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REVIEW 4 major objections 4 minor 2 references

Quantum Simulation and Optimization of Water Distribution Networks

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read QNR-VQLS, a Newton-Raphson solver with a variational quantum linear subroutine, reproduces EPANET pressures and flowrates on a 7-node water network.

desk verdict 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. read the letter →

arxiv 2507.06862 v1 pith:HUPYNR6Z submitted 2025-07-09 quant-ph

Carlos Romero Rocha , Nicolas Renaud , Koen Leijnse , Samuel van Beek , Mario Castro-Gama This is my paper
classification quant-ph
keywords waterdistributionnetworksNewton-RaphsonglobalgradientalgorithmvariationalquantumlinearsolverannealingQUBOleast-costdesignEPANET
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

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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 / 4 minor

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.

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 (4)
  1. [3.1 (HHL paragraph, Fig. 2)] 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.
  2. [3.1 (VQLS and QUBO-LS results, Figs. 1 and 3)] 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.
  3. [3.1 (VQLS scaling paragraph)] 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.
  4. [3.2 (Fig. 4) and 3.3 (Fig. 5)] 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.
minor comments (4)
  1. [2.3 and 3.3] 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.
  2. [Throughout] 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.
  3. [References and text] 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.
  4. [3.1 (HHL paragraph)] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: QNR-VQLS results are benchmarked against external EPANET references using published quantum linear-solver algorithms, with no fitted parameter or self-citation chain doing load-bearing work.

full rationale

The paper's derivation chain is self-contained and externally benchmarked. QNR variants solve the NR-GGA linear systems using published quantum linear-solver algorithms (VQLS from Bravo-Prieto et al., HHL from Harrow et al., and QUBO-LS via QA reductions); no parameter is fitted to the EPANET reference pressures or flowrates that are used as ground truth. EPANET and WNTR are external classical tools, and the comparison figures report predicted versus reference values, so the central claim that QNR-VQLS reproduces EPANET results is not an input to the method. The HHL failure explanation invokes unmeasured condition numbers, but this is an evidential weakness about a hypothesized mechanism, not a circular reduction: the HHL result is not defined in terms of the conclusion, and the paper explicitly leaves dynamic circuit recreation as future work. The same applies to the stated limitations that simulations were run on emulators without hardware noise; those are acknowledged scope constraints, not circularity. Neither self-citation nor imported uniqueness theorems plays a load-bearing role; the only self-references are to the project's open-source code repositories and the Quantum Application Lab, which do not supply the algorithm's validity. No circular step can be exhibited by quote and reduction, so the score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted to data; the 10% tolerance is a reporting threshold, not a fitted value. The paper assumes the standard hydraulic equations, the correctness of NR-GGA, and EPANET as ground truth. It also assumes that a noiseless emulator is a valid proxy for evaluating the quantum algorithms, which the paper itself notes is not the case for noisy hardware.

assumptions (4)
  • domain assumption Water distribution networks obey the standard nonlinear hydraulic equations used in EPANET/NR-GGA.
    The entire simulation and its benchmarks rely on this model; it is standard in WDN modeling but unstated in the paper.
  • domain assumption The Newton-Raphson Global Gradient Algorithm converges to the correct solution when its linear systems are solved exactly.
    The paper replaces only the linear solver; the convergence of NR-GGA itself is not re-proven. This is the background method from Todini and Pilati.
  • domain assumption EPANET reference values are correct solutions of the hydraulic model.
    All quantum results are benchmarked against EPANET; the paper treats it as ground truth.
  • ad hoc to paper A noiseless quantum emulator is a sufficient proxy for evaluating algorithm feasibility.
    The paper uses emulators and explicitly says noise sources are not accounted for, yet draws feasibility conclusions from them. This is an acknowledged simplification that could affect practical claims.

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Cite this review

Pith. "Pith review of Quantum Simulation and Optimization of Water Distribution Networks." pith.science (2026). https://pith.science/paper/HUPYNR6Z

@misc{pith2026250706862,
  author       = {Pith},
  title        = {Pith review of: Quantum Simulation and Optimization of Water Distribution Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HUPYNR6Z}},
  note         = {Machine review of arXiv:2507.06862}
}
read the original abstract

To compute models for Water Distribution Networks (WDN), a large system of non-linear equations needs to be solved. The hallmark algorithm for computing these models is the Newton-Raphson Global Gradient Algorithm (NR-GGA), which solves these systems iteratively. Even so, large networks can take multiple days to model and the complexity of networks is only expected to increase in the future. It is therefore important to explore different algorithms using innovative technologies, to improve the tractability of modelling large networks. Quantum computing is such an innovative technology that is still in its early stages of development, paired with a different computational paradigm. In this research we have determined the feasibility of using quantum computing algorithms as a subroutine of NR-GGA and alternatively for replacing NR-GGA with a quantum algorithm in its entirety. Calculations were run on emulators of gate-based quantum computers and using simulated annealing while models were tested on small 2-loop networks of 7 nodes. To improve NR-GGA, three different quantum subroutines were used: the hybrid Variational Quantum Linear Solver (VQLS) showed the best results on this small dataset. To replace NR-GGA by a quantum algorithm in its entirety, we also used a Quantum Annealing-based approach for simulating higher-order polynomials to determine the Least-Cost Design (LCD) of a small 3 node network.

Figures

Figures reproduced from arXiv: 2507.06862 by the authors.

Figure 4
Figure 4. Several annealing runs are sampled, each providing a different associated energy, with lower energy being closer the optimal ground-state solution of the translated annealing problem. The solution with minimum energy, marked with blue dots, displays values within the 10% error range at the exception of one flow rate. The solutions for all the optimization paths lead to values of the pressure and flow rate well outsi… view at source ↗
Figure 1
Figure 1. Simulated water pressures using QNR-VQLS for a 2-loop network for a wide range of pipe diameters, length, roughness and demand. The x-axis marks the reference values obtained with EPANET while the y-axis shows the values obtained with the QNR-VQLS approach [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Simulated water pressures using QNR-HHL for a 2-loop network for a wide range of pipe diameters, length, roughness and demand [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figures from the paper (2 more)
Figure 3
Figure 3. Figure 3: Simulated water pressures using QNR-QUBOLS for a 2-loop network for a wide range of pipe diameters, length, roughness and demand [PITH_FULL_IMAGE:figures/full_fig_p007_3.png]
Figure 4
Figure 4. Figure 4: Solution of the QUBO formulation of the hydraulics equations for the 0-loop network (top) and the 2-loop network (bottom). The minimum energy solution is marked in blue while the yellow markers indicate the results of other sampling paths [PITH_FULL_IMAGE:figures/full…

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Reference graph

Works this paper leans on

2 extracted references · 1 canonical work pages

  1. [1]

    Abbas A, King R, Huang HY, Huggins WJ, Movassagh R, Gilboa D, McClean J (202 3) On quantum backpropagation, information reuse, and cheating measurement collapse , Advances in Neural Information Processing Systems, 36 Babayen A, Kapelan Z (2005) Least-cost design of water distribution networks under demand uncertainty, Journal of Water Resources Planning a...

    arXiv 2005

  2. [2]

    Agency, Washington, DC, EPA/600/R -20/133 Todini E, Pilati S (1998) A gradient algorithm for the analysis of pipe networks, Computer Applications in Water Supply, John Wiley & Sons, 1 -20pp. Todini E, Rossman LA (2012) Unified framework for deriving simultaneous equation algorithms for water distribution networks, Journal of Hydraulic Engineering, 139 (5)...

    work page 1998

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Reviewed August 6, 2026 · model on record in the stance chip above.