Solving approximate hidden subgroup problems: quantum heuristics to detect weak entanglement

Quantum Physics [Submitted on 16 Mar 2026] Solving approximate hidden subgroup problems: quantum heuristics to detect weak entanglement Petar Simidzija, Eugene Koskin, Elton Yechao Zhu, Michael Dascal, Maria Schuld How can we use a quantum computer to detect the entanglement structure of a quantum state? Bouland et al. (2024) recently provided an algorithm that, given multiple input copies of the state, finds the "hidden cuts"-partitions into fully unentangled qubit registers. Their solution is based on turning cuts into a symmetry which can be detected with a Shor-type quantum algorithm for hidden subgroup problems, the hidden cut algorithm. In this paper we derive heuristics that can find "approximate symmetries", or weakly entangled qubit registers, to unlock this powerful idea for a much broader range of problems. Our core contribution is a rigorous link between the output distribution of the hidden cut algorithm and the reward function that measures the quality of a cut. This implies that reducing the number of state copies in the original hidden cut algorithm leads to measurement samples from which patterns of weak entanglement can be extracted. We believe that these insights are an important step in making quantum algorithms for hidden subgroup problems useful for applications beyond cryptography. Comments: 12 pages, 11 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.15733 [quant-ph]   (or arXiv:2603.15733v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.15733 Focus to learn more Submission history From: Maria Schuld [view email] [v1] Mon, 16 Mar 2026 18:00:01 UTC (1,654 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?)