Quantum Annealing: Optimisation, Sampling, and Many-Body Dynamics
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Quantum Physics arXiv:2605.06857 (quant-ph) [Submitted on 7 May 2026] Title:Quantum Annealing: Optimisation, Sampling, and Many-Body Dynamics Authors:Steven Abel, Andrei Constantin, Luca A. Nutricati View a PDF of the paper titled Quantum Annealing: Optimisation, Sampling, and Many-Body Dynamics, by Steven Abel and 2 other authors View PDF HTML (experimental) Abstract:Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial Hamiltonian into one whose ground state encodes the solution, the system traverses a complex landscape via a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Unlike gate-based quantum computing, quantum annealing is a specialised and near-term approach aimed primarily at discrete optimisation and sampling tasks. While it is not expected to provide polynomial-time solutions to NP-hard problems in the worst case, it offers a physically motivated heuristic for navigating rugged energy landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, placing them among the largest controllable quantum devices currently available. As a result, their significance extends beyond optimisation: they also function as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are difficult to access using classical simulation. In this review we present an accessible introduction to the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse how tunnelling, spectral gaps, and open-system effects shape computational performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges in benchmarking, scaling, and control. These perspectives position quantum annealing as a distinctive framework at the interface of optimisation, stochastic sampling, and programmable quantum dynamics, with a role that is complementary to both classical algorithms and gate-based quantum computing. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Emerging Technologies (cs.ET) Cite as: arXiv:2605.06857 [quant-ph] (or arXiv:2605.06857v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.06857 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Andrei Constantin [view email] [v1] Thu, 7 May 2026 18:57:31 UTC (786 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Annealing: Optimisation, Sampling, and Many-Body Dynamics, by Steven Abel and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cond-mat cond-mat.dis-nn cond-mat.stat-mech cs cs.ET 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?)