Topological Obstructions in Quantum Adiabatic Algorithms

Quantum Physics [Submitted on 20 Mar 2026] Topological Obstructions in Quantum Adiabatic Algorithms Prathamesh S. Joshi, Emil Prodan 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 Submission history From: Emil Prodan Dr. [view email] [v1] Fri, 20 Mar 2026 23:54:31 UTC (8,476 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)