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arxiv: 2606.23045 · v1 · pith:KJZN7ZL7new · submitted 2026-06-22 · 🪐 quant-ph

Satellite Mission Planning with Rydberg Atoms

Michel Nowak , Benjamin Marchand , Yassine Naghmouchi , Serge Rainjonneau , Wesley Coelho , Louis Vignoli , Louis-Paul Henry This is my paper

Pith reviewed 2026-06-26 08:16 UTC · model grok-4.3

classification 🪐 quant-ph
keywords satellite mission planningRydberg atomsmaximum independent setQUBOquantum optimizationEarth observationscheduling
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The pith

Formulating satellite mission planning as a maximum independent set problem allows solution on a Rydberg-atom quantum processor.

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

The paper encodes daily scheduling for Earth-observation satellite fleets as a graph problem solvable by cold-atom hardware. It begins with a basic version of the task and then adds satellite agility constraints drawn from existing literature. The central step recasts the problem as finding a maximum independent set, which the Rydberg QPU can address either directly on graphs or, more effectively, through a QUBO formulation. Numerical experiments on the hardware confirm that the QUBO route is practical. The work indicates this approach could support operational planning when target density is high.

Core claim

By formulating the planning problem as a Maximum Independent Set problem, we are able to solve the problem with a QPU based on Rydberg atoms. We explore two ways of solving the MIS problem on the QPU, one relying on the graphs and on the Quadratic Unconstrained Binary Optimization Framework (QUBO). We show that the QUBO methodology is the most relevant and explore it more deeply with numerical experiments.

What carries the argument

Reduction of satellite scheduling constraints to a Maximum Independent Set instance, solved on the Rydberg QPU via either direct graph methods or QUBO encoding.

If this is right

  • Daily schedules for multi-satellite fleets become generatable by solving the MIS instance on the quantum device.
  • Agility constraints remain compatible with the same MIS encoding.
  • The QUBO formulation outperforms direct graph solving for this hardware.
  • Rydberg QPUs become applicable to this class of combinatorial scheduling tasks.

Where Pith is reading between the lines

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

  • If encoding overhead stays manageable at larger scales, quantum methods could shorten planning cycles for satellite operators.
  • The same MIS reduction might transfer to other resource-allocation problems in space operations.
  • Hybrid classical-quantum pipelines could appear, with the QPU handling the combinatorial core after classical preprocessing.

Load-bearing premise

Satellite scheduling constraints can be faithfully encoded into an MIS or QUBO instance whose solution on the Rydberg QPU yields a usable operational schedule without prohibitive overhead or approximation error.

What would settle it

Running the encoded MIS or QUBO instance on real Rydberg hardware and obtaining a schedule that violates agility limits, target coverage, or other operational constraints.

Figures

Figures reproduced from arXiv: 2606.23045 by Benjamin Marchand, Louis-Paul Henry, Louis Vignoli, Michel Nowak, Serge Rainjonneau, Wesley Coelho, Yassine Naghmouchi.

Figure 1
Figure 1. Figure 1: FIG. 1. Visualization of requests of cities’ observations and satel [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Formulation of the Maximum Independent Set problem with [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Left: solving graph whose MIS needs to be extracted to [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Autoencoder method [34]. (a) The solving graph is computed [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. QUBO method (a) The solving graph is computed and (b,c) [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Benchmark: classical. Top figure: global satisfaction rate. It [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Time vs subgraph size: agile method [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Time vs subgraph size: edges method. The colors represent [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Performance metric/completion rate (top figures) and time to solution (bottom figures) against number of requests for a scenario with [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
read the original abstract

Quantum computers relying on cold atoms are being built and promise a high flexibility in the way information in encoded into the physical system. In particular, the analog mode is spiking interest in the field of optimization as a classically intractable number of configurations can be tackled. In this work, we investigate a problem that requires every-day scheduling of critical tasks involving a large number of actors. Namely, fixing the planning for a Earth Observation satellite fleet composed of several of units exposed to a high density of targets to be scanned. We explore numerical schemes that convert the formulated problem into a cold-atoms friendly setup. We begin by a naive formulation of the Satellite Mission Planning problem without taking account for the agility of the satellites. We then extend the problem to take it into account based on the literature. By formulating the planning problem as a Maximum Independent Set problem, we are able to solve the problem with a QPU based on Rydberg atoms. We explore two ways of solving the MIS problem on the QPU, one relying on the graphs and on the Quadratic Unconstrained Binary Optimization Framework (QUBO). We show that the QUBO methodology is the most relevant and explore it more deeply with numerical experiments. We conclude on the potential utility of using a QPU to solve the Satellite Mission Planning problem in an operational context.

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 / 0 minor

Summary. The manuscript claims that the satellite mission planning problem for Earth-observation satellite fleets can be encoded as a Maximum Independent Set (MIS) instance (first in a naive form ignoring agility, then extended per literature), solved on a Rydberg-atom QPU either directly via the graph or via a QUBO mapping, that the QUBO route is preferable, and that numerical experiments support the potential operational utility of such QPUs.

Significance. If the encoding is faithful and the QPU experiments demonstrate scalable, accurate solutions on instances of operational size, the work would illustrate a concrete use-case for analog Rydberg hardware in combinatorial scheduling. The exploratory framing and focus on a practical domain are positive, but the absence of any quantitative results, error analysis, or classical baselines in the provided text limits the ability to assess whether a genuine advantage is shown.

major comments (2)
  1. [Numerical experiments (abstract)] The abstract states that numerical experiments were performed and that the QUBO methodology is 'the most relevant,' yet no problem sizes, success probabilities, runtime comparisons, or error metrics are supplied. Without these data it is impossible to verify whether the claimed preference for QUBO or the overall utility conclusion is supported.
  2. [Formulation and mapping (abstract)] The central mapping claim ('By formulating the planning problem as a Maximum Independent Set problem, we are able to solve the problem with a QPU') is presented without any description of how satellite-specific constraints (visibility windows, agility, target density) are encoded into the MIS/QUBO Hamiltonian or how solution quality is validated against the original scheduling semantics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. We address the two major comments point by point below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Numerical experiments (abstract)] The abstract states that numerical experiments were performed and that the QUBO methodology is 'the most relevant,' yet no problem sizes, success probabilities, runtime comparisons, or error metrics are supplied. Without these data it is impossible to verify whether the claimed preference for QUBO or the overall utility conclusion is supported.

    Authors: We agree that the abstract is insufficiently specific regarding the numerical experiments. The manuscript body contains the experiments (simulations and QPU runs) that led to the preference for the QUBO route, but the abstract does not report the supporting metrics. We will revise the abstract to include a concise summary of the tested instance sizes, observed success probabilities for the two mappings, and the classical baseline comparisons performed. revision: yes

  2. Referee: [Formulation and mapping (abstract)] The central mapping claim ('By formulating the planning problem as a Maximum Independent Set problem, we are able to solve the problem with a QPU') is presented without any description of how satellite-specific constraints (visibility windows, agility, target density) are encoded into the MIS/QUBO Hamiltonian or how solution quality is validated against the original scheduling semantics.

    Authors: The encoding procedure and validation approach are described in the main text: the naive MIS formulation maps targets to vertices with conflicts as edges; the agile extension augments the conflict graph using maneuver-time constraints drawn from the satellite-scheduling literature; visibility windows restrict the vertex set per satellite; and the QUBO is obtained from the MIS Ising Hamiltonian via the standard quadratic penalty transformation. Solution quality is checked by verifying that returned independent sets satisfy the original non-overlap and agility constraints when decoded back to schedules. We acknowledge that the abstract is too terse to convey these steps. We will add one or two sentences to the abstract (or a short paragraph in the introduction) that outline the constraint encoding and validation method. revision: yes

Circularity Check

0 steps flagged

No significant circularity; formulation is an application of known MIS/QUBO mapping

full rationale

The paper's core contribution is a direct encoding of satellite scheduling constraints into an MIS (or QUBO) instance for solution on a Rydberg-atom QPU, followed by numerical experiments comparing graph-based and QUBO approaches. No derivation step reduces by construction to its own inputs, no fitted parameters are relabeled as predictions, and no load-bearing uniqueness or ansatz is imported via self-citation. The work is self-contained as an exploratory mapping exercise with no internal reduction to tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is supplied; no equations, parameters, or modeling assumptions can be extracted. All ledger entries are therefore empty.

pith-pipeline@v0.9.1-grok · 5776 in / 1026 out tokens · 21535 ms · 2026-06-26T08:16:37.009963+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

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