Exploring Topologies in Quantum Annealing: A Hardware-Aware Perspective

Quantum Physics arXiv:2511.03327 (quant-ph) [Submitted on 5 Nov 2025] Title:Exploring Topologies in Quantum Annealing: A Hardware-Aware Perspective Authors:Mario Bifulco, Luca Roversi View a PDF of the paper titled Exploring Topologies in Quantum Annealing: A Hardware-Aware Perspective, by Mario Bifulco and Luca Roversi View PDF HTML (experimental) Abstract:Quantum Annealing (QA) offers a promising framework for solving NP-hard optimization problems, but its effectiveness is constrained by the topology of the underlying quantum hardware. Solving an optimization problem $P$ via QA involves a hardware-aware circuit compilation which requires representing $P$ as a graph $G_P$ and embedding it into the hardware connectivity graph $G_Q$ that defines how qubits connect to each other in a QA-based quantum processing unit (QPU). Minor Embedding (ME) is a possible operational form of this hardware-aware compilation. ME heuristically builds a map that associates each node of $G_P$ -- the logical variables of $P$ -- to a chain of adjacent nodes in $G_Q$ by means of one of its minors, so that the arcs of $G_P$ are preserved as physical connections among qubits in $G_Q$. The static topology of hardwired qubits can clearly lead to inefficient compilations because $G_Q$ cannot be a clique, currently. We propose a methodology and a set of criteria to evaluate how the hardware topology $G_Q$ can negatively affect the embedded problem, thus making the quantum optimization more sensible to noise. We evaluate the result of ME across two QPU topologies: Zephyr graphs (used in current D-Wave systems) and Havel-Hakimi graphs, which allow controlled variation of the average node degree. This enables us to study how the ratio `number of nodes/number of incident arcs per node' affects ME success rates to map $G_P$ into a minor of $G_Q$. Our findings, obtained through ME executed on classical, i.e. non-quantum, architectures, suggest that Havel-Hakimi-based topologies, on average, require shorter qubit chains in the minor of $G_P$, exhibiting smoother scaling of the largest embeddable $G_P$ as the QPU size increases. These characteristics indicate their potential as alternative designs for QA-based QPUs. Subjects: Quantum Physics (quant-ph); Performance (cs.PF) Cite as: arXiv:2511.03327 [quant-ph] (or arXiv:2511.03327v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.03327 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mario Bifulco [view email] [v1] Wed, 5 Nov 2025 09:45:56 UTC (293 KB) Full-text links: Access Paper: View a PDF of the paper titled Exploring Topologies in Quantum Annealing: A Hardware-Aware Perspective, by Mario Bifulco and Luca RoversiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: cs cs.PF 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)