{"id":"7159a543-b0d2-4416-addb-7c2792a51e16","arxiv_id":"2501.18432","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Q4DR splits drone routing into QAOA clustering plus D-Wave annealing routing, matches OR-Tools on the simplest case, and leaves two cases unvalidated.","lead":"A hybrid quantum workflow splits drone routing into two steps: QAOA divides the map into two clusters, then D-Wave annealers route each cluster. The method matches a classical solver in the simplest test case, but lacks classical comparisons for two of three scenarios and shows no quantum advantage.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central weakness is the unvalidated MaxCut clustering assumption: no evidence shows that a maximum-cut partition is compatible with optimal two-drone routes, and UC2/UC3 lack classical baselines.","rationale":"I read the paper as an integration demonstration rather than a formal optimality guarantee. The strongest claim is that Q4DR reliably solves the three use cases, evidenced primarily by OR-Tools agreement on UC1. The weakest load-bearing premise is indeed the MaxCut clustering: the routing phase solves two independent ATSP/CQM problems on fixed clusters, so any suboptimality introduced by the partition cannot be recovered. The paper provides no theoretical or empirical argument that maximum inter-cluster cut weight correlates with minimum two-route cost, and the UC2/UC3 experiments have no classical baselines. The reader identified exactly this vulnerability, and my independent reading agrees. The suggested OR-Tools benchmark on UC2/UC3 is the minimal check that would confirm or refute the concern; the paper itself lists extensive benchmarking with classical methods as future work, which supports the conditional verdict. Therefore I do not change the reader's CONDITIONAL verdict.","tokens_in":10396,"tokens_out":4366,"duration_ms":43548,"concrete_test":"Use Google OR-Tools (the same implementation used for UC1) to solve the full two-drone problem on the UC2 and UC3 instances from the published Mendeley dataset, with the respective depot assignments and charging-station termination rules, and compare the total route cost against Q4DR's reported results; if OR-Tools achieves a strictly lower cost on any instance, the clustering decomposition is lossy and the reliability claim is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The pipeline's correctness rests on the clustering phase: nodes are partitioned by solving MaxCut, and this partition is never re-optimized in the routing phase. The MaxCut objective (maximize inter-cluster edge weight) is not the routing objective (minimize total route cost), and nothing in the paper shows these objectives align for asymmetric costs, forbidden paths, or multiple depots. The only empirical validation is UC1, where Q4DR matched OR-Tools on three instances (N=12, 16, 22). Three small instances of one topology do not establish that the decomposition is lossless or near-lossless. The paper explicitly states in Section IV-C that no classical comparison was possible for UC3, and Section IV-B gives no baseline for UC2. Thus the 'demonstrated utility' claim for UC2 and UC3 rests entirely on the unvalidated assumption that MaxCut produces clusters from which near-optimal two-drone routes can be assembled.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces Q4DR, a two-phase hybrid solver for drone routing: a clustering phase based on QAOA MaxCut implemented in Eclipse Qrisp, followed by a routing phase that uses D-Wave hybrid/annealing solvers to solve an ATSP-like problem on each cluster. The method is tested on three use cases with asymmetric costs, forbidden paths, and, in UC3, itinerant charging stations, each with 12, 16, and 22 visiting points. The authors report that UC1 matches Google OR-Tools on all three tested instances, while UC2 has no classical baseline and UC3 explicitly defers classical comparison to future work. The central claim is that the system is reliable and demonstrates utility across the three use cases.","tokens_in":10610,"tokens_out":5263,"duration_ms":48282,"significance":"If fully supported, the paper would be a useful systems-integration demonstration: it combines gate-based QAOA clustering with D-Wave annealing in a single routing pipeline, provides an explicit CQM formulation for open routes with charging points, and shares benchmark data and code in [29]. The main strengths are the reproducible artifacts and the honest modeling of real-world constraints. However, the evidence is currently narrow: only UC1 has a head-to-head comparison against a classical solver, and the MaxCut clustering step, which fixes the routes before the routing phase, is never validated against alternative clustering strategies. The contribution is therefore a working integration example rather than a demonstrated speedup, scalability gain, or general reliability result. The absence of error bars and repeated runs further weakens the reliability claim.","major_comments":[{"comment":"The MaxCut clustering phase uses an undirected, symmetric distance graph built from coordinates via geopy, whereas the routing problem is defined by an asymmetric cost matrix with forbidden arcs (Section III, cij ≠ cji, cij = ∞). The MaxCut objective maximizes inter-cluster edge weight and is not shown to align with the two-route ATSP cost; because the partition is fixed before routing and never repaired, any suboptimal split is unrecoverable. The only head-to-head validation is UC1 against OR-Tools on N=12, 16, 22 (Section IV-A), which does not establish that the decomposition is near-lossless for UC2/UC3. I ask for an ablation or a bound: compare the final Q4DR cost against the same routing solvers applied to alternative clusterings (random, k-means, or a direct two-route assignment), or prove a performance ratio for the decomposition.","section":"Section III-A"},{"comment":"UC2 reports no classical baseline and no quantitative cost table. Figure 4 displays only route maps, and the conclusion that the system \"demonstrates its utility\" (Section V) therefore lacks support for this use case. Please add route-cost values and a baseline, at minimum OR-Tools on the same depot-assignment procedure, for all three UC2 instances.","section":"Section IV-B"},{"comment":"The paper explicitly states that \"it has not been possible to conduct a comparison with a classical method\" for UC3 and defers this to future work. Given that Equations (2)-(5) define a small MILP-like problem with at most 22 visiting nodes plus M=N/3 charging stations, a classical MILP solver or dynamic program should be straightforward to run. Without such a baseline, the UC3 results cannot be distinguished from arbitrary feasible solutions. Please provide a classical baseline or explicitly rescope the conclusions to exclude UC3.","section":"Section IV-C"},{"comment":"The choice of NL-Hybrid for UC1 and UC2 is justified only by \"extensive laboratory research, partially described in [28]\", which is the authors' own prior work. No in-paper comparison among the QPU, BQM-Hybrid, CQM-Hybrid, and NL-Hybrid solvers is reported for the presented instances. Because the paper's contribution is a working hybrid pipeline, the reader needs at least summary performance numbers (solution cost and time) for the alternative solvers, or a clear statement that NL-Hybrid is used as a baseline method rather than as evidence of a quantum advantage.","section":"Section III-B"},{"comment":"No repeated runs or statistical dispersion are reported. The sentence \"in all examined cases, both methods yielded identical results\" is based on a single execution per instance for stochastic solvers (QAOA with COBYLA and D-Wave hybrid). Please report the number of runs or annealing reads and give best/median results, or a small table with variance, so the reader can assess the reliability of the match.","section":"Section IV-A"}],"minor_comments":[{"comment":"In the text describing the MaxCut cost function, \"contributes to the overall cost if it belongs to the same partition\" contradicts the formula (1 - xu xv)/2 * wuv, which counts edges between different partitions; please fix this wording.","section":"Section III-A"},{"comment":"The caption spells the system name \"Q4RD\" instead of \"Q4DR\"; please check all occurrences of this typo.","section":"Figure 3 caption"},{"comment":"The parameter ranges γ ∈ {0, 2π} and β ∈ {0, π} appear to be set literals rather than intervals; use [0, 2π) and [0, π) for clarity.","section":"Section III-A"},{"comment":"The claim that the two-step approach \"allows us to tackle problems of a significantly larger size\" is not supported by the experiments, since no instance exceeds 22 visiting points; either soften the claim or provide a direct size comparison.","section":"Section II-A"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is an honest engineering report with open code and data, and the authors are transparent about the lack of a UC3 classical comparison. However, the central reliability claim rests on a single baseline comparison and an unvalidated clustering decomposition. I see no evidence of misconduct, but the selection of NL-Hybrid based on the authors' own prior work [28] should be more prominently disclosed in the main text. The paper is within the journal's scope as an application paper; with the requested ablation and baselines, major revision is appropriate rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: it's a solid integration paper, not a breakthrough. The new bit is connecting Qrisp's QAOA MaxCut clustering to D-Wave's NL-hybrid and CQM routing for drone problems with asymmetric costs, forbidden paths and charging points. That gives logistics folks a concrete template. Code and benchmark data are public, which is real evidence.\n\nWhat's good: the writing is clear and honest. UC1 matching OR-Tools on 12, 16, and 22 nodes is a legitimate sanity check. The UC3 CQM formulation is a reasonable extension and the authors explicitly say a classical comparison is future work. They disclose the use of Copilot, which is transparent.\n\nSoft spots: the clustering phase is the load-bearing assumption and it's unvalidated. MaxCut maximizes inter-cluster edge weight, not the routing objective of minimizing total route cost. For asymmetric costs and forbidden paths there's no reason to expect those objectives to align. The paper doesn't compare against other clustering schemes or check how much the final route suffers from the fixed partition. UC2 and UC3 have no classical baseline, so the 'demonstrated utility' claim for those two rests on confidence in the clustering plus the solver. Also, NL-hybrid was chosen after experiments on the same problem family, backed by the authors' own performance analysis; that's not circular but it's weak evidence for this pipeline. No repeated runs or error bars anywhere, which matters for stochastic solvers.\n\nNone of this is fatal for the paper's actual scope. The main overreach is the conclusion sentence claiming efficacy across all three use cases. Tighten that, add one classical baseline for UC2, and offer some justification for the MaxCut decomposition, and the paper is sound for what it is.\n\nWho is it for: researchers and practitioners who want a worked example of combining gate-based QAOA with D-Wave's hybrid solvers. It deserves a serious referee. I'd send it to review; it's publishable after revision. I probably wouldn't cite it in my own next paper unless I was building directly on this integration, because the empirical claims are modest.","headline":"A useful integration paper with honest experiments; the clustering step needs validation and the conclusions overreach slightly.","tokens_in":11168,"tokens_out":2019,"would_cite":false,"duration_ms":18239,"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":"To solve two-drone routing problems, Q4DR splits visiting points with a QAOA MaxCut and routes each cluster on a quantum annealer, and the paper reports that in its benchmarked use case the results match a classical optimizer.","keywords":["quantum computing","drone routing","QAOA","quantum annealing","hybrid quantum-classical optimization","MaxCut clustering","asymmetric traveling salesman problem","vehicle routing"],"falsifier":"On a new two-drone instance with asymmetric costs and forbidden edges, compute the exact optimal pair of routes by exhaustive search and run Q4DR on the same instance; any instance where Q4DR's total cost exceeds the exact optimum shows the clustering-then-routing decomposition is not reliably lossless. A simpler check is to rerun the released UC1 instances with the classical optimizer used in the paper: any mismatch would directly contradict the reported reliability result.","tokens_in":10225,"feed_emoji":"🚁","tokens_out":12039,"duration_ms":101000,"temperature":0.7,"pith_summary":"Q4DR is a two-phase solver for two-drone routing problems: a QAOA MaxCut first splits the visiting points into two clusters, and each cluster is then routed independently on a quantum annealer. The paper claims this pipeline can absorb realistic constraints—asymmetric travel costs, forbidden paths, separate depots, and itinerant charging stations—and demonstrates it on instances with 12, 16, and 22 visiting points across three use cases. In the only use case compared against a classical optimizer, the reported route costs are identical in every tested instance, which the authors present as evidence of reliability; the other two use cases come with no classical comparison. The contribution is an integration demonstration: showing that gate-based and annealing quantum paradigms can be combined in a logistics pipeline, rather than claiming a speedup or a scaling advantage.","feed_headline":"Hybrid quantum pipeline routes two drones, matches classical solver","feed_subtitle":"QAOA splits the map, an annealer routes each half, and results match a classical optimizer in the one use case compared.","key_machinery":"The key mechanism is the cluster-then-route decomposition, which keeps problem size small enough for current quantum hardware. In the clustering stage, a weighted MaxCut graph is built from the visiting-point coordinates, and QAOA returns a binary partition of the nodes. In the routing stage, each partition is converted into an asymmetric traveling-salesman problem or, for the charging-station case, an open-route constrained quadratic model, and a hybrid quantum-classical annealer minimizes the route cost with forbidden paths set to infinite cost. The two stages are connected by the assumption that maximizing the cut between clusters yields a partition from which the two independently optimized drone routes are the best overall solution.","core_discovery":"On the paper's own terms, the central discovery is that Q4DR—the two-phase pipeline sketched above—solves the designed drone routing problems. The clustering phase maximizes the weighted cut between two groups of visiting points using QAOA; the routing phase then solves an asymmetric traveling-salesman problem for each group on a quantum annealer, with forbidden paths encoded as infinite costs. For the open-route charging-station use case, the paper designs a constrained quadratic model with a node-based binary encoding and solves it with the same hybrid annealing service. After running all three use cases at sizes 12, 16, and 22, the paper concludes that the system \"effectively addresses\" the problems and, for use case 1, that the results demonstrate the reliability of the system because they coincide with the classical optimizer's solutions.","pith_inferences":["A test the paper leaves open is to keep the routing phase fixed and replace the MaxCut clustering with other partitioning schemes; if any alternative produces a lower total route cost, then the clustering stage, not the routing stage, is where optimality is lost.","Because MaxCut maximizes edge weights between clusters but ignores the direction of asymmetric costs and the presence of forbidden edges, it may place two points in different clusters even when an optimal route would keep them together; this scenario is not examined in the paper.","In the charging-station use case, the stations are deliberately excluded from the clustering graph, so the partition cannot react to where the charging points are; including them in the first phase is a concrete variant that might yield cheaper routes.","The exact agreement with the classical solver in use case 1 may be an artifact of small instance sizes; repeating the comparison on larger or denser maps would show whether the agreement persists."],"forward_implications":["On the nine tested instances (three use cases at 12, 16, and 22 visiting points), the complete Q4DR pipeline produces feasible two-drone routes, so this is an end-to-end integration of gate-based and annealing hardware rather than a single-algorithm experiment.","For the single-depot, two-drone use case, Q4DR's route costs match a classical state-of-the-art TSP solver on every tested instance, so the two-stage decomposition did not lose optimality in those particular tests.","The routing formulations can express asymmetric costs, forbidden paths, separate depots, and routes that must end at exactly one of several charging stations, all constraints that appear in real drone logistics.","The paper makes no runtime, scaling, or quantum-advantage claim; its stated result is reliability of the integrated system, with extensive classical benchmarking listed as future work."],"supporting_citations":[{"why":"Defines QAOA, the gate-based algorithm used in the clustering phase.","marker":"[6]"},{"why":"Documents the hybrid solver service whose three solvers are used in the routing phase.","marker":"[12]"},{"why":"Shows prior quantum drone delivery work capped at 12 visiting points, the size baseline Q4DR claims to exceed.","marker":"[16]"},{"why":"Supplies the two-step cluster-then-route decomposition that Q4DR adapts for larger problem sizes.","marker":"[21]"},{"why":"Presents the gate-based programming framework that provides the QAOA module used for clustering.","marker":"[22]"},{"why":"Reports the QAOA implementation comparison the paper cites to justify its choice of gate-based framework.","marker":"[24]"},{"why":"Describes the structure of the hybrid quantum-classical solver used in the charging-station use case.","marker":"[27]"},{"why":"Reports the performance analysis that led the authors to select the nonlinear-program solver for the first two use cases.","marker":"[28]"},{"why":"Introduces the node-based binary encoding that the open-route charging-point formulation builds on.","marker":"[30]"}],"fun_headline_variants":["Hybrid quantum pipeline: QAOA clusters, annealer routes drones","Quantum annealing + QAOA: drone routing solved, matches classical","Two quantum approaches, one drone routing solution: QAOA + annealer","Hybrid quantum drone router: QAOA splits map, annealer solves routes","QAOA plus annealing: hybrid quantum pipeline for drone paths"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that splitting the map into two clusters by maximizing the cut between them before routing does not discard the optimal two-drone solution, and this premise is never checked against other clustering strategies or exact solutions.","fun_headline_variants_meta":{"raw":{"variants":["Hybrid quantum pipeline: QAOA clusters, annealer routes drones","Quantum annealing + QAOA: drone routing solved, matches classical","Two quantum approaches, one drone routing solution: QAOA + annealer","Hybrid quantum drone router: QAOA splits map, annealer solves routes","QAOA plus annealing: hybrid quantum pipeline for drone paths"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001132,"raw_usage":{"total_tokens":4662,"prompt_tokens":863,"completion_tokens":3799,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":479,"completion_tokens_details":{"reasoning_tokens":3708}},"tokens_in":479,"tokens_out":3799,"duration_ms":24690,"temperature":1.0,"reasoning_tokens":3708,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T23:31:05.299773+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a new two-drone instance with asymmetric costs and forbidden edges, compute the exact optimal pair of routes by exhaustive search and run Q4DR on the same instance; any instance where Q4DR's total cost exceeds the exact optimum shows the clustering-then-routing decomposition is not reliably lossless. A simpler check is to rerun the released UC1 instances with the classical optimizer used in the paper: any mismatch would directly contradict the reported reliability result.","supporting_citations":[{"cited_title":"D-Wave Hybrid Solver Service: An Overview,","cited_arxiv_id":null,"evidence_quote":"Documents the hybrid solver service whose three solvers are used in the routing phase."},{"cited_title":"Testing quantum and simulated annealers on the drone delivery packing problem,","cited_arxiv_id":null,"evidence_quote":"Shows prior quantum drone delivery work capped at 12 visiting points, the size baseline Q4DR claims to exceed."},{"cited_title":"Measuring Performance of the Leap Constrained Quadratic Model Solver,","cited_arxiv_id":null,"evidence_quote":"Describes the structure of the hybrid quantum-classical solver used in the charging-station use case."},{"cited_title":"D-wave’s nonlinear-program hybrid solver: Description and performance analysis,","cited_arxiv_id":null,"evidence_quote":"Reports the performance analysis that led the authors to select the nonlinear-program solver for the first two use cases."},{"cited_title":"Solving a real-world package delivery routing problem using quantum annealers,","cited_arxiv_id":null,"evidence_quote":"Introduces the node-based binary encoding that the open-route charging-point formulation builds on."}],"review_version":1}