{"id":"2a5586d9-57f2-48e8-a795-8a0293f7aa9b","arxiv_id":"2412.06177","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Preconditioned HHL and VQLS can solve small DC and AC optimal power flow cases with solution costs equal to those from a classical interior point method.","lead":"The paper applies two quantum linear solvers, HHL and VQLS, with classical preconditioning, to solve small optimal power flow (OPF) problems. The simulations show these hybrid methods converge to the same optimal cost as the classical interior point solver on the tested MATPOWER cases.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's central empirical claim relies on an unspecified Hermitian encoding and preconditioning of the KKT system; without this, the reported HHL/VQLS results are not reproducible and may reflect a classical solve.","rationale":"The reader identified the same weakest assumption: the Hermitian/preconditioned encoding of Eq. (2) is never specified. I agree. This is load-bearing because HHL and VQLS cannot operate on an arbitrary non-Hermitian, non-normalized matrix. The paper's reported exact agreement of costs (746.25 etc.) and near-identical iteration counts is suspicious: an approximate quantum solve would typically perturb the search direction slightly, altering the outer iterations or final cost. Without reporting the approximation error, condition numbers, or quantum execution details, the equal iteration counts suggest the linear systems may have been solved exactly, effectively classically. The limitations section honestly notes qubit requirements and numerical instability, but that does not fill the gap. A concrete check—requesting the explicit Hermitian form and reproducing Table I with an exact solver—would settle whether the reported results are genuine. I do not see a need to change the reader's CONDITIONAL verdict; the conditions should include full disclosure of the encoding, conditioning, and quantum-simulation parameters.","tokens_in":7546,"tokens_out":6010,"duration_ms":61207,"concrete_test":"Request the explicit Hermitian encoding and ILU-preconditioned matrix for case3 DC-OPF at iteration 1: give the matrix A' used as input to VQLS/HHL, its dimension, Pauli decomposition, norm, and condition number. Then independently run the same SC-PDIPM loop using those matrices with an exact classical linear solver for all iterations and compare the resulting outer iteration counts and costs to Table I. If the condition number is large (>10^3) or the Pauli decomposition has exponential terms, or if the exact classically solved trajectory does not reproduce the reported costs, the central claim fails. As a minimal check, request the VQLS optimization curves and HHL measurement statistics for one iteration to confirm that a genuinely quantum (or simulated-quantum) solve was performed rather than a direct classical solve.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that preconditioned HHL and VQLS match SC-PDIPM costs (Table I: 746.25, 2393.31, 4131.03) and iteration counts—depends on the KKT system (Eq. 2) being solvable by HHL/VQLS. Both algorithms require the coefficient matrix to be Hermitian, have bounded norm (typically ||A||≤1 for VQLS), and be representable as a linear combination of unitaries (VQLS) or efficiently block-encoded (HHL). The paper never describes this encoding. The KKT matrix (2) is symmetric but indefinite, its (2,2) block [μ/Z] changes by orders of magnitude as the barrier parameter γ→0, and ILU left-preconditioning M^{-1}A is generally non-symmetric, so it cannot be fed directly to HHL/VQLS. If the authors instead embed the system in a Hermitian form (e.g., [[0,M^{-1}A],[(M^{-1}A)^†,0]]), the dimension and qubit count double and the condition number changes; none of this is reported. No condition numbers, Pauli-term counts, VQLS ansatz/optimizer settings, or HHL error parameters are given. As a result, the equality of iteration counts to the classical solver cannot be explained by an approximate quantum solve; the most parsimonious explanation is that the 'quantum' search directions were computed classically to machine precision. This makes the central empirical claim unreproducible and unverified.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes hybrid quantum-classical solvers for optimal power flow (OPF) by replacing the classical linear-system solve inside a step-controlled primal-dual interior-point method (SC-PDIPM) with HHL or VQLS, using ILU left preconditioning. The authors report simulations on small MATPOWER cases (case3, case6ww, case9 for DC-OPF, and case3 for AC-OPF) and claim that the quantum-assisted methods produce the same optimal costs and similar iteration counts as the classical SC-PDIPM solver, with preconditioning controlling the growth of the condition number.","tokens_in":7931,"tokens_out":3158,"duration_ms":35555,"significance":"If substantiated, the result would be a useful empirical step toward hybrid quantum-classical OPF solvers and would directly address the concern raised by Pareek et al. about the poor asymptotic scalability of HHL for power-flow problems. The comparison against MATPOWER's classical solutions is an external benchmark, so the central empirical claim is not circular. The use of standard test cases and the focus on preconditioning are sensible and relevant to the quantum-optimization community. However, the manuscript currently lacks the essential algorithmic details needed to verify that a quantum linear-system solve actually took place: no Hermitian encoding of the KKT system is described, no condition numbers are reported, and no error tolerances or readout procedures are given. As written, the reported agreement in iteration counts and costs is not reproducible and could be explained by a classical solve of the search-direction system.","major_comments":[{"comment":"The manuscript never specifies how the KKT linear system in Eq. (2) is encoded as an operator suitable for HHL or VQLS. The KKT matrix is symmetric but indefinite, its (2,2) block [μ/Z] varies by orders of magnitude as the barrier parameter γ changes, and left ILU preconditioning produces the generally non-symmetric matrix M^{-1}A. VQLS, as stated in §IV-B, requires A to be a linear combination of Hermitian unitaries with bounded norm (typically ||A||≤1), and HHL requires a Hermitian or block-encoded operator with bounded norm. The authors must describe the actual encoding used (for example, a doubled Hermitian embedding), the resulting qubit count, the number of Pauli terms, the norm scaling, and the condition number after preconditioning for each test case. Without this information, the equivalence of iteration counts in Table I cannot be attributed to a quantum solve.","section":"§V, Algorithm 2 line 9; §IV-B; Eq. (2)"},{"comment":"No stopping criteria, error tolerances, or readout procedures are reported for the inner HHL/VQLS solves. The SC-PDIPM outer loop requires a search direction Δ = (ΔX, ΔZ, Δλ, Δμ); it is never explained how the quantum state |x⟩ is converted into these classical vectors, nor how approximation error in that readout affects the convergence conditions (feascond, gradcond, compcond, costcond). The paper should report the inner-solve tolerance, the number of VQLS outer iterations, the ansatz depth, the optimizer settings, and the HHL phase-estimation precision for each case, together with a sensitivity study showing how perturbing the search direction changes the reported iteration counts.","section":"§VI, Table I; Algorithm 2"},{"comment":"The claim that preconditioning leads to 'controlled growth in the condition number' is not supported by any numerical evidence. No condition numbers are given for the original KKT matrix or for the preconditioned system, for any test case. Since the stated complexity of HHL is O(log(N) s^2 κ^2/ε) and VQLS performance also degrades with κ, reporting κ before and after ILU preconditioning is essential to evaluate whether the quantum part is feasible at all. The authors should add a table or figure with these values.","section":"§VI, Figures 1–4; §V"},{"comment":"The empirical basis is very small: only three DC-OPF cases and one AC-OPF case, with HHL missing for case9 and entirely missing for AC-OPF. The conclusion that 'quantum approaches are comparable to classical approaches' is stronger than the data support. Either restrict the conclusion to the tested instances or add more cases and error bars on the reported costs and iteration counts.","section":"§VI, Table I and Table II"}],"minor_comments":[{"comment":"There are several typographical errors, including 'quadricatically', 'acutal', 'pseduo-code', 'f alse', and 'SC-PDIM' in place of 'SC-PDIPM'. These should be corrected in a revision.","section":"Throughout"},{"comment":"The dash for HHL in the case9 row is unexplained; the text in §VI discusses Figure 3 only for classical and VQLS, so the reader cannot tell whether HHL failed, was not run, or was omitted for another reason. Please clarify.","section":"Table I"},{"comment":"The figures do not include axis labels or error bars, and the text describing 'slight variations' and 'fluctuations' is qualitative. Adding labeled axes and, where possible, error bars or multiple runs would improve interpretability.","section":"§VI, Figures 1–4"},{"comment":"The abstract states that the results 'substantially improve the results in [1]', but no quantitative comparison with [1] is provided anywhere in the paper. Either include that comparison or soften the claim.","section":"Abstract and §VI"}],"recommendation":"major_revision","confidential_remarks":"The central concern is reproducibility: the current text does not establish that a quantum linear-system solver was actually used for the reported iteration counts. This is fixable if the authors disclose the encoding, preconditioning details, condition numbers, and inner-solver tolerances. I also note heavy reliance on the authors' own prior work [1] without a quantitative baseline; this is not disqualifying but should be clarified."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What's new here is narrow but real: the authors drop preconditioned HHL and VQLS into the search-direction solve of an interior-point OPF loop and report that on three tiny MATPOWER cases the resulting costs match classical SC-PDIPM. The iteration counts are equal or within one of classical, and the gradcond plots show similar convergence. That is a legitimate data point for hybrid quantum-classical optimization, and the paper is honest about its limits: they only did case3, 6ww, 9 for DC-OPF and case3 for AC-OPF, and they say larger cases are out of reach. The comparison is against external classical solutions, so the central result is not circular. Credit where due: the combination of ILU preconditioning with VQLS inside an OPF loop appears to be new, and the empirical agreement, if it holds up, is useful evidence that quantum linear solvers are not automatically useless inside interior-point methods.\n\nNow the soft spots, and one of them is load-bearing. The paper never describes how the KKT matrix from Eq. (2) is encoded for HHL or VQLS. That matrix is symmetric but indefinite, and the [mu/Z] block changes by orders of magnitude as the barrier parameter shrinks. The authors say they use left ILU preconditioning, but M^{-1}A is generally non-symmetric, so it cannot be fed directly to HHL or VQLS as-is. If they embed it in a Hermitian form like [[0, M^{-1}A], [(M^{-1}A)^†, 0]], the dimension doubles and the condition number changes; none of that is reported. No condition numbers, no Pauli-term counts, no VQLS ansatz or optimizer settings, no HHL precision parameters, no error bars. Without those, I cannot tell whether the reported equal costs reflect a genuine approximate quantum solve or a solve that is effectively classical to machine precision. The stress-test note makes this point forcefully, and after reading the paper I think it lands.\n\nThe other weaknesses are more minor. The HHL entry for case9 is missing with no explanation. The AC-OPF results cover only one case. And the novelty over the authors' own load-flow paper [1] and prior quantum DC-OPF work is incremental, though the specific OPF-plus-preconditioning combination is new. The complexity theory from [10] is cited but not engaged numerically; the paper does not claim to overturn it, so this is a limitation rather than a flaw.\n\nWho is this for? Readers working on hybrid quantum solvers for power systems will want to know this exists, but they will need the missing details before trusting the table. A serious referee could help extract those details. I would not cite it in my own work yet because the reproducibility bar is not met.\n\nRecommendation: send it to peer review. It is small and incomplete, but the question is timely, the experiment is well-defined, and the missing information is fixable. A good referee should push for the encoding, conditioning data, and error bars, and should also ask for at least one run with a deliberately noisy/crude quantum readout to show the method still behaves like an approximate solver.","headline":"A small, honest empirical study that plausibly shows preconditioned VQLS/HHL can match classical OPF costs on tiny cases, but it omits the exact encoding and conditioning details needed to make the result reproducible or to rule out a semiclassical solve.","tokens_in":8450,"tokens_out":1139,"would_cite":false,"duration_ms":13812,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P68","90C51"],"pacs":[],"model":"deepseek-v4-flash","headline":"For the small power-flow problems tested, preconditioned HHL and VQLS reproduce the classical optimal cost and iteration counts.","keywords":["optimal power flow","quantum linear systems","HHL algorithm","variational quantum linear solver","interior point methods","preconditioning","AC-OPF","DC-OPF"],"falsifier":"Rerun one of the reported cases while recording the condition number and residual of the preconditioned KKT system before every interior-point step; if the preconditioned matrix is too ill-conditioned for the quantum error bounds to hold, or if the approximate search direction fails to reduce gradcond on a fresh test case, the parity claim is refuted.","tokens_in":7343,"feed_emoji":"⚡","tokens_out":9561,"duration_ms":84128,"temperature":0.7,"pith_summary":"The paper asks whether the search-direction solves inside an interior-point optimal power flow solver can be replaced by quantum linear-system algorithms without losing accuracy. On the small direct-current (DC-OPF) cases it could simulate, preconditioned HHL (a quantum linear-system algorithm) and VQLS (a variational quantum linear solver) converge to the same generation cost as the classical solver, matching the classical iteration count on the smallest case and adding one iteration on another. On the one small alternating-current (AC-OPF) case it could run, VQLS again matches the classical cost and iteration count. The authors' conclusion is not that quantum solves are faster, but that they are accurate enough at this scale to justify further work on scaling the hybrid approach.","feed_headline":"Hybrid quantum solvers match classical on small power-flow tests","feed_subtitle":"Preconditioned HHL and VQLS reach the same optimal cost as the classical interior-point solver on small test cases.","key_machinery":"The load-bearing object is the KKT linear system (Eq. 2) that an interior-point method solves at every iteration to obtain the Newton search directions ($\\Delta X$, $\\Delta Z$, $\\Delta \\lambda$, $\\Delta \\mu$). The hybrid method replaces the classical solve of this system with a quantum linear-system algorithm: HHL as a direct quantum solver and VQLS as a variational one. Left preconditioning with incomplete LU factorization is applied before the quantum solve, and the paper argues that this controls the condition number whose growth dominates HHL's complexity. The convergence measure gradcond ties the approximate quantum search directions to the classical convergence criteria.","core_discovery":"The paper's central claim is that the KKT linear system arising inside a step-controlled primal-dual interior-point method for optimal power flow can be preconditioned and then solved with HHL or VQLS, and that the resulting hybrid algorithm reaches the same optimal cost as the classical solver on the test cases it could simulate. The reported costs match exactly in every completed run — 746.25 (DC case 3), 2393.31 (case 6ww), 4131.03 (case 9), and 758.21 (AC case 3) — with quantum iteration counts equal or one above the classical counts. The paper presents these runs as a substantial improvement over the earlier load-flow results in [1], and as evidence that the condition-number growth identified in [10] can be contained by ILU preconditioning. It does not claim an asymptotic speedup; the claim is parity and viability at small scale.","pith_inferences":["The paper never reports condition numbers or the precise oracle encoding of the non-Hermitian KKT matrix; measuring both on the same four cases would separate the value of preconditioning from the value of the quantum solver.","Because VQLS convergence depends on the classical optimizer and the ansatz, the equal costs on tiny cases do not yet reveal how error scales with system size; a controlled test with artificial matrices of known condition number would be the natural next benchmark.","Interior-point methods for other network optimization problems, such as gas or water networks, have the same KKT structure, so the same preconditioned hybrid pattern is a transferable template if the parity result holds."],"forward_implications":["If the parity holds beyond the four test cases, a practical division of labor emerges: classical globalization from the interior-point method plus an approximate quantum KKT solve is enough to reach the true optimum.","The preconditioning result isolates the condition number as the manageable bottleneck, so better preconditioners may extend the parity to larger DC-OPF cases and to more AC-OPF cases.","Since iteration counts are equal or within one, the number of quantum solves required is roughly the same as the number of classical solves, so the cost of read-in and read-out, rather than iteration count, becomes the main scaling question."],"supporting_citations":[{"why":"Earlier hybrid quantum load-flow results that this paper's OPF simulations improve on.","marker":"[1]"},{"why":"Complexity study of HHL for DC power flow that motivates replacing HHL and containing condition-number growth.","marker":"[10]"},{"why":"Introduces VQLS, the variational quantum linear solver used as the hybrid quantum step.","marker":"[11]"},{"why":"Introduces ILUT preconditioning, used to contain condition-number growth before the quantum solve.","marker":"[12]"},{"why":"Supplies the standard power-system test cases and the classical solver comparison used in the simulations.","marker":"[18]"},{"why":"Defines the step-controlled primal-dual interior-point method whose KKT system is solved by the quantum algorithms.","marker":"[19]"},{"why":"Introduces the HHL quantum linear-system algorithm used for the search direction.","marker":"[24]"}],"fun_headline_variants":["Quantum + HHL/VQLS matches classical OPF cost on small grids","Preconditioned HHL and VQLS tie classical on power-flow small cases","Small-scale quantum power flow hits same optimal cost as classical","Hybrid quantum algorithms achieve parity with classical OPF at small scale","HHL and VQLS solve power flow as well as classical on tiny grids"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The comparison stands on the assumption that an approximate solution read out of HHL or VQLS for the preconditioned KKT system is accurate enough for the interior-point method to keep converging to the true optimum; the paper's own limitations section restricts the tests to three small DC cases and one AC case because of qubit count and numerical instability, and the condition numbers and quantum residuals are never reported.","fun_headline_variants_meta":{"raw":{"variants":["Quantum + HHL/VQLS matches classical OPF cost on small grids","Preconditioned HHL and VQLS tie classical on power-flow small cases","Small-scale quantum power flow hits same optimal cost as classical","Hybrid quantum algorithms achieve parity with classical OPF at small scale","HHL and VQLS solve power flow as well as classical on tiny grids"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000476,"raw_usage":{"total_tokens":2279,"prompt_tokens":784,"completion_tokens":1495,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":400,"completion_tokens_details":{"reasoning_tokens":1408}},"tokens_in":400,"tokens_out":1495,"duration_ms":10279,"temperature":1.0,"reasoning_tokens":1408,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T19:55:13.733499+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rerun one of the reported cases while recording the condition number and residual of the preconditioned KKT system before every interior-point step; if the preconditioned matrix is too ill-conditioned for the quantum error bounds to hold, or if the approximate search direction fails to reduce gradcond on a fresh test case, the parity claim is refuted.","supporting_citations":[{"cited_title":"A hybrid quantum algorithm for load flow","cited_arxiv_id":null,"evidence_quote":"Earlier hybrid quantum load-flow results that this paper's OPF simulations improve on."},{"cited_title":"Ilut: A dual threshold incomplete lu factorization","cited_arxiv_id":null,"evidence_quote":"Introduces ILUT preconditioning, used to contain condition-number growth before the quantum solve."},{"cited_title":"Matpower: Steady-state operations, planning, and analysis tools for power systems research and education","cited_arxiv_id":null,"evidence_quote":"Supplies the standard power-system test cases and the classical solver comparison used in the simulations."},{"cited_title":"On computational issues of market-based optimal power flow","cited_arxiv_id":null,"evidence_quote":"Defines the step-controlled primal-dual interior-point method whose KKT system is solved by the quantum algorithms."},{"cited_title":"Harrow, Avinatan Hassidim, and Seth Lloyd","cited_arxiv_id":null,"evidence_quote":"Introduces the HHL quantum linear-system algorithm used for the search direction."}],"review_version":1}