quantum-computing

Topological Obstructions in Quantum Adiabatic Algorithms

arXiv Quantum Physics

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⚡ Quantum Brief

Researchers Prathamesh S. Joshi and Emil Prodan reveal topological obstructions in quantum adiabatic algorithms (QAAs) when solving optimization problems with multiple solutions, causing spectral branches to cross the energy gap and potentially undermining algorithm validity. Their March 2026 study demonstrates that, despite these obstructions, QAAs can simultaneously detect all solutions in a single run—a capability previously unrecognized in quantum optimization frameworks. Using the Max-Cut problem as a case study, the authors prove QAAs correctly identify multiple solutions, challenging assumptions about their limitations in degenerate solution spaces. This discovery suggests QAAs may outperform classical variational algorithms in problems with solution degeneracy, offering a new advantage for quantum-enhanced optimization tasks. The findings could reshape future quantum algorithm design, particularly in variational methods, by leveraging topological effects rather than avoiding them.

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Quantum Physics arXiv:2603.20567 (quant-ph) [Submitted on 20 Mar 2026] Title:Topological Obstructions in Quantum Adiabatic Algorithms Authors:Prathamesh S. Joshi, Emil Prodan View a PDF of the paper titled Topological Obstructions in Quantum Adiabatic Algorithms, by Prathamesh S. Joshi and 1 other authors View PDF HTML (experimental) Abstract:We point out that, when an optimization problem has more than one solution, the quantum adiabatic algorithms (QAA) encounter topological obstructions leading to adiabatic spectral flows where spectral branches unavoidably traverse the spectral gap above the ground states of the quantum Hamiltonians. This raises serious doubts about the validity of the algorithms in such situations. However, using the Max-Cut problem as an example, we explain and demonstrate here that QAAs correctly detect all existing solutions in one single run. This newly discovered capacity of QAAs to simultaneously detect multiple solutions to an optimization problem can have an important impact on future developments of quantum variational algorithms Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20567 [quant-ph] (or arXiv:2603.20567v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.20567 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Emil Prodan Dr. [view email] [v1] Fri, 20 Mar 2026 23:54:31 UTC (8,476 KB) Full-text links: Access Paper: View a PDF of the paper titled Topological Obstructions in Quantum Adiabatic Algorithms, by Prathamesh S. Joshi and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)

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Source: arXiv Quantum Physics

Website: https://arxiv.org/rss/quant-ph