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REVIEW 4 major objections 6 minor 35 references

Quantum Hardware-in-the-Loop for Optimal Power Flow in Renewable-Integrated Power Systems

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Quantum annealers match Newton-Raphson in real-time grid test

desk verdict Genuine quantum-hardware-in-the-loop integration demo, but the OPF validation is not there yet; worth a careful referee, not a desk reject. read the letter →

arxiv 2505.13356 v2 pith:7GG6JDQS submitted 2025-05-19 eess.SY cs.NAcs.SYmath.NA

Zeynab Kaseb , Rahul Rane , Aleksandra Lekic , Matthias Moller , Amin Khodaei , Peter Palensky , Pedro P. Vergara This is my paper · ORCID
classification eess.SYcs.NAcs.SYmath.NA
keywords adiabaticquantumcomputingannealingoptimalpowerflowanalysisQUBOhardware-in-the-loopreal-timesimulationrenewableenergyintegration
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 tries to establish that power-flow (PF) and optimal-power-flow (OPF) calculations can be run in a closed loop with actual quantum and quantum-inspired annealing hardware, not just in offline simulation. It couples a real-time digital simulator of an IEEE 9-bus grid, with and without solar and wind farms, to two annealers, encodes the power-balance equations and operational limits as a binary optimization problem, and reports that the decoded voltages, angles, and powers closely match the classical Newton-Raphson benchmark. The reason this matters is that future grids with high renewable penetration will need fast combinatorial optimization inside the control loop; a hardware-in-the-loop proof shows that annealers can at least occupy that role on small systems. The paper claims convergence within a predefined tolerance of $1\times10^{-2}$ for voltage and angle, and explicitly lists scalable qubit access and hardware proximity as current barriers.

What carries the argument

$\mathbf{x}$ is a vector of binary decision variables that discretize the real and imaginary parts of every bus voltage: $\mu_i = \mu_i^0 + x^{\mu}_{i,0}\Delta\mu_i - x^{\mu}_{i,1}\Delta\mu_i$ and $\omega_i = \omega_i^0 + x^{\omega}_{i,0}\Delta\omega_i - x^{\omega}_{i,1}\Delta\omega_i$. Substituting these into the expanded power-balance equations and squaring the mismatches produces the objective Hamiltonian $H_{\text{obj}}(\mathbf{x})$; adding the OPF inequality constraints as penalty terms and the generation cost as a penalty term gives the total Hamiltonian $H(\mathbf{x}) = H_{\text{obj}}(\mathbf{x}) + H_{\text{const}}(\mathbf{x}) + H_{\text{cost}}(\mathbf{x})$, a fourth-order binary polynomial. The inequality constraints enter as penalties of the form $\lambda\max(0,g(x))^2$, which the paper states must be converted with slack binary variables for the available solvers. For the quantum annealer, which accepts only quadratic terms, triple and quadruple products are reduced to quadratic form by introducing auxiliary variables $z_{ij} = x_i x_j$ with penalty functions; the digital annealer handles the higher-order terms directly. The hardware-in-the-loop mechanism is a TCP link between the real-time simulator and the annealers, with a middleware process for the digital annealer, so that demands and renewable outputs leave the simulator, set points return, and the simulation continues.

What would settle it

Retrieve the recorded bitstrings from the AQOPF runs, decode them into voltages, angles, and generator outputs, and test the decoded values against the inequality limits (10c)-(10f). If any decoded solution violates a limit while still matching Newton-Raphson on net powers, the central OPF feasibility claim fails. A complementary check is to feed the decoded set points to a classical OPF solver and compare objective values: a large gap would indicate the annealer found a power-flow-consistent but non-optimal point.

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Extended reading notes

Core claim

On its own terms, the paper claims that the adiabatic quantum power flow (AQPF) and adiabatic quantum optimal power flow (AQOPF) algorithms execute correctly on quantum and quantum-inspired annealing hardware while that hardware is coupled to a real-time digital simulator of the IEEE 9-bus system. For the 9-bus case, the decoded voltage magnitudes and phase angles from the annealers match the classical Newton-Raphson solution within the predefined tolerance, with small mean deviations in active and reactive power; the renewable-integrated 13-bus case gives mean deviations of $6.92\times10^{-2}$ MW and $1.15$ MVAR against Newton-Raphson. The paper further claims that the quantum annealer outperformed the digital annealer by up to 90% in net active and reactive power accuracy for power flow, while the digital annealer compiled and iterated much faster.

Load-bearing premise

The load-bearing premise is that the penalty terms built from slack binary variables make low-energy annealer configurations satisfy the OPF inequality constraints (10c)-(10f); the paper does not display that conversion or directly verify feasibility of the decoded solutions.

Editorial extensions

If this is right

  • Closing the loop around annealing hardware lets quantum solvers be tested under dynamic operating conditions: measured demands and renewable outputs leave the simulator, the annealer returns generator set points, and the simulation continues.
  • At the tested 9-bus and 13-bus scale, annealer solutions track the Newton-Raphson benchmark closely enough to meet the predefined tolerance, so the main barrier to use in grid state estimation is hardware access and scalability, not basic accuracy.
  • Running the same encoding on a quantum annealer and a digital annealer separates algorithmic accuracy from hardware behavior: the quantum annealer was up to 90% more accurate in net powers, while the digital annealer was far faster per compilation and iteration.
  • The renewable-integrated case indicates that variable solar and wind injections can be absorbed by the AQOPF formulation without degrading voltage and angle accuracy beyond tolerance, at least at the tested scale.

Reading between the lines

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

  • A direct check of OPF feasibility would decode the recorded bitstrings and test the generator, voltage, and angle limits; the reported Newton-Raphson comparison certifies power-flow agreement, not constraint satisfaction.
  • If the penalty encoding is made explicit and verified, the same QUBO construction could be carried over to unit commitment, reactive-power planning, or other combinatorial grid problems, since the machinery is generic.
  • The large speed gap between the two annealers suggests a practical hybrid division of labor: let the fast digital annealer propose candidates and let the quantum annealer refine or verify them.
  • The real-time claim is tied to the discretization steps $\Delta\mu$ and $\Delta\omega$: smaller steps would improve accuracy but grow the QUBO variable count, a trade-off the paper leaves implicit.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes a quantum hardware-in-the-loop (QHIL) framework that interfaces the RTDS real-time digital simulator with Fujitsu's digital annealer (QIIO) and D-Wave's Advantage quantum annealer to solve power flow (PF) and optimal power flow (OPF) problems. The PF and OPF problems are encoded as QUBO Hamiltonians using the AQPF and AQOPF algorithms from the authors' prior work, and experiments are reported on an IEEE 9-bus system and a modified 13-bus system with solar and wind generation. The results are compared against Newton-Raphson (NR) power-flow benchmarks, and the authors report small deviations in voltage, phase angle, and active/reactive power, concluding that both quantum and quantum-inspired solvers produce accurate solutions.

Significance. If the OPF results were properly validated, this would be a valuable early demonstration of RTDS coupled with quantum and quantum-inspired annealers for power-system optimization, with potential relevance to future real-time control. The authors do show a working hardware integration and report convergence within a stated tolerance, which is a useful proof-of-concept. However, the current manuscript does not establish that the reported AQOPF solutions are feasible or optimal for the OPF problem, because the validation is performed only against a power-flow solver and because the OPF Hamiltonian encoding is incomplete. The significance is therefore conditional on a corrected and more complete validation.

major comments (4)
  1. [II.D, Eqs. (13)-(15)] The AQOPF Hamiltonian H(x) is not fully specified. The text states that slack binary variables are needed to convert the inequality constraints (10c)-(10f) into a QUBO-compatible form, but this conversion is never shown. The penalty weights λ0–λ8 are not reported, so the relative scaling of Hobj, Hconst, and Hcost is unknown. Furthermore, Eq. (13) contains the term λ3 max(0,P^G_i − Q^G_i)^2, which mixes active and reactive power and is dimensionally inconsistent; this appears to be a typo for an upper-bound penalty on reactive power. As written, the Hamiltonian cannot be reproduced from the manuscript, and the QUBO encoding for AQOPF is not documented in the text. This is load-bearing because the central claim is that AQOPF solves the OPF problem (9)-(10); without the encoding details and penalty parameters, the feasibility and optimality of the reported solutions cannot be assessed.
  2. [IV.C, Table VI, Figs. 5-6] The OPF results are benchmarked only against the Newton-Raphson method. NR solves the power-balance equalities (8) but does not enforce the inequality constraints (10c)-(10f) or minimize the cost objective (9). Agreement with NR therefore demonstrates only that the AQOPF output satisfies the power-flow equations to some tolerance; it does not demonstrate that generation limits, voltage limits, or angle limits are respected, nor that the generation cost is minimized. The authors should benchmark AQOPF against a classical OPF solver (for example, the pandapower OPF module already used in the paper) and report constraint violations, the achieved objective value, and a comparison of generator setpoints. Without this, the claim that AQOPF solves the OPF problem is unsupported.
  3. [Algorithm 1] Algorithm 1 is introduced as the pseudo-code for both AQPF and AQOPF, but the loop only evaluates the power-flow residual Hobj (11). The constraint term Hconst (13) and the cost term Hcost (14) do not appear anywhere in the algorithm. Consequently, as written, Algorithm 1 cannot be the algorithm used for the reported AQOPF experiments. The authors should either extend the algorithm to include the full OPF Hamiltonian or explicitly state that the OPF-specific steps (slack-variable encoding, penalty evaluation) are taken from [32] and provide enough detail in the manuscript for the reader to reproduce the actual optimization.
  4. [VI] The conclusion states that 'both Fujitsu's QIIO and D-Wave's Advantage system (QA) produce solutions with high accuracy, closely aligning with classical NR benchmarks.' However, the reported OPF experiments (Table V) use only QIIO; QA is used only for the AQPF experiments. The OPF results cannot be attributed to both hardware platforms. The conclusion overstates the evidence presented in the manuscript and should be corrected.
minor comments (6)
  1. [II.B, Eqs. (10c)-(10f)] The notation for lower and upper limits is ambiguous because the same symbol is used for the variable and for the bounds. For example, in (10d), QG_i appears as the variable and as both the minimum and maximum limit. Please introduce distinct symbols such as QG_i^min and QG_i^max.
  2. [II.D, Eq. (14)] The rationale for squaring the cost function f_k(P^G_k) in Hcost is not explained. If f_k is nonnegative for all feasible P^G_k, the square is a monotone transform and preserves the minimizer, but this should be stated explicitly, especially since the constraint-penalty derivation refers to equality constraints rather than an objective term.
  3. [IV.B, Table V] The column 'It. Time (s)' is ambiguous: it is not clear whether this is the time per iteration, the total time for all iterations, or the wall-clock time including compilation and communication. For example, the 9-bus AQPF QA row reports 238.48 s with 152 iterations; clarifying the definition would help the reader interpret the scalability discussion.
  4. [Fig. 4] The caption describes a top row with computed values and a bottom row with absolute errors, but the figure appears to contain more than four panels and the subplot layout is not clearly labeled. Please label subfigures (a)–(h) and describe each panel precisely.
  5. [III.B] The statement that 'The RTDS can be directly interfaced with D-Wave's quantum annealer' is unclear, since the actual communication path still involves local Python scripts and a separate computer. Please specify the communication links and the role of the middleware in both the D-Wave and Fujitsu cases.
  6. [IV.A] The modified system is referred to sometimes as the 'IEEE 9-bus with integrated RES' and sometimes as a '13-bus test system.' Please clarify that the RES integration adds buses (with step-up transformers and RL branches) and that the 13-bus system is the modified version used in the experiments.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the QHIL claim is validated against an external NR benchmark; self-citations to [32] are implementation details, not load-bearing premises.

full rationale

The paper's central claim is that a QHIL loop coupling RTDS with D-Wave and Fujitsu annealers can solve PF and OPF, with results close to classical Newton-Raphson. The AQPF objective (11) is the sum of squared power-balance residuals, so minimizing it is a standard reformulation of PF rather than a prediction derived from the answer; the comparison to NR is an external sanity check, not a fitted target. No parameter is fitted to the NR output and then renamed a prediction. The AQOPF construction (13)-(15) is never fully specified—the slack-variable conversion of inequalities is admitted but not shown—and comparing OPF results against an NR power-flow benchmark does not validate inequality feasibility or cost optimality; however, these are gaps in evidence and correctness, not circularity by construction. The paper repeatedly defers to prior work [32] by the same authors for the expanded fourth-order binary formulation and algorithm details. That self-citation is real but not load-bearing for the new hardware-in-the-loop claim: the present experiments re-run the algorithms on new hardware and compare against an independent classical solver, so the central result does not reduce to the cited paper's authority. Under the rule that externally falsifiable, code-reproduced results do not raise the circularity score, the self-citation does not constitute circularity. Overall, no step in the claimed derivation chain is equivalent to its input by definition.

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

The central claim rests on hand-chosen step sizes, unreported penalty weights, and hardware behavior assumptions. The discretization and penalty parameters are the main free choices; no physical constants are fitted and no new entities are introduced.

free parameters (5)
  • Discretization steps delta_mu and delta_omega = 1e-2 and 1e-3
    Algorithm 1 sets these step sizes; they control the resolution of the voltage search and were chosen by hand.
  • Penalty weights lambda_0 through lambda_8 = not reported
    Equations (13) and (14) introduce eight penalty weights that balance feasibility and cost objective; no values or tuning procedure are given, yet the QUBO behavior depends on them.
  • Convergence tolerance epsilon = 1e-2
    Algorithm 1 defines epsilon = 1e-2 as the stopping threshold for power mismatch; all convergence claims are relative to this chosen threshold.
  • Number of readouts = 5000
    Every annealer call returns 5000 samples; the best-solution selection is not specified, so the readout count is a choice affecting result quality.
  • Maximum iterations it_max = not specified
    Algorithm 1 references it_max but the value is never given, so the stopping criterion is incompletely defined.
assumptions (5)
  • standard math Power balance equations (8) describe steady-state operation; the Y-bus formulation from (1)-(3) is accepted network theory.
    The PF and OPF objectives follow from standard circuit laws, which are not re-derived here.
  • domain assumption RES units with voltage controllers can be modeled as PV buses in the PF/OPF formulation.
    The paper states this in Section IV-A, and the RTDS models are assumed to hold constant voltage at the RES buses.
  • domain assumption Quantum and digital annealers return low-energy states that solve the QUBO with high probability when the number of readouts is large enough.
    The QHIL validation depends on annealer behavior; no chain-break statistics or sampling distributions are reported.
  • standard math The higher-order-to-quadratic reductions (19)-(21) preserve the minimum of the original polynomial when the auxiliary penalty is large enough.
    Used to map the fourth-order PF/OPF polynomial to QUBO; the paper then neglects some auxiliary variables.
  • ad hoc to paper Squaring the cost function in Hcost (14) preserves the optimal dispatch.
    Costs are positive, so the transform is monotone, but this is an unstated modeling choice for the penalty Hamiltonian.

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Cite this review

Pith. "Pith review of Quantum Hardware-in-the-Loop for Optimal Power Flow in Renewable-Integrated Power Systems." pith.science (2026). https://pith.science/paper/7GG6JDQS

@misc{pith2026250513356,
  author       = {Pith},
  title        = {Pith review of: Quantum Hardware-in-the-Loop for Optimal Power Flow in Renewable-Integrated Power Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7GG6JDQS}},
  note         = {Machine review of arXiv:2505.13356}
}
read the original abstract

Quantum computing has emerged as a promising computational paradigm to address unresolved challenges in the modeling and control of modern power systems. However, most existing studies focus on offline simulations, and a practical framework for validating quantum algorithms in real-time operational environments remains lacking. This study proposes a quantum hardware-in-the-loop framework that integrates a real-time digital simulator with quantum and quantum-inspired hardware to solve combinatorial power flow and optimal power flow formulations under dynamic operating conditions. The proposed framework is validated using the IEEE 9-bus test system and a modified version with integrated solar and wind farms. The results confirm successful integration and convergence within a predefined tolerance. The study also identifies key limitations and challenges, such as limited access to quantum and digital annealers and current scalability limitations, that must be considered in future developments. Nevertheless, the results highlight the potential of quantum computing to significantly enhance the modeling and control of future power systems with high penetration of renewable energy sources.

Figures

Figures reproduced from arXiv: 2505.13356 by the authors.

Figure 1
Figure 1. Computational and information flow within the QHIL framework [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Hardware configuration of the proposed QHIL framework for real-time [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. IEEE 9-bus test system with integrated RES. The system includes [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: PF results for the IEEE 9-bus system using the AQPF algorithm on QA and QIIO, compared to the classical NR method. The top row shows the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: OPF results for the IEEE 9-bus system using the AQOPF algorithm on QIIO, compared to the classical NR method. The top row shows the computed [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: OPF results for the IEEE 9-bus system with integrated RES using the AQOPF algorithm on QIIO, compared to the classical NR method. The top [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

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    2023

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.