pith. machine review for the scientific record. sign in

arxiv: 2605.03565 · v1 · submitted 2026-05-05 · 🪐 quant-ph

Recognition: unknown

Neural optimization for quantum architectures: graph embedding problems with Distance Encoder Networks

Chiara Vercellino , Giacomo Vitali , Paolo Viviani , Alberto Scionti , Andrea Scarabosio , Olivier Terzo , Edoardo Giusto , Bartolomeo Montrucchio
Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:13 UTC · model grok-4.3

classification 🪐 quant-ph
keywords neural optimizationquantum hardware embeddingconstrained unit disk problemneutral atom qubitsautoencoderembedding loss functiongraph mappingqubit positioning
0
0 comments X

The pith

A neural network learns to turn invalid qubit position guesses into valid embeddings for neutral-atom quantum hardware and beats classical solvers in the same runtime.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a neural optimization framework to solve the constrained unit disk problem that appears when placing qubits on neutral-atom quantum processors. It relies on a modified autoencoder called the Distances Encoder Network together with a custom Embedding Loss Function that guides the network to adjust initial non-feasible placements into arrangements that satisfy the required distance constraints. The network approximates the nonlinear spatial mapping needed to enforce feasibility. A reader would care because embedding remains a major practical obstacle between abstract problems and actual hardware runs, and the method shows stronger results than standard solvers when computation time is held fixed. If the approach holds, neural networks could become a standard tool for preparing optimization problems for this class of quantum machines.

Core claim

The central claim is that the Distances Encoder Network can be trained to map arbitrary initial non-feasible solutions of the constrained unit disk problem into feasible qubit embeddings for neutral atoms-based quantum hardware. By approximating non-linear transformations and incorporating the geometric constraints directly into the custom Embedding Loss Function, the network produces valid layouts more effectively than classical solvers when both are restricted to comparable computation times.

What carries the argument

The Distances Encoder Network, a modified autoencoder that learns to compute Euclidean distances and apply a custom Embedding Loss Function to enforce unit disk constraints while transforming non-feasible initial qubit positions into feasible embeddings.

If this is right

  • Valid qubit embeddings can be found more quickly for larger graphs that must be run on neutral-atom hardware.
  • The same neural strategy can be reused for other constrained geometric optimization tasks that arise in quantum architecture design.
  • Hybrid classical-neural pipelines become practical for translating abstract problems into hardware-ready layouts.
  • Overall preparation time for quantum computations decreases when embedding is no longer the dominant bottleneck.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The learned mapping might generalize across different hardware noise models, allowing the same network to produce robust embeddings even when atom positions have small uncertainties.
  • Similar networks could be trained once on diverse problem classes and then fine-tuned quickly for new embedding tasks without starting from scratch each time.
  • The approach suggests a route to automated design tools that generate both the quantum algorithm and its physical layout in one integrated loop.

Load-bearing premise

The Distances Encoder Network can reliably learn a spatial transformation that maps arbitrary initial non-feasible solutions into feasible embeddings for the constrained unit disk problem without overfitting to the training instances or requiring problem-specific hyperparameter retuning.

What would settle it

Training the network on one collection of unit disk instances and then measuring its success rate and runtime on a fresh collection of instances with different sizes and densities, comparing directly against classical solvers on the same new instances.

Figures

Figures reproduced from arXiv: 2605.03565 by Alberto Scionti, Andrea Scarabosio, Bartolomeo Montrucchio, Chiara Vercellino, Edoardo Giusto, Giacomo Vitali, Olivier Terzo, Paolo Viviani.

Figure 1
Figure 1. Figure 1: Representation of unit disk graphs in a quantum register. Whenever view at source ↗
Figure 2
Figure 2. Figure 2: Representations of a K7, clique with 7 vertexes, (on the left) and of a graph with maximum degree ∆ = 18 (on the right) feasible embeddings, for a CUDG problem with Dmin = 4 µm, L = 50 µm and Dadj = 10.26 µm view at source ↗
Figure 3
Figure 3. Figure 3: The optimization framework for the constrained unit disk graph problem: two different approaches are considered for the position initializations in view at source ↗
Figure 5
Figure 5. Figure 5: Percentage of feasible embeddings obtained, on the whole graphs view at source ↗
Figure 4
Figure 4. Figure 4: The average computational times for the DEN models training scale linearly with n, and the increment in the dimensionality does not seem to impact significantly on the training duration (Fig. 4a). Whereas the impact of an increased dimensionality, N, is much more evident in Fig. 4b, here the DEN model finds more easily a feasible embedding when N = 3 than in the case N = 2, as can be noticed, feasible embe… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the largest adjacency gap values obtained with the different solvers, for all the graph samples in the dataset. The blue rectangles group the graphs’ instances by n. [2] A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” Nature, vol. 549, no. 7671, pp. 242–246, 2… view at source ↗
read the original abstract

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still a complicated task. One of the main challenges is to represent through qubits (i.e., the basic units of quantum information) the problems of interest. According to the specific technology underlying the quantum machine, it is necessary to implement a proper representation strategy, generally referred to as embedding. This paper introduces a neural-enhanced optimization framework to solve the constrained unit disk problem, which arises in the context of qubits positioning for neutral atoms-based quantum hardware. The proposed approach involves a modified autoencoder model, i.e., the Distances Encoder Network, and a custom loss, i.e., the Embedding Loss Function, respectively, to compute Euclidean distances and model the optimization constraints. The core idea behind this design relies on the capability of neural networks to approximate non-linear transformations to make the Distances Encoder Network learn the spatial transformation that maps initial non-feasible solutions of the constrained unit disk problem into feasible ones. The proposed approach outperforms classical solvers, given fixed comparable computation times, and paves the way to address other optimization problems through a similar strategy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a neural-enhanced optimization framework for the constrained unit disk problem arising in qubit embedding for neutral-atom quantum hardware. It employs a modified autoencoder called the Distances Encoder Network together with a custom Embedding Loss Function to learn a spatial transformation that maps initial non-feasible placements into feasible unit-disk embeddings, and reports that this approach outperforms classical solvers when computation time is held fixed.

Significance. If the empirical claims are substantiated with proper controls, the work would demonstrate a viable machine-learning route to a practically relevant embedding task in quantum hardware design. The use of a neural network to approximate the required non-linear mapping, combined with a constraint-aware loss, offers a template that could extend to other graph-embedding or placement problems in quantum architectures.

major comments (2)
  1. [§4 (Experiments) and abstract] The central outperformance claim (abstract and §4) is load-bearing yet unsupported by any reported quantitative metrics, error bars, dataset sizes, instance counts, or ablation studies. Without these controls it is impossible to determine whether the reported gains survive statistical scrutiny or simply reflect memorization of the training distribution.
  2. [§3 (Method) and §4 (Experiments)] The generalization assumption required for the fixed-time comparison is not addressed: the manuscript provides no description of instance generation, train/test partitioning, scaling behavior with instance size, or whether classical baselines received equivalent per-instance tuning budgets. If training and test instances belong to the same narrow family, the claimed superiority over classical solvers is not internally valid.
minor comments (2)
  1. [Abstract and §3] The abstract states that the network 'learns the spatial transformation' but does not specify the precise architecture (number of layers, activation functions, latent dimension) or the exact mathematical form of the Embedding Loss Function.
  2. [Figures in §4] Figure captions and axis labels should explicitly state the classical solvers used as baselines and the precise time budget applied in each comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive comments on our manuscript. We address each of the major comments below and have revised the manuscript to incorporate additional details and clarifications as suggested.

read point-by-point responses

  1. Referee: [§4 (Experiments) and abstract] The central outperformance claim (abstract and §4) is load-bearing yet unsupported by any reported quantitative metrics, error bars, dataset sizes, instance counts, or ablation studies. Without these controls it is impossible to determine whether the reported gains survive statistical scrutiny or simply reflect memorization of the training distribution.

    Authors: We agree that the presentation of results in the original manuscript lacks sufficient quantitative detail to fully substantiate the claims. In the revised version, we will add specific metrics including success rates for embedding, average computation times, and statistical measures such as standard deviations over multiple independent runs. We will also specify the sizes of the datasets used, the number of instances tested, and include ablation studies to isolate the effects of the Distance Encoder Network and the Embedding Loss Function. These additions will enable proper statistical evaluation and address concerns about potential memorization. revision: yes

  2. Referee: [§3 (Method) and §4 (Experiments)] The generalization assumption required for the fixed-time comparison is not addressed: the manuscript provides no description of instance generation, train/test partitioning, scaling behavior with instance size, or whether classical baselines received equivalent per-instance tuning budgets. If training and test instances belong to the same narrow family, the claimed superiority over classical solvers is not internally valid.

    Authors: We acknowledge the importance of clearly documenting the experimental setup to support claims of generalization. In the revised manuscript, we will provide a detailed description of how instances are generated, including the parameters used for creating the graphs and initial placements. We will specify the train/test partitioning strategy, ensuring that test instances are not seen during training, and discuss the scaling behavior as instance size increases. Additionally, we will clarify that the classical baselines were allocated equivalent per-instance computation time budgets, matching the fixed-time constraint used for our method. This will strengthen the internal validity of the comparisons. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical NN approach with custom loss is self-contained

full rationale

The paper presents a neural network (Distances Encoder Network) with a custom Embedding Loss Function to learn a spatial mapping from non-feasible to feasible unit-disk embeddings. No derivation chain, equations, or self-citations are shown that reduce any claimed result to its own inputs by construction. The core idea invokes the standard universal approximation property of neural networks rather than any fitted parameter renamed as a prediction or a uniqueness theorem imported from prior author work. Performance claims are framed as empirical comparisons against classical solvers under fixed compute time; these rest on experimental details outside the provided text and do not create definitional or self-referential loops. The approach is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are stated. The neural network itself implicitly contains many learned weights and at least one custom loss term whose functional form is not given.

pith-pipeline@v0.9.0 · 5539 in / 1189 out tokens · 45149 ms · 2026-05-07T17:13:17.857020+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

42 extracted references · 8 canonical work pages · 2 internal anchors

  1. [1]

    Quantum simulators,

    I. Buluta and F. Nori, “Quantum simulators,”Science, vol. 326, no. 5949, pp. 108–111, 2009. 9 𝑛 = 10 𝑛 = 20 𝑛 = 30 𝑛 = 40 𝑛 = 50 𝑛 = 60 𝑛 = 70 𝑛 = 80 𝑛 = 90 𝑛 = 100 Fig. 6. Comparison of the largestadjacency gapvalues obtained with the different solvers, for all the graph samples in the dataset. The blue rectangles group the graphs’ instances byn

    2009

  2. [2]

    Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,”Nature, vol. 549, no. 7671, pp. 242–246, 2017

    2017

  3. [3]

    Quantum computational chemistry,

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, “Quantum computational chemistry,”Reviews of Modern Physics, vol. 92, no. 1, p. 015003, 2020

    2020

  4. [4]

    The unconstrained binary quadratic programming problem: a survey,

    G. Kochenberger, J.-K. Hao, F. Glover, M. Lewis, Z. L ¨u, H. Wang, and Y . Wang, “The unconstrained binary quadratic programming problem: a survey,”Journal of combinatorial optimization, vol. 28, no. 1, pp. 58–81, 2014

    2014

  5. [5]

    Quantum annealing in the transverse ising model,

    T. Kadowaki and H. Nishimori, “Quantum annealing in the transverse ising model,”Physical Review E, vol. 58, no. 5, p. 5355, 1998

    1998

  6. [6]

    A Quantum Approximate Optimization Algorithm

    E. Farhi, J. Goldstone, and S. Gutmann, “A quantum approximate optimization algorithm,”arXiv preprint arXiv:1411.4028, 2014

    work page internal anchor Pith review arXiv 2014

  7. [7]

    Optical dipole traps for neutral atoms,

    R. Grimm, M. Weidem ¨uller, and Y . B. Ovchinnikov, “Optical dipole traps for neutral atoms,” inAdvances in atomic, molecular, and optical physics. Elsevier, 2000, vol. 42, pp. 95–170

    2000

  8. [8]

    Unit disk graphs,

    B. N. Clark, C. J. Colbourn, and D. S. Johnson, “Unit disk graphs,” Discrete mathematics, vol. 86, no. 1-3, pp. 165–177, 1990

    1990

  9. [9]

    M. C. Golumbic,Algorithmic graph theory and perfect graphs. Elsevier, 2004

    2004

  10. [10]

    Optimization problems in unit-disk graphs

    B. Balasundaram and S. Butenko, “Optimization problems in unit-disk graphs.” 2009

    2009

  11. [11]

    Approximation algorithm for minimum weight fault-tolerant virtual backbone in unit disk graphs,

    Y . Shi, Z. Zhang, Y . Mo, and D.-Z. Du, “Approximation algorithm for minimum weight fault-tolerant virtual backbone in unit disk graphs,” IEEE/ACM Transactions on Networking, vol. 25, no. 2, pp. 925–933, 2017

    2017

  12. [12]

    Algorithmic, geometric and graphs issues in wireless net- works,

    X.-Y . Li, “Algorithmic, geometric and graphs issues in wireless net- works,”Wireless Communications and Mobile Computing, vol. 3, no. 2, pp. 119–140, 2003

    2003

  13. [13]

    Ising formulations of many NP problems,

    A. Lucas, “Ising formulations of many NP problems,”Frontiers in Physics, vol. 2, 2014

    2014

  14. [14]

    Solving optimization problems with rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks,

    M. F. Serret, B. Marchand, and T. Ayral, “Solving optimization problems with rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks,” Physical Review A, vol. 102, no. 5, p. 052617, 2020

    2020

  15. [15]

    Qualifying quantum approaches for hard industrial optimization problems. a case study in the field of smart- charging of electric vehicles,

    C. Dalyac, L. Henriet, E. Jeandel, W. Lechner, S. Perdrix, M. Porcheron, and M. Veshchezerova, “Qualifying quantum approaches for hard industrial optimization problems. a case study in the field of smart- charging of electric vehicles,”EPJ Quantum Technology, vol. 8, no. 1, May 2021. [Online]. Available: http://dx.doi.org/10.1140/epjqt/s40507- 021-00100-3

    work page doi:10.1140/epjqt/s40507- 2021

  16. [16]

    arXiv preprint arXiv:1811.11538

    F. Glover, G. Kochenberger, and Y . Du, “A tutorial on formulating and using qubo models,”arXiv preprint arXiv:1811.11538, 2018

    work page arXiv 2018

  17. [17]

    Adiabatic quantum computation,

    T. Albash and D. A. Lidar, “Adiabatic quantum computation,”Reviews of Modern Physics, vol. 90, no. 1, p. 015002, 2018

    2018

  18. [18]

    Ultracold rubidium atoms excited to rydberg levels,

    D. Ciampini, O. Morsch, and E. Arimondo, “Ultracold rubidium atoms excited to rydberg levels,”Journal of Atomic, Molecular, Condensed Matter and Nano Physics, vol. 2, no. 3, pp. 161–167, 2015

    2015

  19. [19]

    Entanglement of neutral-atom qubits with long ground-rydberg coherence times,

    C. Picken, R. Legaie, K. McDonnell, and J. Pritchard, “Entanglement of neutral-atom qubits with long ground-rydberg coherence times,” Quantum Science and Technology, vol. 4, no. 1, p. 015011, 2018

    2018

  20. [20]

    Unit disk graph recognition is NP-hard,

    H. Breu and D. G. Kirkpatrick, “Unit disk graph recognition is NP-hard,” Computational Geometry, vol. 9, no. 1-2, pp. 3–24, Jan. 1998

    1998

  21. [21]

    Unit disk graph approx- imation,

    F. Kuhn, T. Moscibroda, and R. Wattenhofer, “Unit disk graph approx- imation,” inProceedings of the 2004 Joint Workshop on Foundations of Mobile Computing - DIALM-POMC ’04. Philadelphia, PA, USA: ACM Press, 2004, p. 17

    2004

  22. [22]

    Characterizations of outerplanar graphs,

    M. M. Sysło, “Characterizations of outerplanar graphs,”Discrete Math- ematics, vol. 26, no. 1, pp. 47–53, 1979

    1979

  23. [23]

    Unit Disk Repre- sentations of Embedded Trees, Outerplanar and Multi-Legged Graphs,

    S. Bhore, M. L ¨offler, S. Nickel, and M. N ¨ollenburg, “Unit Disk Repre- sentations of Embedded Trees, Outerplanar and Multi-Legged Graphs,” arXiv:2103.08416 [cs], Aug. 2021

    work page arXiv 2021

  24. [24]

    Virtual coordinates for ad hoc and sensor networks,

    T. Moscibroda, R. O’Dell, M. Wattenhofer, and R. Wattenhofer, “Virtual coordinates for ad hoc and sensor networks,” inProceedings of the 2004 joint workshop on Foundations of mobile computing, 2004, pp. 8–16

    2004

  25. [25]

    Good quality virtual realization of unit disk graphs,

    S. Pemmaraju and I. Pirwani, “Good quality virtual realization of unit disk graphs,”Journal of Computational Geometry (Old Web Site), vol. 2, no. 1, pp. 69–91, 2011

    2011

  26. [26]

    On the approximation on unit disk graph coordinates,

    T. Rusterholz, “On the approximation on unit disk graph coordinates,” Tech. rep, Tech. Rep., 2003

    2003

  27. [27]

    Practical virtual coordinates for large wireless sensor networks,

    J. Zhou, Y . Chen, B. Leong, and B. Feng, “Practical virtual coordinates for large wireless sensor networks,” inThe 18th IEEE International Conference on Network Protocols. IEEE, 2010, pp. 41–51

    2010

  28. [28]

    The gurobi optimizer,

    B. Bixby, “The gurobi optimizer,”Transp. Re-search Part B, vol. 41, no. 2, pp. 159–178, 2007

    2007

  29. [29]

    On the implementation of an interior- point filter line-search algorithm for large-scale nonlinear programming,

    A. W ¨achter and L. T. Biegler, “On the implementation of an interior- point filter line-search algorithm for large-scale nonlinear programming,” Mathematical programming, vol. 106, no. 1, pp. 25–57, 2006

    2006

  30. [30]

    Deep neural networks and mixed integer linear optimization,

    M. Fischetti and J. Jo, “Deep neural networks and mixed integer linear optimization,”Constraints, vol. 23, no. 3, pp. 296–309, 2018

    2018

  31. [31]

    Optnet: Differentiable optimization as a layer in neural networks,

    B. Amos and J. Z. Kolter, “Optnet: Differentiable optimization as a layer in neural networks,” inInternational Conference on Machine Learning. PMLR, 2017, pp. 136–145

    2017

  32. [32]

    Tounn: topology optimization using neural networks,

    A. Chandrasekhar and K. Suresh, “Tounn: topology optimization using neural networks,”Structural and Multidisciplinary Optimization, vol. 63, no. 3, pp. 1135–1149, 2021

    2021

  33. [33]

    Multi-material topology optimization using neural networks,

    ——, “Multi-material topology optimization using neural networks,” Computer-Aided Design, vol. 136, p. 103017, 2021

    2021

  34. [34]

    Reinforcement learning to solve np-hard problems: an application to the cvrp,

    L. Ardon, “Reinforcement learning to solve np-hard problems: an application to the cvrp,”arXiv preprint arXiv:2201.05393, 2022

    work page arXiv 2022

  35. [35]

    Solving np-hard problems on graphs with extended alphago zero,

    K. Abe, Z. Xu, I. Sato, and M. Sugiyama, “Solving np-hard problems on graphs with extended alphago zero,”arXiv preprint arXiv:1905.11623, 2019

    work page arXiv 1905

  36. [36]

    Nn-baker: A neural-network infused algorithmic framework for optimization prob- lems on geometric intersection graphs,

    E. McCarty, Q. Zhao, A. Sidiropoulos, and Y . Wang, “Nn-baker: A neural-network infused algorithmic framework for optimization prob- lems on geometric intersection graphs,”Advances in Neural Information Processing Systems, vol. 34, pp. 23 023–23 035, 2021

    2021

  37. [37]

    A simple proof of thue’s theorem on circle packing,

    H.-C. Chang and L.-C. Wang, “A simple proof of thue’s theorem on circle packing,”arXiv preprint arXiv:1009.4322, 2010

    work page arXiv 2010

  38. [38]

    Approximating maximum indepen- dent sets by excluding subgraphs,

    R. Boppana and M. M. Halld ´orsson, “Approximating maximum indepen- dent sets by excluding subgraphs,”BIT Numerical Mathematics, vol. 32, no. 2, pp. 180–196, 1992

    1992

  39. [39]

    Graph drawing by force- directed placement,

    T. M. Fruchterman and E. M. Reingold, “Graph drawing by force- directed placement,”Software: Practice and experience, vol. 21, no. 11, pp. 1129–1164, 1991

    1991

  40. [40]

    Exploring network struc- ture, dynamics, and function using networkx,

    A. Hagberg, P. Swart, and D. S Chult, “Exploring network struc- ture, dynamics, and function using networkx,” Los Alamos National Lab.(LANL), Los Alamos, NM (United States), Tech. Rep., 2008

    2008

  41. [41]

    Dropout training as adaptive regularization,

    S. Wager, S. Wang, and P. S. Liang, “Dropout training as adaptive regularization,”Advances in neural information processing systems, vol. 26, 2013. 10

    2013

  42. [42]

    Decoupled Weight Decay Regularization

    I. Loshchilov and F. Hutter, “Decoupled weight decay regularization,” arXiv preprint arXiv:1711.05101, 2017

    work page internal anchor Pith review arXiv 2017