Set-Packing and Sequence-Pair QUBOs for the 2D Cutting Stock Problem on Quantum Annealing Hardware

Quantum Physics arXiv:2609.20853 (quant-ph) [Submitted on 26 Aug 2026] Title:Set-Packing and Sequence-Pair QUBOs for the 2D Cutting Stock Problem on Quantum Annealing Hardware Authors:Miguel Sánchez-Beato, Raul Martinez, Matilde Osa, Jorge Parra, Mario Calonge View a PDF of the paper titled Set-Packing and Sequence-Pair QUBOs for the 2D Cutting Stock Problem on Quantum Annealing Hardware, by Miguel S\'anchez-Beato and 3 other authors View PDF HTML (experimental) Abstract:The two-dimensional Cutting Stock Problem (2D-CSP) is an NP-hard problem with direct economic and environmental impacts on manufacturing and logistics. We encode its fixed-plate variant, with free piece repetition and full non-overlap and containment constraints, as a Quadratic Unconstrained Binary Optimization (QUBO) problem for quantum annealing and compare two formulations from opposite encoding paradigms. The first was a coordinate-based set-packing model with one binary variable per candidate placement. Its variable count grows linearly with plate area and resolution, but its ground state is, by construction, a geometrically feasible maximum-area packing. The second is a coordinate-free sequence-pair model whose variable count is independent of plate resolution and size. We prove that this compactness has a structural limit: no coordinate-free QUBO of bounded interaction degree whose penalties vanish on every geometrically feasible layout can have a geometrically feasible ground state for 2D containment, because containment is a longest-path constraint that bounded-degree penalties cannot enforce on chains longer than their interaction order. We evaluate both formulations under multi-seed simulated annealing, simulated quantum annealing, and an exact integer-programming baseline. Hardware experiments include D-Wave minor embedding, a calibrated direct-QPU sweep, and Leap hybrid solvers in both penalty and constraint-native form, across a six-instance campaign with per-instance calibration. The hybrid solver returns our certificate configuration, tying its energy to thirteen decimal places while overflowing the plate. We claim no quantum speedup. Our contribution is an impossibility result characterizing the limits of compact packing QUBOs, and a practical rule for choosing between the two formulations. Comments: Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC) Cite as: arXiv:2609.20853 [quant-ph] (or arXiv:2609.20853v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.20853 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Raul Martinez Pavon [view email] [v1] Wed, 26 Aug 2026 07:28:05 UTC (572 KB) Full-text links: Access Paper: View a PDF of the paper titled Set-Packing and Sequence-Pair QUBOs for the 2D Cutting Stock Problem on Quantum Annealing Hardware, by Miguel S\'anchez-Beato and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: math math.OC References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)