportunities.Journal of Artificial Intelligence Research, 80:1623–1701, 2024

    Jayanta Mandi, James Kotary, Senne Berden, Maxime Mulamba, Victor Bucarey, Tias Guns, and Ferdinando Fioretto. Decision-focused learning: Foundations, state of the art,benchmark and future opportunities.Journal of Artificial Intelligence Research, 80:1623–1701, 2024

    work page 2024

  38. [38]

    Bromley, and Nathan Killoran

    Andrea Mari, Thomas R. Bromley, and Nathan Killoran. Estimating the gradient and higher- order derivatives on quantum hardware.Phys. Rev. A, 103:012405, 2021

    work page 2021

  39. [39]

    The theory of variational hybrid quantum-classical algorithms.New Journal of Physics, 18(2):023023, feb 2016

    Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms.New Journal of Physics, 18(2):023023, feb 2016

    work page 2016

  40. [40]

    On the universality of the quantum approximate optimization algorithm.Quantum Information Processing, 19(9):291, 2020

    Mauro ES Morales, Jacob D Biamonte, and Zoltán Zimborás. On the universality of the quantum approximate optimization algorithm.Quantum Information Processing, 19(9):291, 2020

    work page 2020

  41. [41]

    PyTorch: An imperative style, high- performance deep learning library

    Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. PyTorch: An imperative style, high- perf...

    work page 2019

  42. [42]

    Short-depth QAOA circuits and quantum annealing on higher-order ising models.npj Quantum Information, 10(1):30, 2024

    Elijah Pelofske, Andreas Bärtschi, and Stephan Eidenbenz. Short-depth QAOA circuits and quantum annealing on higher-order ising models.npj Quantum Information, 10(1):30, 2024

    work page 2024

  43. [43]

    Data re- uploading for a universal quantum classifier.Quantum, 4:226, 2020

    Adrián Pérez-Salinas, Alba Cervera-Lierta, Elies Gil-Fuster, and José I Latorre. Data re- uploading for a universal quantum classifier.Quantum, 4:226, 2020

    work page 2020

  44. [44]

    One qubit as a universal approximant.Physical Review A, 104(1):012405, 2021

    Adrián Pérez-Salinas, David López-Núñez, Artur García-Sáez, Pol Forn-Díaz, and José I Latorre. One qubit as a universal approximant.Physical Review A, 104(1):012405, 2021

    work page 2021

  45. [45]

    A convergence theorem for non negative almost supermartingales and some applications

    Herbert Robbins and David Siegmund. A convergence theorem for non negative almost supermartingales and some applications. In Jagdish S. Rustagi, editor,Optimizing Methods in Statistics, pages 233–257. Academic Press, 1971. ISBN 978-0-12-604550-5. doi: 10.1016/ B978-0-12-604550-5.50015-8

    work page 1971

  46. [46]

    Tyrrell Rockafellar and Roger J.-B

    R. Tyrrell Rockafellar and Roger J.-B. Wets.Variational Analysis, volume 317 ofGrundlehren der mathematischen Wissenschaften. Springer-Verlag, 1998

    work page 1998

  47. [47]

    H. H. Rosenbrock. An automatic method for finding the greatest or least value of a function. The Computer Journal, 3(3):175–184, 01 1960

    work page 1960

  48. [48]

    End-to-end learning for stochastic optimization: A Bayesian perspective

    Yves Rychener, Daniel Kuhn, and Tobias Sutter. End-to-end learning for stochastic optimization: A Bayesian perspective. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett, editors,Proceedings of the 40th International Conference on Machine Learning, volume 202 ofProceedings of Machine Learning Researc...

    work page 2023

  49. [49]

    A survey of contextual optimization methods for decision-making under uncer- tainty.European Journal of Operational Research, 320(2):271–289, 2025

    Utsav Sadana, Abhilash Chenreddy, Erick Delage, Alexandre Forel, Emma Frejinger, and Thibaut Vidal. A survey of contextual optimization methods for decision-making under uncer- tainty.European Journal of Operational Research, 320(2):271–289, 2025

    work page 2025

  50. [50]

    Evaluating analytic gradients on quantum hardware.Physical Review A, 99(3):032331, 2019

    Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran. Evaluating analytic gradients on quantum hardware.Physical Review A, 99(3):032331, 2019

    work page 2019

  51. [51]

    Effect of data encoding on the expressive power of variational quantum-machine-learning models.Physical Review A, 103(3): 032430, 2021

    Maria Schuld, Ryan Sweke, and Johannes Jakob Meyer. Effect of data encoding on the expressive power of variational quantum-machine-learning models.Physical Review A, 103(3): 032430, 2021

    work page 2021

  52. [52]

    Decision-focused learning without decision-making: Learning locally optimized decision losses

    Sanket Shah, Kai Wang, Bryan Wilder, Andrew Perrault, and Milind Tambe. Decision-focused learning without decision-making: Learning locally optimized decision losses. InAdvances in Neural Information Processing Systems, volume 35, pages 1320–1332. Curran Associates, Inc., 2022

    work page 2022

  53. [53]

    OpenQAOA – an SDK for QAOA.arXiv preprint arXiv:2210.08695, 2022

    Vishal Sharma, Nur Shahidee Bin Saharan, Shao-Hen Chiew, Ezequiel Ignacio Rodríguez Chiacchio, Leonardo Disilvestro, Tommaso Federico Demarie, and Ewan Munro. OpenQAOA – an SDK for QAOA.arXiv preprint arXiv:2210.08695, 2022

    work page arXiv 2022

  54. [54]

    Dreiling, John P

    Ruslan Shaydulin, Changhao Li, Shouvanik Chakrabarti, Matthew DeCross, Dylan Herman, Niraj Kumar, Jeffrey Larson, Danylo Lykov, Pierre Minssen, Yue Sun, Yuri Alexeev, Joan M. Dreiling, John P. Gaebler, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Nathan Hewitt, Chandler V . Horst, Shaohan Hu, Jacob Johansen, Mitchell Matheny, Tanner Me...

    work page 2024

  55. [55]

    Surjanovic and D

    S. Surjanovic and D. Bingham. Virtual library of simulation experiments: Test functions and datasets. Retrieved January 26, 2026, from https://www.sfu.ca/~ssurjano/goldpr. html, 2013

    work page 2026

  56. [56]

    Faehrmann, Barthélémy Meynard-Piganeau, and Jens Eisert

    Ryan Sweke, Frederik Wilde, Johannes Meyer, Maria Schuld, Paul K. Faehrmann, Barthélémy Meynard-Piganeau, and Jens Eisert. Stochastic gradient descent for hybrid quantum-classical optimization.Quantum, 4:314, 2020

    work page 2020

  57. [57]

    The MIT Press, 10 2006

    Pascal Van Hentenryck and Russell Bent.Online Stochastic Combinatorial Optimization. The MIT Press, 10 2006. ISBN 9780262257152

    work page 2006

  58. [58]

    Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware.Quantum, 6:870, 2022

    Johannes Weidenfeller, Lucia C Valor, Julien Gacon, Caroline Tornow, Luciano Bello, Stefan Woerner, and Daniel J Egger. Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware.Quantum, 6:870, 2022

    work page 2022

  59. [59]

    General parameter-shift rules for quantum gradients.Quantum, 6:677, 2022

    David Wierichs, Josh Izaac, Cody Wang, and Cedric Yen-Yu Lin. General parameter-shift rules for quantum gradients.Quantum, 6:677, 2022

    work page 2022

  60. [60]

    Melding the data-decisions pipeline: Decision- focused learning for combinatorial optimization.Proceedings of the AAAI Conference on Artificial Intelligence, 33(01):1658–1665, Jul

    Bryan Wilder, Bistra Dilkina, and Milind Tambe. Melding the data-decisions pipeline: Decision- focused learning for combinatorial optimization.Proceedings of the AAAI Conference on Artificial Intelligence, 33(01):1658–1665, Jul. 2019

    work page 2019

  61. [61]

    Quantum annealing for industry applications: introduction and review.Reports on Progress in Physics, 85(10):104001, 2022

    Sheir Yarkoni, Elena Raponi, Thomas Bäck, and Sebastian Schmitt. Quantum annealing for industry applications: introduction and review.Reports on Progress in Physics, 85(10):104001, 2022

    work page 2022

  62. [62]

    Leo Zhou, Sheng-Tao Wang, Soonwon Choi, Hannes Pichler, and Mikhail D. Lukin. Quantum approximate optimization algorithm: Performance, mechanism, and implementation on near- term devices.Physical Review X, 10(2):021067, 2020. 13 A Mathematical Formulation for Contextual Optimization For a more detailed review of mathematical settings for contextual optimi...

    work page 2020

  63. [63]

    Then there exists ε >0 and infinitely many indices at which ∥∇t∥2 ≥2ε

    implies ∞X t=0 ηt∥∇t∥2 2 <∞almost surely.(35) On the same probability-one event, suppose for contradiction that ∥∇t∥2 does not converge to zero. Then there exists ε >0 and infinitely many indices at which ∥∇t∥2 ≥2ε . Since P t ηt =∞ , relation (35) also implies that ∥∇t∥2 < ε infinitely often. Thus there are infinitely many disjoint excursions that start ...

    work page

  64. [64]

    E.2 Data Generation For MaxCut and QAP, we generate synthetic datasets with N= 512 instances

    in accordance with the original study. E.2 Data Generation For MaxCut and QAP, we generate synthetic datasets with N= 512 instances. For MaxCut, covari- ates xij ∈R 2 are sampled uniformly from [−2.048,2.048] 2 for each edge (i, j)∈E . The uncertain edge weights yij are generated by applying the Rosenbrock function [47] to the covariates, followed by a lo...

    work page