arxiv: 2605.04736 · v1 · submitted 2026-05-06 · 🪐 quant-ph

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Neural-powered unit disk graph embedding: qubits connectivity for some QUBO problems

Chiara Vercellino , Paolo Viviani , Giacomo Vitali , Alberto Scionti , Andrea Scarabosio , Olivier Terzo , Edoardo Giusto , Bartolomeo Montrucchio

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:28 UTC · model grok-4.3

classification 🪐 quant-ph

keywords unit disk graph embeddingQUBORydberg atomsquantum optimizationneural networksqubit connectivitygraph embedding

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The pith

A neural network converts arbitrary qubit placements into valid unit disk embeddings that match target QUBO matrices for Rydberg hardware.

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 network that takes an initial qubit arrangement and adjusts the positions so the resulting unit disk graph exactly reproduces the adjacency pattern demanded by a given QUBO problem. This step is required because Rydberg atom processors allow interactions only between atoms closer than the blockade radius. A sympathetic reader would care because traditional solvers for this embedding task become slow for larger problems and limit what quantum hardware can actually run. If the network succeeds across instances, the mapping from classical optimization problems to physical qubit layouts becomes faster and more automatic.

Core claim

The authors demonstrate that a neural network can transform an initial embedding configuration into a feasible unit disk arrangement whose connectivity pattern matches the target QUBO matrix, and that the resulting procedure runs faster than the Gurobi solver on the tested cases.

What carries the argument

A neural network trained to enforce unit disk constraints on qubit coordinates while preserving the exact pairwise interactions specified by the QUBO matrix.

If this is right

QUBO problems can be prepared for Rydberg hardware from a wider set of starting placements without manual intervention.
The embedding step no longer dominates the total runtime of quantum optimization workflows.
Larger problem instances become practical because the neural transformation scales better than classical solvers.
The same trained network can handle multiple distinct QUBO matrices without per-instance redesign.

Where Pith is reading between the lines

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

The method could be adapted to other hardware topologies that impose geometric constraints on qubit interactions.
Embedding could be performed on-the-fly inside hybrid quantum-classical loops if the network generalizes across problem sizes.
Real-device experiments would be needed to check whether the produced embeddings also improve solution quality beyond faster preparation.

Load-bearing premise

The neural network produces coordinates that always satisfy the exact unit disk property and reproduce the required QUBO adjacencies without problem-specific retraining or extra correction steps.

What would settle it

An input embedding and QUBO matrix for which the network outputs positions that either create distances violating the blockade radius for some pairs or fail to produce the exact target adjacency pattern.

Figures

Figures reproduced from arXiv: 2605.04736 by Alberto Scionti, Andrea Scarabosio, Bartolomeo Montrucchio, Chiara Vercellino, Edoardo Giusto, Giacomo Vitali, Olivier Terzo, Paolo Viviani.

**Figure 1.** Figure 1: Representation of a qubit register composed of neutral atoms arranged in a 2D array. Interaction between qubits is regulated by the Rydberg blockade effect: only atoms falling within the Rydberg radius are subject to interaction. the coordinates of a unit disk embedding for a given QUBO problem. 2 Related Work The qubits placement problem is well-known in the context of quantum computing. Despite the sp… view at source ↗

**Figure 2.** Figure 2: GEAN architecture: 5 qubits embedding in 2D, the initial coordinates ( view at source ↗

**Figure 3.** Figure 3: Representation of the maximal clique, K7, fig. 3a), and of the maximal degree, fig. 3b), that can be embedded on the register. The baseline embedding is the regular hexagonal packing with l = 4 µm side and the Rydberg blockade radius is the maximum available on the machine ˜rb ≈ 10.26 µm. 3.5 Adding new dimensions: the 3D embedding case To be able to embed a greater set of QUBO problems and with a view … view at source ↗

**Figure 4.** Figure 4: Transformation into feasible 2D embeddings of the view at source ↗

**Figure 5.** Figure 5: Embedding for the QUBO protein folding problem corresponding to G17 7: the initial position, fig. 5a), are computed through Fruchterman-Reingold method and are mapped into a feasible 2D UD embedding reported in fig. 5b). Fig. 5c) shows the behaviour of the loss function along the epochs. of the distances, relying on loss function definition, and the exploitation of very effective optimizers for neural netw… view at source ↗

**Figure 6.** Figure 6: Embedding for the full QUBO MIS antennas problem in 3D: the initial positions with z-coordinates set to 0, fig. 6a), are mapped into a feasible 3D embedding, fig. 6b). a) a’) view at source ↗

**Figure 7.** Figure 7: QUBO graph coloring embedding in 3D corresponding to GGC : starting from the red graph on the left, the one-hot-encoding QUBO formulation is built to take into account 3 colors. The initial qubits positions shown on fig. 7a) are mapped into a feasible configuration as in fig. 7a’). Acknowledgment This work has been supported by the CINECA consortium and by Pasqal in the context of the Iscra-C project QOPS… view at source ↗

read the original abstract

Graph embedding is a recurrent problem in quantum computing, for instance, quantum annealers need to solve a minor graph embedding in order to map a given Quadratic Unconstrained Binary Optimization (QUBO) problem onto their internal connectivity pattern. This work presents a novel approach to constrained unit disk graph embedding, which is encountered when trying to solve combinatorial optimization problems in QUBO form, using quantum hardware based on neutral Rydberg atoms. The qubits, physically represented by the atoms, are excited to the Rydberg state through laser pulses. Whenever qubits pairs are closer together than the blockade radius, entanglement can be reached, thus preventing entangled qubits to be simultaneously in the excited state. Hence, the blockade radius determines the adjacency pattern among qubits, corresponding to a unit disk configuration. Although it is straightforward to compute the adjacency pattern given the qubit coordinates, identifying a feasible unit disk arrangement that matches the desired QUBO matrix is, on the other hand, a much harder task. In the context of quantum optimization, this issue translates into the physical placement of the qubits in the 2D/3D register to match the machine's Ising-like Hamiltonian with the QUBO formulation of the optimization problems. The proposed solution exploits the power of neural networks to transform an initial embedding configuration, which does not match the quantum hardware requirements or does not account for the unit disk property, into a feasible embedding properly representing the target optimization problems. Experimental results show that this new approach overcomes in performance Gurobi solver.

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

1 major / 0 minor

Summary. The manuscript presents a neural-network approach for transforming initial embeddings into valid unit-disk configurations whose induced adjacency exactly reproduces the interaction graph of a target QUBO, with the goal of mapping combinatorial optimization problems onto the connectivity constraints of neutral-atom Rydberg processors. Experimental results are claimed to show superior performance relative to the Gurobi solver.

Significance. A reliable, general-purpose method for unit-disk embedding would directly address a practical bottleneck in deploying QUBO problems on Rydberg-atom hardware. The approach is presented as an external transformation rather than a self-referential construction, which is a positive feature if the experimental claims hold.

major comments (1)

The central performance claim (that the neural method overcomes Gurobi) is load-bearing for the paper's contribution, yet the manuscript supplies no architecture details, training procedure, dataset description, success metrics, or statistical comparison. Without these, the experimental assertion cannot be evaluated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment below and will revise the manuscript to provide the requested details.

read point-by-point responses

Referee: The central performance claim (that the neural method overcomes Gurobi) is load-bearing for the paper's contribution, yet the manuscript supplies no architecture details, training procedure, dataset description, success metrics, or statistical comparison. Without these, the experimental assertion cannot be evaluated.

Authors: We acknowledge that the current manuscript version does not provide sufficient details on the neural network architecture, training procedure, dataset, success metrics, or statistical comparisons, which limits the evaluability of the performance claims. This omission was unintentional. In the revised version, we will add a dedicated experimental section that fully specifies the neural network model (including layer structure, activation functions, and input/output dimensions), the training procedure (including loss function, optimizer, hyperparameters, and convergence criteria), the dataset generation process (including how initial embeddings and target QUBO instances are created), the definition of success metrics (such as validity rate of unit-disk embeddings and runtime comparisons), and statistical analysis (including number of independent runs, variance, and direct comparisons to Gurobi). These additions will enable independent verification of the results. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract and available description present a neural-network transformation method for converting initial embeddings into valid unit-disk configurations that reproduce a target QUBO interaction graph. No equations, derivations, or self-referential definitions appear in the text. The central claim is an external algorithmic technique whose performance is asserted via experimental comparison to Gurobi; no load-bearing step reduces by construction to a fitted parameter, self-citation chain, or renamed input. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract provides no explicit free parameters, axioms, or invented entities; the approach is described at a high level as a neural network transformation without detailing any fitted constants or new physical postulates.

pith-pipeline@v0.9.0 · 5598 in / 1060 out tokens · 82754 ms · 2026-05-08T17:28:48.574146+00:00 · methodology

discussion (0)

Reference graph

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