{"id":"ad660806-f95b-43be-8e40-f66440f6a045","arxiv_id":"2507.06862","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"On small water distribution networks, a quantum-classical hybrid using VQLS reproduces EPANET pressures and flows, while HHL fails and quantum annealing gives only approximate results.","lead":"The paper tests three quantum algorithms (VQLS, HHL, and QUBO-based annealing) as replacements for the linear solver inside the standard Newton-Raphson water network simulator, on tiny 2-loop and 3-node networks. The hybrid VQLS approach matched classical EPANET results, while HHL failed and quantum annealing produced usable but noisy results, suggesting hybrid quantum-classical methods are the most plausible near-term route for this problem.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The VQLS-vs-HHL comparison in §3.1 lacks measured condition numbers and inner-solver residuals, leaving the paper's central explanation under-evidenced.","rationale":"The reader's weakest assumption is the same one I identify: the conditioning of the inner linear systems and the lack of quantitative verification of the VQLS solves. This concern is load-bearing because the paper's central conclusion is not merely that QNR-VQLS matches EPANET on small instances, but that a quantum linear solver is serving as a working NR-GGA subroutine while HHL is not. The performance of both VQLS and HHL depends on the condition number spectrum of the linear systems encountered, so the absence of condition-number measurements and per-iteration residuals leaves the mechanism unverified. I do not require a scaling demonstration for the small-instance feasibility claim; the missing diagnostics already affect the small-instance comparison. The paper's open-source code is a positive and independently checkable asset, and the limitations are partially acknowledged, but the conditional verdict is appropriate until the inner-solver quantities are reported and used to test the proposed explanation.","tokens_in":6606,"tokens_out":10216,"duration_ms":122977,"concrete_test":"Instrument the released QNR code to log, for every NR-GGA iteration in a stratified subset of 50 scenarios spanning the tested pipe and demand ranges: the spectral condition number of the inner linear system, the VQLS relative residual ||A x - b||/||b|| after optimization, and the HHL truncation/cutoff parameter. Then replot Figs. 1-2 with points colored by condition number. The conditioning explanation is supported only if HHL failures occur for high condition numbers beyond its cutoff while VQLS residuals remain small in the same scenarios; if HHL fails at low condition numbers or VQLS succeeds despite large residuals, the comparative claim needs revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is comparative: QNR-VQLS succeeds while QNR-HHL fails, and the paper attributes HHL's failure to the condition numbers of the inner linear systems exceeding the fixed HHL circuit's capability. That attribution is load-bearing because it is what turns the scatter plots into a conclusion about which quantum linear-solver subroutine is suitable for NR-GGA. However, the paper never reports the condition number of the inner system matrix at any NR-GGA iteration, never reports the VQLS relative residual or fidelity for those solves, and never reports the eigenvalue truncation level used in HHL. Without these diagnostics, two concrete failure modes remain: (1) HHL's failure may reflect an under-powered fixed circuit rather than intrinsic ill-conditioning of the hydraulics systems, and (2) QNR-VQLS's final pressure agreement may be accompanied by per-iteration inner-solver errors that the outer NR-GGA iteration happens to tolerate, in which case the inferred mechanism 'VQLS correctly solves the linear systems' is not established. The paper explicitly lists dynamic circuit recreation as future work, so the HHL comparison is implementation-specific. This is not an internal inconsistency, but it is the least secured premise of the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an early feasibility study of using quantum computing algorithms as subroutines in the Newton-Raphson Global Gradient Algorithm (NR-GGA) for water distribution network (WDN) modeling. The authors implement three quantum linear-system subroutines within QNR: VQLS, HHL, and a QUBO-based linear solver, and benchmark them against EPANET reference pressures and flowrates on a 7-node, 2-loop network. They also explore replacing NR-GGA entirely with a higher-order QUBO formulation solved by simulated annealing, for both direct WDN simulation and least-cost design on a small 3-node network. The main empirical claim is that QNR-VQLS reproduces the reference values across a wide range of pipe parameters, QNR-HHL fails to converge to within 10% accuracy, and QNR-QUBO performs similarly to VQLS but with outliers. All gate-based simulations are run on noiseless quantum emulators, and the code is released open-source.","tokens_in":6840,"tokens_out":2689,"duration_ms":29145,"significance":"If the central claim holds, the paper would be a useful proof-of-concept that a variational quantum linear solver can serve as a subroutine in standard hydraulic network solvers, at least for very small instances. The work is commendable for benchmarking against an external classical reference (EPANET), and for making the implementation publicly available on GitHub, which strengthens reproducibility. However, the significance is currently limited by the absence of quantitative accuracy metrics, missing condition-number and inner-solver diagnostics, and the speculative scaling statements. The paper is a plausible feasibility demonstration rather than a quantitative comparative evaluation, and its conclusions about the relative merits of VQLS versus HHL are not yet backed by the reported evidence.","major_comments":[{"comment":"The central comparative claim is that QNR-HHL fails because the condition numbers of the inner linear systems along the Newton-Raphson trajectory exceed the capability of the fixed HHL circuit, but the paper never reports condition numbers for any NR-GGA iteration, nor the HHL eigenvalue truncation level, nor the accuracy/residual of the HHL solve at any step. Without these diagnostics, the explanation is not established: the failure could be due to an under-powered fixed circuit rather than intrinsic ill-conditioning of the hydraulics systems. This is load-bearing for the paper's conclusion that HHL is more suitable for fault-tolerant quantum computers, so the authors should either measure these quantities or explicitly present the HHL comparison as implementation-specific rather than as evidence about conditioning.","section":"3.1 (HHL paragraph, Fig. 2)"},{"comment":"The statement that QNR-VQLS results are 'in very good agreement' and that QNR-QUBO has 'a few outliers' is supported only by visual inspection of scatter plots; the paper reports no quantitative metrics such as R², mean absolute error, maximum deviation, or the fraction of points within the 10% tolerance for any of the three QNR variants. Since the conclusion ranks the subroutines by accuracy, these numerical measures are necessary to substantiate the ranking, especially the claimed small difference between VQLS and QUBO.","section":"3.1 (VQLS and QUBO-LS results, Figs. 1 and 3)"},{"comment":"The sentence 'Since variational quantum algorithms have access to a more complex parameter space compared to classical machine learning algorithms of the same size, it is expected that QNR-VQLS will scale well' is a speculative extrapolation that is not derived from any measurement, scaling analysis, or cited theoretical result. As stated, it overstates what the experiments can support and should be removed or substantially qualified with an explicit scaling test or a reference to a rigorous complexity bound.","section":"3.1 (VQLS scaling paragraph)"},{"comment":"The higher-order QUBO results are reported only through representative scatter plots and qualitative statements about 'reasonable results' and 'pronounced local minima'. For a feasibility assessment, the paper should quantify the success rate (e.g., number of annealing runs reaching the 10% tolerance or the exact least-cost configuration), the spread of energies, and the number of runs used. Without these numbers, the claim that the approach is 'technically feasible' for LCD remains anecdotal rather than demonstrated.","section":"3.2 (Fig. 4) and 3.3 (Fig. 5)"}],"minor_comments":[{"comment":"The terminology '0-loop network' is used in Figs. 4 and 5 without definition; the text in Section 3.3 refers to a '3-node network with 2 pipes', which likely corresponds to a tree network, but this should be stated explicitly.","section":"2.3 and 3.3"},{"comment":"The solver naming is inconsistent: 'QUBO-LS', 'QNR-QUBO', and 'QNR-QUBOLS' are used interchangeably; the authors should pick one name and use it consistently.","section":"Throughout"},{"comment":"There are several typographical errors, e.g., 'Babayen' should likely be 'Babayan', and the affiliation lines contain misspellings such as 'esiencecenter.nl' and 'Netherland eScience Center'; these should be corrected in a revision.","section":"References and text"},{"comment":"The phrase 'from increasing the accuracy of the quantum circuit, and therefore the number of qubit and the compute time' contains a grammar error ('qubit' should be 'qubits') and should be rephrased for clarity.","section":"3.1 (HHL paragraph)"}],"recommendation":"major_revision","confidential_remarks":"The paper is a feasibility study aimed at a conference proceedings, and the general direction is reasonable for the venue. The main concern is that the comparative conclusion between VQLS and HHL—which is central to the paper's message—rests on an unmeasured explanation. However, the required fixes are within the paper's scope: adding condition numbers, residuals, and quantitative accuracy metrics would address most of the concerns. The speculative scaling statement should also be tempered. I would not reject the paper, but it needs a substantial revision to support its claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my read. The paper is a small-scale feasibility test: it takes three existing quantum linear-solver subroutines (VQLS, HHL, QUBO-LS) and drops them into the Newton-Raphson Global Gradient Algorithm for water distribution networks, then checks results against EPANET on a 7-node, 2-loop network. The VQLS variant tracks EPANET well across a range of pipe parameters. That combination is new as an application, even though no new algorithm is proposed. The open-source code and the benchmark against a standard engineering tool are real pluses.\n\nThe paper does not oversell. The conclusion is careful and the limitations are stated. That said, the central comparative claim is only partly supported. The authors attribute HHL's failure to the condition numbers of the inner linear systems, but they never measure those condition numbers, never report the VQLS residual or fidelity, and never report the HHL eigenvalue truncation. So the mechanism is plausible, not demonstrated. The stress-test note is right: the scatter plots show VQLS works on a small network, but the \"why\" is under-evidenced. Also missing are error bars and quantitative accuracy metrics; the scaling argument for VQLS is speculation.\n\nThese are real weaknesses but not fatal for a feasibility study. The claim \"QNR-VQLS can reproduce EPANET results on a small network\" is supported by the data. The quality drops when they try to explain why HHL fails and why VQLS would scale.\n\nFor a referee, I'd ask for condition numbers, residuals, and a clearer statement that scalability is untested. I would not desk-reject this. It's a legitimate engineering application paper for a niche audience: quantum-application researchers and water-network modelers. The code is reusable. I'd accept it for peer review with major revisions, and I'd want the authors to either measure the conditioning or soften the HHL explanation.","headline":"A modest but honest feasibility demo of quantum linear solvers inside NR-GGA for water networks; the VQLS result looks real, the HHL failure explanation is under-evidenced.","tokens_in":7327,"tokens_out":2269,"would_cite":false,"duration_ms":24098,"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":"QNR-VQLS, a Newton-Raphson solver with a variational quantum linear subroutine, reproduces EPANET pressures and flowrates on a 7-node water network.","keywords":["water distribution networks","Newton-Raphson global gradient algorithm","variational quantum linear solver","quantum annealing","QUBO","least-cost design","EPANET"],"falsifier":"Run the identical 7-node, 2-loop stability tests on a real gate-based quantum processor with standard error mitigation: if QNR-VQLS fails to keep pressures and flowrates within the 10% tolerance of EPANET across the tested pipe-length, diameter, roughness, and demand ranges, the emulator-based success does not transfer to real hardware.","tokens_in":6446,"feed_emoji":"💧","tokens_out":9438,"duration_ms":94256,"temperature":0.7,"pith_summary":"The paper tries to establish that a standard water distribution network model can be solved with quantum help today, at least on small networks. It builds a hybrid solver, QNR-VQLS, by taking the classical Newton-Raphson Global Gradient Algorithm and replacing its inner linear-system solve with the variational quantum linear solver. On a 7-node, 2-loop network, with hundreds of scenarios varying pipe length, diameter, roughness and demand, QNR-VQLS reproduces EPANET reference pressures and flowrates within tolerance. The same structure with HHL as the inner solver fails, and the QUBO-based version works except for outliers. The paper concludes that hybrid quantum-classical methods are the near-term route, and separately shows that quantum annealing can formulate the least-cost design of a 3-node network.","feed_headline":"Variational quantum solver matches EPANET on water networks","feed_subtitle":"A variational quantum linear solver inside Newton-Raphson reproduces EPANET results; HHL fails.","key_machinery":"The machine that carries the argument is the Newton-Raphson Global Gradient Algorithm, an iterative solver for the nonlinear system of pressure and flow equations in a water distribution network. At each iteration NR-GGA needs to solve a linear system for a gradient step, and the paper swaps that inner solve among three quantum subroutine candidates: the variational quantum linear solver, a parameterized quantum circuit whose parameters are trained classically; the HHL algorithm; and a QUBO formulation of the linear system solved by simulated annealing. For the full-replacement route, higher-order hydraulic polynomials are quadratized into QUBO form so that a quantum annealer can directly minimize the hydraulic energy. The contrast between the same NR-GGA outer loop with different inner solvers is what isolates the subroutine performance.","core_discovery":"On the paper's own terms, the central discovery is that VQLS is a viable subroutine for iteratively solving the nonlinear hydraulic equations of a water distribution network. The authors' QNR-VQLS matches EPANET across a wide parameter range on a 7-node, 2-loop network, while QNR-HHL does not and QNR-QUBO does with occasional outliers. The paper attributes HHL's failure to the condition numbers of the linear systems encountered along the NR-GGA trajectory exceeding what a fixed HHL circuit can handle, and treats the variational solver's robustness as evidence that learning-based algorithms are better suited to the near-term, emulator-tested regime. A second line of results shows that a higher-order QUBO formulation solved by simulated annealing can directly simulate hydraulics and optimize least-cost pipe diameters, though only on very small networks.","pith_inferences":["An easy instrumented extension is to record the condition number of each inner linear system during QNR-VQLS runs; if VQLS accuracy degrades exactly when condition numbers grow, the paper's explanation for HHL's failure becomes a testable resource criterion.","A cheap experiment the paper does not report is post-selecting QNR-QUBO solutions by annealing energy; if outliers disappear, the bottleneck is the sampler, not the QUBO encoding.","The same emulator harness could be run with varying VQLS ansatz depth to map the minimal circuit resources that keep all scenarios inside the 10% hydraulic tolerance, producing a practical budget for a real-hardware pilot.","A natural next benchmark is a network large enough that the classical inner solve dominates runtime, since only there can a quantum subroutine change the practical tractability that the paper motivates."],"forward_implications":["If QNR-VQLS stays accurate on larger networks, utilities could keep the structure of existing EPANET-based solvers while offloading the hardest inner linear solves to a quantum device.","The HHL failure implies that fixed-depth, non-adaptive quantum linear-solver circuits are a poor fit for iterative algorithms whose intermediate condition numbers vary.","The QUBO-LS result, with outliers, implies that annealing-based linear solving is competitive only when the sampler can avoid local minima, e.g., through more samples or better schedules.","The LCD demonstration implies that quantum annealing can in principle optimize pipe diameters and hydraulics together, but the QUBO overhead currently limits it to tiny networks.","The authors' own conclusion is that hybrid methods are more plausible than replacing NR-GGA entirely with a quantum algorithm in the near term."],"supporting_citations":[{"why":"Defines the Newton-Raphson Global Gradient Algorithm whose inner linear system is replaced by quantum solvers in the QNR variants.","marker":"Todini&Pilati, 1998"},{"why":"Provides the unified simultaneous-equation framework that the NR-GGA formulation belongs to.","marker":"Todini&Rossman, 2012"},{"why":"Supplies the variational quantum linear solver, the subroutine that achieves the best accuracy.","marker":"Bravo-Prieto et al., 2023"},{"why":"Defines the HHL linear-system algorithm used as the failing comparator subroutine.","marker":"Harrow et al., 2009"},{"why":"Provides the quantum annealing and QUBO background used for the annealing-based subroutines and their overhead analysis.","marker":"Yarkoni et al., 2022"},{"why":"Gives the quadratization method for expressing higher-order hydraulic polynomials as QUBO problems.","marker":"Chang et al., 2019"},{"why":"Supplies EPANET, the classical reference simulator against which all pressures and flowrates are benchmarked.","marker":"Rossman et al., 2020"},{"why":"Provides the WNTR code and network data structures on which the QNR implementation is built.","marker":"Klise et al., 2020"},{"why":"Defines the least-cost design problem used in the quantum-annealing optimization demonstration.","marker":"Babayen&Kapelan, 2005"}],"fun_headline_variants":["VQLS matches EPANET on 7-node water network","Quantum variational solver replicates EPANET hydraulics","HHL fails, VQLS succeeds for quantum water simulation","Hybrid quantum solver rivals classical water modelling","Quantum annealing and VQLS tested on water networks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the linear systems encountered along the Newton-Raphson trajectory stay well-conditioned enough for a low-depth variational circuit to solve accurately, and that the noiseless emulator behaviour carries over to real, error-prone hardware.","fun_headline_variants_meta":{"raw":{"variants":["VQLS matches EPANET on 7-node water network","Quantum variational solver replicates EPANET hydraulics","HHL fails, VQLS succeeds for quantum water simulation","Hybrid quantum solver rivals classical water modelling","Quantum annealing and VQLS tested on water networks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000474,"raw_usage":{"total_tokens":2354,"prompt_tokens":949,"completion_tokens":1405,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":565,"completion_tokens_details":{"reasoning_tokens":1326}},"tokens_in":565,"tokens_out":1405,"duration_ms":12519,"temperature":1.0,"reasoning_tokens":1326,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T18:51:43.283594+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the identical 7-node, 2-loop stability tests on a real gate-based quantum processor with standard error mitigation: if QNR-VQLS fails to keep pressures and flowrates within the 10% tolerance of EPANET across the tested pipe-length, diameter, roughness, and demand ranges, the emulator-based success does not transfer to real hardware.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Newton-Raphson Global Gradient Algorithm whose inner linear system is replaced by quantum solvers in the QNR variants."}],"review_version":1}