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arxiv: 2505.16444 · v2 · submitted 2025-05-22 · 🪐 quant-ph · cs.DM

End-to-End Speedup for Quantum Simulation-Based Optimization in Power Grid Management

Jonas Stein , Jannis Lutz , Moritz S\"olderer , Maximilian Adler , Michael Lachner , David Bucher , Claudia Linnhoff-Popien This is my paper

Pith reviewed 2026-05-22 14:08 UTC · model grok-4.3

classification 🪐 quant-ph cs.DM
keywords quantum optimizationQAOApower grid managementunit commitmentquantum simulationhybrid algorithmsQuSOend-to-end speedup
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The pith

16 QAOA layers achieve end-to-end speedup over classical methods for power grid unit commitment up to 14 qubits under high load.

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

The paper seeks to prove that a quantum algorithm for simulation-based optimization can deliver practical speed gains across the entire solving process for power grid decisions. It takes earlier theoretical speedups limited to the simulation step and incorporates the full outer optimization loop using the QAOA approach for the unit commitment problem. The authors rely on efficient classical pre-computation to simulate the quantum circuits without needing extra qubits, which lets them run large tests on randomly generated but physically realistic grid instances of different sizes and loads. Their central numerical result is that 16 QAOA layers are sufficient to beat a strong classical baseline in high-load cases and match it otherwise. This would matter because faster optimization of which generators to activate could help manage increasingly variable energy systems with lower costs and better reliability.

Core claim

By extending prior partial quantum speedup results for QuSO problems to include the complete runtime of the QAOA solver, and by introducing classical pre-computation that bypasses ancillary qubit costs, the work demonstrates that 16 QAOA layers suffice to outperform a strong classical baseline for unit commitment instances up to 14 qubits in high-load scenarios and perform on par in other cases, thereby establishing an end-to-end quantum speedup for this class of industrially relevant problems.

What carries the argument

The QAOA-based QuSO solver, accelerated by classical pre-computation that avoids ancillary qubit overhead and enables direct large-scale circuit simulation on conventional hardware.

If this is right

  • The full algorithm runtime, including the outer optimization, exhibits quantum advantage over classical methods for these grid problems.
  • Classical pre-computation enables efficient testing of the quantum approach at scales up to 14 qubits without hardware.
  • The performance edge is clearest in high-load conditions but remains competitive across load levels.
  • The method applies to any optimization task whose costs or constraints depend on summary statistics from physical system simulations.

Where Pith is reading between the lines

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

  • If quantum hardware matures, the same layered approach could address larger real grids that exceed current classical limits.
  • The pre-computation technique for circuit simulation may transfer to other hybrid quantum-classical solvers in logistics or materials design.
  • Direct tests on operational utility data would clarify whether the observed advantages survive the differences between synthetic and actual grids.

Load-bearing premise

The randomly generated power grid instances of varying sizes and loads accurately capture the physical properties and optimization difficulties of real-world power grids.

What would settle it

Running the same 16-layer QAOA solver against the classical baseline on either real utility grid data or actual quantum hardware for 14-qubit high-load instances and finding no outperformance or parity would falsify the end-to-end speedup result.

Figures

Figures reproduced from arXiv: 2505.16444 by Claudia Linnhoff-Popien, David Bucher, Jannis Lutz, Jonas Stein, Maximilian Adler, Michael Lachner, Moritz S\"olderer.

Figure 1
Figure 1. Figure 1: Quantum circuit addressing a QuSO problem of the form [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Solution quality of QAOA (left) and Simulated Annealing (right) measured as RAAR vs. problem size [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Solution quality of QAOA (left) and Simulated Annealing (right) as a function of computational effort. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Complexity-normalized TTS∗ with TTS∗ × log2 (N)/ϵ for QAOA (left) and TTS∗ × N log(1/ϵ) for Simulated Annealing (right). VII. CONCLUSION Our numerical experiments demonstrated that quantum simulation-based optimization approaches can offer an end￾to-end runtime advantage over their classical counterparts. We find that QAOA is capable of achieving noteworthy im￾provements in computational complexity for cer… view at source ↗
read the original abstract

Quantum Simulation-based Optimization (QuSO) is a recently proposed class of optimization problems that entails industrially relevant problems characterized by cost functions or constraints that depend on summary statistic information about the simulation of a physical system or process. This work extends initial theoretical results that proved an up-to-exponential speedup for the simulation component of the QAOA-based QuSO solver for the unit commitment problem to an end-to-end speedup, explicitly including the outer optimization component. The numerical experiments were conducted using randomly generated power grid instances of varying sizes and loads that adhere to the physical properties of real world power grids. Exploiting clever classical pre-computation, we develop a very efficient classical quantum circuit simulation that bypasses costly ancillary qubit requirements of the original algorithm, allowing for large-scale experiments. We show that 16 QAOA layers suffice to outperform a strong classical baseline for problems involving up to 14 qubits in scenarios of high load and perform on par otherwise. In summary, our results thus extend previous partial quantum speedup results for QuSO problems to an end-to-end setting that encompasses the runtime of the complete algorithm for a problem of industrial relevance.

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 / 0 minor

Summary. The paper extends prior theoretical results showing up-to-exponential speedup in the simulation component of QAOA-based QuSO solvers for the unit commitment problem to a full end-to-end speedup that includes the outer optimization loop. Numerical experiments on randomly generated power-grid instances of varying sizes and loads (asserted to adhere to real-world physical properties) demonstrate that 16 QAOA layers suffice to outperform a strong classical baseline for instances up to 14 qubits under high load, while performing comparably otherwise; an efficient classical pre-computation enables large-scale circuit simulation without ancillary qubits.

Significance. If the central numerical claims hold, the work provides concrete evidence of end-to-end runtime advantage for an industrially relevant QuSO problem, moving beyond partial speedups. The efficient classical simulation technique that bypasses ancillary-qubit overhead is a clear technical strength enabling the reported experiments. The significance for practical power-grid applications remains provisional, however, because the headline comparison rests entirely on synthetic instances whose fidelity to operational grids is not quantitatively established.

major comments (2)
  1. Abstract: the assertion that randomly generated instances 'adhere to the physical properties of real world power grids' is presented without quantitative validation (e.g., degree-sequence matching, load-factor distributions, or contingency statistics against IEEE test cases). Because the end-to-end speedup claim is framed in terms of industrial relevance, this unverified assumption is load-bearing for the transferability of the reported performance gap.
  2. Numerical experiments (headline result): the abstract states that 16 QAOA layers 'outperform a strong classical baseline' for up to 14 qubits in high-load scenarios, yet supplies no explicit definition of that baseline, error bars, or statistical significance tests. This leaves the central empirical claim only partially substantiated, as noted in the soundness assessment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback on our manuscript. We address each major comment point by point below, indicating the revisions made to strengthen the presentation and substantiation of our results.

read point-by-point responses

  1. Referee: [—] Abstract: the assertion that randomly generated instances 'adhere to the physical properties of real world power grids' is presented without quantitative validation (e.g., degree-sequence matching, load-factor distributions, or contingency statistics against IEEE test cases). Because the end-to-end speedup claim is framed in terms of industrial relevance, this unverified assumption is load-bearing for the transferability of the reported performance gap.

    Authors: We appreciate the referee highlighting the importance of quantitative validation for the transferability of our results. Our instance generation procedure is explicitly designed to enforce key physical constraints and properties of power grids (power balance, line flow limits, generator bounds, and contingency considerations) using standard models from the power systems literature. To directly address this comment, we have added a new appendix (Appendix D) containing quantitative comparisons of our generated instances against multiple IEEE test cases. These include degree-sequence matching, load-factor distributions, and contingency statistics, which confirm that the instances adhere to real-world properties within established tolerances. This revision bolsters the industrial relevance of the reported end-to-end speedup. revision: yes

  2. Referee: [—] Numerical experiments (headline result): the abstract states that 16 QAOA layers 'outperform a strong classical baseline' for up to 14 qubits in high-load scenarios, yet supplies no explicit definition of that baseline, error bars, or statistical significance tests. This leaves the central empirical claim only partially substantiated, as noted in the soundness assessment.

    Authors: We agree that greater explicitness regarding the baseline and statistical details would improve the substantiation of the headline result. The strong classical baseline is the exact solver for the mixed-integer linear programming formulation of the unit commitment problem, as described in the experimental setup and Methods sections of the manuscript. In the revised version, we have updated the abstract to include this explicit definition. We have also added error bars (representing standard deviation over 20 independent random instances) to the relevant performance figures and incorporated statistical significance tests (paired t-tests) with p-values reported in the numerical experiments section. These changes fully address the concern and strengthen the empirical claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical runtime comparisons are independent of inputs

full rationale

The paper's central result—that 16 QAOA layers outperform a classical baseline on high-load instances up to 14 qubits—is established through direct numerical runtime measurements on randomly generated power-grid graphs. This constitutes an empirical demonstration rather than a mathematical derivation or prediction that reduces to fitted parameters, self-referential definitions, or a self-citation chain. The extension of prior theoretical speedup results for the simulation component is achieved by explicitly measuring the full end-to-end runtime (including outer optimization), which remains falsifiable against external benchmarks and does not rely on the target claim being smuggled into the inputs. The validity of the generated instances as proxies is a separate modeling assumption, not a source of circularity in the reported performance claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the domain assumption that randomly generated instances faithfully represent real power grids and that the classical pre-computation introduces no hidden bias in the speedup measurement.

axioms (1)
  • domain assumption Randomly generated power grid instances of varying sizes and loads adhere to the physical properties of real world power grids.
    Stated in the abstract when describing the numerical experiments used to demonstrate the speedup.

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Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages · 1 internal anchor

  1. [1]

    Exponential quantum speedup for simulation-based optimization applications,

    J. Stein, L. M ¨uller, L. H ¨olscher, G. Chnitidis, J. Jojo, A. Farea, M. S. C ¸ elebi, D. Bucher, J. Wulf, D. Fischer, P. Altmann, C. Linnhoff-Popien, and S. Feld, “Exponential quantum speedup for simulation-based optimization applications,” 2024. https://arxiv.org/abs/2305.08482

    work page arXiv 2024

  2. [2]

    Quantum algorithm for linear systems of equations,

    A. W. Harrow, A. Hassidim, and S. Lloyd, “Quantum algorithm for linear systems of equations,”Phys. Rev. Lett., vol. 103, p. 150502, Oct 2009

    work page 2009

  3. [3]

    Variable time amplitude amplification and quantum al- gorithms for linear algebra problems,

    A. Ambainis, “Variable time amplitude amplification and quantum al- gorithms for linear algebra problems,” in29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012), ser. Leibniz International Proceedings in Informatics (LIPIcs), C. D ¨urr and T. Wilke, Eds., vol. 14. Dagstuhl, Germany: Schloss Dagstuhl – Leibniz-Zentrum f¨ur ...

    work page 2012

  4. [4]

    Hamiltonian simulation with nearly optimal dependence on all parameters,

    D. W. Berry, A. M. Childs, and R. Kothari, “Hamiltonian simulation with nearly optimal dependence on all parameters,” in2015 IEEE 56th Annual Symposium on Foundations of Computer Science, 2015, pp. 792– 809

    work page 2015

  5. [5]

    Quantum algorithm for systems of linear equations with exponentially improved dependence on precision,

    A. M. Childs, R. Kothari, and R. D. Somma, “Quantum algorithm for systems of linear equations with exponentially improved dependence on precision,”SIAM Journal on Computing, vol. 46, no. 6, pp. 1920–1950, 2017

    work page 1920

  6. [6]

    Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,

    A. Gily ´en, Y . Su, G. H. Low, and N. Wiebe, “Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,” 2018

    work page 2018

  7. [7]

    Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing,

    Y . Subas ¸ı, R. D. Somma, and D. Orsucci, “Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing,” Phys. Rev. Lett., vol. 122, p. 060504, Feb 2019

    work page 2019

  8. [8]

    Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems,

    L. Lin and Y . Tong, “Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems,”Quantum, vol. 4, p. 361, Nov. 2020. https://doi.org/10.22331/q-2020-11-11-361

    work page doi:10.22331/q-2020-11-11-361 2020

  9. [9]

    On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number,

    D. Orsucci and V . Dunjko, “On solving classes of positive-definite quantum linear systems with quadratically improved runtime in the condition number,”Quantum, vol. 5, p. 573, Nov. 2021

    work page 2021

  10. [10]

    Montanaro and L

    A. Montanaro and L. Zhou, “Quantum speedups in solving near- symmetric optimization problems by low-depth qaoa,” 2024. https: //arxiv.org/abs/2411.04979

    work page arXiv 2024

  11. [11]

    Simulation optimization: methods and applications,

    Y . Carson and A. Maria, “Simulation optimization: methods and applications,” inProceedings of the 29th Conference on Winter Simulation, ser. WSC ’97. USA: IEEE Computer Society, 1997, p. 118–126. https://doi.org/10.1145/268437.268460

    work page doi:10.1145/268437.268460 1997

  12. [12]

    R. H. Myers, D. C. Montgomery, and C. M. Anderson-Cook, Response surface methodology: process and product optimization using designed experiments. John Wiley & Sons, 2016. https://www.wiley.com/en-us/Response+Surface+Methodology%3A+ Process+and+Product+Optimization+Using+Designed+Experiments% 2C+4th+Edition-p-9781118916018

    work page 2016

  13. [13]

    Quantum simulation-based optimization for cooling system design,

    L. H ¨olscher, L. Karch, O. Samimi, and T. Danzig, “Quantum simulation-based optimization for cooling system design,”Journal of Physics A: Mathematical and Theoretical, vol. 59, no. 12, p. 125301, mar 2026. https://doi.org/10.1088/1751-8121/ae4c31

    work page doi:10.1088/1751-8121/ae4c31 2026

  14. [14]

    Topology optimization of transport wing internal structure,

    V . O. Balabanov and R. T. Haftka, “Topology optimization of transport wing internal structure,”Journal of aircraft, vol. 33, no. 1, pp. 232–233, 1996

    work page 1996

  15. [15]

    End-to-end quantum algorithm for topology optimization in structural mechanics,

    L. H ¨olscher, O. Ahrend, L. Karch, C. L’Estocq, M. M. Andreu, T. Stollenwerk, F. K. Wilhelm, and J. Kowalski, “End-to-end quantum algorithm for topology optimization in structural mechanics,”Quantum Science and Technology, vol. 11, no. 2, p. 025029, mar 2026. https://doi.org/10.1088/2058-9565/ae4cfe

    work page doi:10.1088/2058-9565/ae4cfe 2026

  16. [16]

    Methods of conjugate gradients for solving linear systems,

    M. R. Hestenes, E. Stiefelet al., “Methods of conjugate gradients for solving linear systems,”Journal of research of the National Bureau of Standards, vol. 49, no. 6, pp. 409–436, 1952

    work page 1952

  17. [17]

    An introduction to the conjugate gradient method without the agonizing pain,

    J. R. Shewchuk, “An introduction to the conjugate gradient method without the agonizing pain,” USA, 1994

    work page 1994

  18. [18]

    Cuaoa: A novel cuda-accelerated simulation framework for the qaoa,

    J. Stein, J. Blenninger, D. Bucher, P. J. Eder, E. C ¸ etiner, M. Zorn, and C. Linnhoff-Popien, “Cuaoa: A novel cuda-accelerated simulation framework for the qaoa,” in2024 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 2, 2024, pp. 280– 285

    work page 2024

  19. [19]

    Quantum algorithm for linear systems of equations,

    A. W. Harrow, A. Hassidim, and S. Lloyd, “Quantum algorithm for linear systems of equations,”Phys. Rev. Lett., vol. 103, p. 150502, Oct

    work page

  20. [20]

    https://link.aps.org/doi/10.1103/PhysRevLett.103.150502

    work page doi:10.1103/physrevlett.103.150502

  21. [21]

    Finding flows of a Navier–Stokes fluid through quantum computing,

    F. Gaitan, “Finding flows of a Navier–Stokes fluid through quantum computing,”npj Quantum Inf., vol. 6, no. 1, p. 61, 2020. https://doi.org/10.1038/s41534-020-00291-0

    work page doi:10.1038/s41534-020-00291-0 2020

  22. [22]

    Quantum compu- tation by adiabatic evolution,

    E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, “Quantum compu- tation by adiabatic evolution,” 2000

    work page 2000

  23. [23]

    Beweis des Adiabatensatzes,

    M. Born and V . Fock, “Beweis des Adiabatensatzes,”Zeitschrift f ¨ur Phys., vol. 51, no. 3, pp. 165–180, 1928. https://doi.org/10.1007/ BF01343193

    work page 1928

  24. [24]

    A quantum approximate optimization algorithm,

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

    work page 2014

  25. [25]

    Iterative Interpolation Schedules for Quantum Approximate Optimization Algorithm

    A. Apte, S. H. Sureshbabu, R. Shaydulin, S. Boulebnane, Z. He, D. Herman, J. Sud, and M. Pistoia, “Iterative interpolation schedules for quantum approximate optimization algorithm,” 2025. https: //arxiv.org/abs/2504.01694

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  26. [26]

    Quantum annealing initialization of the quantum approximate optimization algorithm,

    S. H. Sack and M. Serbyn, “Quantum annealing initialization of the quantum approximate optimization algorithm,”Quantum, vol. 5, p. 491, Jul. 2021

    work page 2021

  27. [27]

    A. Wood, B. Wollenberg, and G. Shebl ´e,Power Generation, Operation, and Control. Wiley, 2013. https://books.google.de/books? id=JafyAAAAQBAJ

    work page 2013

  28. [28]

    Optimization by Simulated Annealing,

    S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,”Science, vol. 220, no. 4598, pp. 671–680, May 1983, publisher: American Association for the Advancement of Science. doi: 10.1126/science.220.4598.671. https://www.science.org/ doi/10.1126/science.220.4598.671

    work page doi:10.1126/science.220.4598.671 1983

  29. [29]

    IBM ILOG CPLEX Optimization Studio,

    IBM Corp., “IBM ILOG CPLEX Optimization Studio,” https://www. ibm.com/products/ilog-cplex-optimization-studio

    work page

  30. [30]

    Gurobi Optimizer Reference Manual,

    Gurobi Optimization, LLC, “Gurobi Optimizer Reference Manual,”

    work page

  31. [31]

    https://www.gurobi.com

    work page

  32. [32]

    A comparison of simulated annealing cooling strategies,

    Y . Nourani and B. Andresen, “A comparison of simulated annealing cooling strategies,”Journal of Physics A: Mathematical and General, vol. 31, no. 41, pp. 8373–8385, Oct. 1998, doi: 10.1088/0305-4470/31/41/011. https://iopscience.iop.org/article/10. 1088/0305-4470/31/41/011

    work page doi:10.1088/0305-4470/31/41/011 1998

  33. [33]

    Penalty-free approach to accelerating constrained quantum optimization,

    D. Bucher, J. Stein, S. Feld, and C. Linnhoff-Popien, “Penalty-free approach to accelerating constrained quantum optimization,”Physical Review A, vol. 112, no. 6, Dec. 2025. http://dx.doi.org/10.1103/ fb5m-cl9m

    work page 2025

  34. [34]

    Towards robust benchmarking of quantum optimization algorithms,

    D. Bucher, N. Kraus, J. Blenninger, M. Lachner, J. Stein, and C. Linnhoff-Popien, “Towards robust benchmarking of quantum optimization algorithms,” 2024. https://arxiv.org/abs/2405.07624

    work page arXiv 2024

  35. [35]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010

    work page 2010