{"id":"7df214bd-b0f4-45f9-abe9-3bdcc1d3e416","arxiv_id":"2505.13356","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A hardware-in-the-loop setup running annealer-based power flow and optimal power flow on RTDS matches Newton-Raphson benchmarks on a renewable-integrated nine-bus grid, with OPF solved only by Fujitsu's digital annealer.","lead":"This paper wires a real-time power-grid simulator to quantum and digital annealers and solves power flow and optimal power flow on a small test grid with solar and wind. The runs converge close to classical results, but optimal power flow is executed only on a digital annealer, not on quantum hardware.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"AQOPF constraint encoding is never shown and the NR benchmark solves only power flow; claimed OPF accuracy is unsupported as reported.","rationale":"The reader's weakest assumption—that OPF inequality constraints are encoded via unreported slack variables and penalty weights, and that constraint satisfaction is only inferred from a PF-matching comparison—is exactly the load-bearing concern. The paper's own text in Section II.D admits that slack binary variables are needed, but never supplies the resulting QUBO; Eq. (13) also contains a dimensional typo that puts the displayed Hamiltonian in doubt. Since the central claim is specifically about solving OPF, and the experimental benchmark does not evaluate OPF feasibility or optimality, the evidence in its current form does not substantiate the headline conclusion. This is not an accusation of fraud; the underlying implementation may well be correct, but it is unverifiable from the manuscript. The appropriate disposition is therefore conditional acceptance, requiring the authors to provide the omitted constraint encoding, penalty weights, and a direct validation against a classical OPF solver. This matches the reader's conditional verdict, so no change to the verdict is needed, but our analysis sharpens the specific reason: the comparison to NR is the wrong benchmark for the OPF claim.","tokens_in":13833,"tokens_out":2489,"duration_ms":23708,"concrete_test":"Obtain or reconstruct the full QUBO matrix for the 9-bus AQOPF case, including the slack-variable encoding of constraints (10c)–(10f) and the penalty weights λ0–λ8. Then solve the same OPF with a classical solver (e.g., MATPOWER or pandapower OPF) and compare: (i) the objective values, and (ii) the maximum constraint violations of the AQOPF solutions. As a minimal check, re-run the reported AQOPF experiment and record whether every returned solution satisfies PG_i ∈ [PG_i, PG_i], QG_i ∈ [QG_i, QG_i], V_i ∈ [V_i, V_i], δ_i ∈ [δ_i, δ_i]; if any reported solution violates a limit, the OPF claim fails.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim—that AQOPF „solves OPF“ and matches classical NR benchmarks—rests on the construction of a Hamiltonian H(x) = Hobj + Hconst + Hcost in Eq. (15). This construction is never actually given. Section II.D states that inequality constraints (10c)–(10f) require slack binary variables, but the conversion is not shown, and no penalty weights λ0–λ8 are reported. Moreover, Eq. (13) is dimensionally inconsistent: the third term is λ3·max(0, PG_i − QG_i)^2, mixing active and reactive power (MW with MVAR), which is presumably a typo but it means the displayed penalty Hamiltonian cannot be the one implemented. The validation is also matched to Newton-Raphson, which solves only the power balance equalities (8), not the OPF inequality constraints or the cost objective. That the AQOPF voltage/angle/power values align with NR therefore only demonstrates consistency with the PF equations; it gives no evidence that generation limits, voltage limits, or angle limits are respected, nor that the generation cost is minimized. The paper's own Algorithm 1 also only shows the PF/OPF iteration, not the QUBO encoding. Thus the strongest stated claim—close alignment with classical benchmarks for OPF—is not supported by the reported evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":14094,"tokens_out":7500,"duration_ms":68180,"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":[{"comment":"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.","section":"II.D, Eqs. (13)-(15)"},{"comment":"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.","section":"IV.C, Table VI, Figs. 5-6"},{"comment":"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.","section":"Algorithm 1"},{"comment":"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.","section":"VI"}],"minor_comments":[{"comment":"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.","section":"II.B, Eqs. (10c)-(10f)"},{"comment":"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.","section":"II.D, Eq. (14)"},{"comment":"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.","section":"IV.B, Table V"},{"comment":"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.","section":"Fig. 4"},{"comment":"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.","section":"III.B"},{"comment":"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.","section":"IV.A"}],"recommendation":"major_revision","confidential_remarks":"The paper's principal contribution is the demonstration of a hardware-in-the-loop setup that connects RTDS to quantum and quantum-inspired annealers. This is a legitimate engineering contribution, but the current manuscript does not verify the OPF claims: the OPF Hamiltonian is not completely specified, and the numerical validation compares against a power-flow solver rather than an OPF solver. These issues are fixable within the scope of a revision, so I recommend major revision rather than rejection. The authors should also be careful to distinguish between the new HIL contributions and the reused AQPF/AQOPF algorithms from their prior work [32]; the current manuscript sometimes blurs this line, making it difficult for the reader to identify the novel technical content."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe genuinely new thing here is the QHIL rig itself: RTDS coupled to D-Wave and Fujitsu's QIIO through a Windows middleware, with end-to-end experiments on a 9-bus and a 13-bus system. That is a real system contribution. The measured convergence and the small deviations from Newton-Raphson are consistent with what you would expect if the loop works, and the authors are reasonably candid about current hardware limitations.\n\nWhat is not new is the AQPF/AQOPF formulation, which they take from their earlier Scientific Reports paper [32]. That is fine—reuse of your own algorithm is not a flaw—but it means the contribution is the integration, not the math. The paper is also honest that D-Wave only runs the PF case; the OPF runs on QIIO. The abstract and conclusion blur that distinction, and the claim that 'both' platforms solve OPF with high accuracy is not what the tables show.\n\nThe soft spots are the usual ones for this literature, but they matter. The AQOPF is validated against NR, which solves power balance equalities only. That tells you the PF equations are satisfied, not that the OPF solution is feasible with respect to generation or voltage limits, and not that the cost is minimized. No classical OPF benchmark is used. On top of that, the penalty Hamiltonian in (13) is typo'd—the λ3 term mixes PG and QG—and the slack-variable conversion to QUBO is described in words but never shown. Penalty weights λ0–λ8 are not reported. Any of these alone would be minor; together they mean the OPF accuracy claim is unsupported as written. The stress-test note is right about that.\n\nThese are fixable issues. The bigger one is the missing classical OPF benchmark, which requires either new experiments or a careful rewriting of what exactly is being claimed.\n\nThe paper deserves peer review. It is a testbed paper and the testbed is new. I would send it out, but with a strong note that the AQOPF results need re-validation against a classical OPF solver and the QUBO encoding must be made explicit. A reader who cares about quantum–power-system integration will get value from the experimental setup; a reader looking for evidence of quantum advantage will not find it here, and the paper does not claim it.\n\nRecommendation: major revision. Not a desk reject.","headline":"Genuine quantum-hardware-in-the-loop integration demo, but the OPF validation is not there yet; worth a careful referee, not a desk reject.","tokens_in":14681,"tokens_out":2247,"would_cite":true,"duration_ms":21588,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Quantum annealers match Newton-Raphson in real-time grid test","keywords":["adiabatic quantum computing","quantum annealing","optimal power flow","power flow analysis","QUBO","hardware-in-the-loop","real-time simulation","renewable energy integration"],"falsifier":"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.","tokens_in":13610,"feed_emoji":"⚡","tokens_out":13048,"duration_ms":109527,"temperature":0.7,"pith_summary":"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.","feed_headline":"Quantum annealers match Newton-Raphson in real-time grid test","feed_subtitle":"Quantum and digital annealers solved OPF on a 9-bus grid with solar and wind, within 0.02 degrees of the classical result.","key_machinery":"$\\mathbf{x}$ 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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the discrete combinatorial AQPF and AQOPF formulation and the expanded Hamiltonian that the experiments execute.","marker":"[32]"},{"why":"Provides the theoretical basis for quantum annealing as a solver for Ising and QUBO optimization problems.","marker":"[27]"},{"why":"Shows annealing-based quantum computing applied to combinatorial optimal power flow, the direct precursor this work extends.","marker":"[31]"},{"why":"Offers quantum algorithms tailored to optimal power flow that motivate the AQOPF encoding used here.","marker":"[30]"},{"why":"Demonstrates quantum annealing on the structurally related unit commitment problem, used to justify AQC for OPF.","marker":"[28]"},{"why":"Presents the quantum-in-the-loop architecture for real-time grid simulation that the QHIL framework adapts.","marker":"[35]"},{"why":"Describes a real-time co-simulation testbed for OPF with hardware in the loop, giving the HIL methodology.","marker":"[33]"}],"fun_headline_variants":["Quantum annealers match Newton-Raphson on live 9-bus test","Real-time quantum power flow: annealers match classical","Hardware-in-the-loop: quantum annealers solve grid OPF live","Quantum vs classical on renewable grid: parity in real-time","Quantum annealers match classical on renewable grid in real-time"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Quantum annealers match Newton-Raphson on live 9-bus test","Real-time quantum power flow: annealers match classical","Hardware-in-the-loop: quantum annealers solve grid OPF live","Quantum vs classical on renewable grid: parity in real-time","Quantum annealers match classical on renewable grid in real-time"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001235,"raw_usage":{"total_tokens":5047,"prompt_tokens":893,"completion_tokens":4154,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":509,"completion_tokens_details":{"reasoning_tokens":4067}},"tokens_in":509,"tokens_out":4154,"duration_ms":29410,"temperature":1.0,"reasoning_tokens":4067,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:14:39.870113+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Power flow analysis using quantum and digital annealers: a discrete combinatorial optimization approach,","cited_arxiv_id":null,"evidence_quote":"Supplies the discrete combinatorial AQPF and AQOPF formulation and the expanded Hamiltonian that the experiments execute."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the theoretical basis for quantum annealing as a solver for Ising and QUBO optimization problems."},{"cited_title":"Annealing-based quantum computing for combinatorial optimal power flow,","cited_arxiv_id":null,"evidence_quote":"Shows annealing-based quantum computing applied to combinatorial optimal power flow, the direct precursor this work extends."},{"cited_title":"Quantum Algorithms for Optimal Power Flow","cited_arxiv_id":"2412.06177","evidence_quote":"Offers quantum algorithms tailored to optimal power flow that motivate the AQOPF encoding used here."},{"cited_title":"A quantum computing approach for the unit commitment problem,","cited_arxiv_id":null,"evidence_quote":"Demonstrates quantum annealing on the structurally related unit commitment problem, used to justify AQC for OPF."},{"cited_title":"Architecture for quantum-in-the loop real-time simulations for designing resilient smart grids,","cited_arxiv_id":null,"evidence_quote":"Presents the quantum-in-the-loop architecture for real-time grid simulation that the QHIL framework adapts."},{"cited_title":"Real-time cyber-physical power system testbed for optimal power flow study using co-simulation framework,","cited_arxiv_id":null,"evidence_quote":"Describes a real-time co-simulation testbed for OPF with hardware in the loop, giving the HIL methodology."}],"review_version":1}