Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms

Alejandra Ruiz; Andreas Oikonomakis; Eneko Osaba; Matic Petri\v{c}; Michail-Alexandros Kourtis; Pablo Miranda-Rodriguez; Sebastian Bock

REVIEW 5 major objections 4 minor 30 references

Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms

T0 review · 5 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict A useful integration paper with honest experiments; the clustering step needs validation and the conclusions overreach slightly. read the letter →

arxiv 2501.18432 v3 pith:6FOE6I7Z submitted 2025-01-30 quant-ph cs.AIcs.ET

Eneko Osaba , Pablo Miranda-Rodriguez , Andreas Oikonomakis , Matic Petrič , Alejandra Ruiz , Sebastian Bock , Michail-Alexandros Kourtis This is my paper · ORCID

classification quant-phcs.AIcs.ET

keywords quantumcomputingdroneroutingQAOAannealinghybridquantum-classicaloptimizationMaxCutclusteringasymmetrictravelingsalesmanproblemvehicle

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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

What'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.

Soft 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.

None 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.

Who 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.

Referee Report

5 major / 4 minor

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.

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 (5)

[Section III-A] 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 IV-B] 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 IV-C] 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 III-B] 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 IV-A] 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.

minor comments (4)

[Section III-A] 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.
[Figure 3 caption] The caption spells the system name "Q4RD" instead of "Q4DR"; please check all occurrences of this typo.
[Section III-A] 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 II-A] 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.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: Q4DR is a heuristic two-phase integration whose reported route costs are outputs of the pipeline, not restatements of its inputs; the minor self-citations used for tool and solver selection are not load-bearing.

full rationale

The paper's derivation chain is not circular. The clustering phase solves a MaxCut objective with Qrisp QAOA and the routing phase solves ATSP/CQM formulations with D-Wave hybrid solvers; the final route costs are outputs of those solves, not inputs. The UC3 objective (Eq. 2) is a direct mathematical encoding of the stated problem, minimizing total route cost under visit and charging-point constraints, not a restatement of the solution. No fitted parameter is later presented as a prediction: QAOA angles are optimized on the MaxCut objective itself, and the D-Wave solver choices are not calibrated to the benchmark results. The only potentially load-bearing self-citations are [24] (Qrisp QAOA performance vs. Qiskit) and [28] (NL-hybrid solver selection), both prior performance comparisons; neither derives the route costs reported here, and UC1 is independently checked against Google OR-Tools with identical outcomes. The lack of classical baselines for UC2 and UC3, and the unvalidated assumption that MaxCut clustering preserves routing optimality, are correctness and validation risks rather than circularity. Thus the appropriate score is at most 2 for a minor, non-load-bearing self-citation.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the clustering-to-routing decomposition, on geodetic distance as a cost model, and on the correctness of D-Wave's hybrid solvers; these are domain assumptions, not derived results. No new physical entities or fitted constants are introduced, but QAOA hyperparameters and instance design choices are unreported.

free parameters (4)

QAOA depth (number of layers) = not reported
Sets circuit depth in the clustering phase; the paper does not state the value or justify the choice.
QAOA max_iter (COBYLA iterations) = not reported
Controls the classical optimization of QAOA angles; unreported, so the clustering quality is not reproducible.
Charging station count M = N/3
In UC3, the number of charging stations is fixed as one third of visiting nodes, a design choice not derived from the problem.
Charging station placement = random, periphery
Stations are randomly distributed in the periphery; the exact seed and distribution are not reported.

assumptions (5)

domain assumption MaxCut clustering of visiting nodes is a valid decomposition for two-drone routing.
The paper assumes that partitioning nodes by maximizing inter-cluster edge weight leads to route sets whose combined cost is near-optimal; this is not proven and is the main unvalidated modeling assumption (Section III-A).
domain assumption Costs c_ij are additive and the route cost is the sum of edge costs.
Standard ATSP assumption; used in Eq. (2) and in the routing phase for UC1 and UC2.
domain assumption Every visiting node must be visited exactly once and the fleet consists of exactly two symmetric drones.
Problem definition imposed by UC1, UC2, and UC3; not derived from any external requirement.
domain assumption Distances computed from latitude and longitude with geopy are appropriate proxies for drone travel cost.
Clustering weights and route costs are based on geodetic distance; no energy, wind, or no-fly-zone model beyond forbidden edges is included.
domain assumption D-Wave HSS and Qrisp QAOA implement the intended optimization correctly and their outputs are trustworthy.
The paper relies on third-party frameworks; no verification of the returned solutions is provided beyond the UC1 comparison.

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Pith. "Pith review of Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms." pith.science (2026). https://pith.science/paper/6FOE6I7Z

@misc{pith2026250118432,
  author       = {Pith},
  title        = {Pith review of: Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6FOE6I7Z}},
  note         = {Machine review of arXiv:2501.18432}
}

read the original abstract

This paper presents a novel hybrid approach to solving real-world drone routing problems by leveraging the capabilities of quantum computing. The proposed method, coined Quantum for Drone Routing (Q4DR), integrates the two most prominent paradigms in the field: quantum gate-based computing, through the Eclipse Qrisp programming language; and quantum annealers, by means of D-Wave System's devices. The algorithm is divided into two different phases: an initial clustering phase executed using a Quantum Approximate Optimization Algorithm (QAOA), and a routing phase employing quantum annealers. The efficacy of Q4DR is demonstrated through three use cases of increasing complexity, each incorporating real-world constraints such as asymmetric costs, forbidden paths, and itinerant charging points. This research contributes to the growing body of work in quantum optimization, showcasing the practical applications of quantum computing in logistics and route planning.

Figures

Figures reproduced from arXiv: 2501.18432 by the authors.

**Figure 2.** D-Wave’s HSS schemes. CM = Classical Module. QM = Quantum [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Results obtained by Q4RD in the UC1. owing to its ease of use, efficiency, and flexibility. Further details are given in the upcoming Section IV-C. IV. DEMONSTRATION This section is dedicated to demonstrating the applicability of the developed system across the three use cases examined. Each case has been tested on three distinct instances, consisting of 12, 16, and 22 visiting points, respectively. Each instance wa… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Results obtained by Q4RD in the UC2. The depots are colored black. (a) UC3 12. (b) UC3 16. (c) UC3 22 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Results obtained by Q4RD in the UC3. The depots are colored black. set X = {X0, . . . , Xn} of lists has been established, where each Xi corresponds to a single node i, with n being the total number of visiting nodes and 0 denoting the depot. Moreover, Xi = {xi,0, . . …

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

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Benchmark dataset and results for

——, “Benchmark dataset and results for ”real-world drone routing problems with quantum computing” experimentation,” http://dx.doi.org/ 10.17632/9fpyr2cdtv.1, 2025, online at Mendeley Data

work page doi:10.17632/9fpyr2cdtv.1 2025

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E. Osaba and P. Miranda-Rodriguez, “D-wave’s nonlinear-program hybrid solver: Description and performance analysis,” IEEE Access , vol. 13, pp. 4724–4736, 2025

work page 2025

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T. Nanda, B. Dhanalakshmi, and B. Lakshmi, “An explorative cross sectional comprehensive survey on quantum computing,” SN Computer Science, vol. 5, no. 8, pp. 1–13, 2024

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