{"citation":{"ieee":"S.-L. Kremer, D. Rudolph, and S. Gharibian, “Quantum k-SAT Related Hypergraph Problems,” <i>arXiv:2506.17066</i>. 2025.","apa":"Kremer, S.-L., Rudolph, D., &#38; Gharibian, S. (2025). Quantum k-SAT Related Hypergraph Problems. In <i>arXiv:2506.17066</i>.","chicago":"Kremer, Simon-Luca, Dorian Rudolph, and Sevag Gharibian. “Quantum K-SAT Related Hypergraph Problems.” <i>ArXiv:2506.17066</i>, 2025.","short":"S.-L. Kremer, D. Rudolph, S. Gharibian, ArXiv:2506.17066 (2025).","ama":"Kremer S-L, Rudolph D, Gharibian S. Quantum k-SAT Related Hypergraph Problems. <i>arXiv:250617066</i>. Published online 2025.","mla":"Kremer, Simon-Luca, et al. “Quantum K-SAT Related Hypergraph Problems.” <i>ArXiv:2506.17066</i>, 2025.","bibtex":"@article{Kremer_Rudolph_Gharibian_2025, title={Quantum k-SAT Related Hypergraph Problems}, journal={arXiv:2506.17066}, author={Kremer, Simon-Luca and Rudolph, Dorian and Gharibian, Sevag}, year={2025} }"},"type":"preprint","publication":"arXiv:2506.17066","date_updated":"2025-06-27T06:57:03Z","title":"Quantum k-SAT Related Hypergraph Problems","_id":"60432","language":[{"iso":"eng"}],"author":[{"full_name":"Kremer, Simon-Luca","last_name":"Kremer","first_name":"Simon-Luca"},{"last_name":"Rudolph","full_name":"Rudolph, Dorian","first_name":"Dorian","id":"57863"},{"orcid":"0000-0002-9992-3379","full_name":"Gharibian, Sevag","last_name":"Gharibian","first_name":"Sevag","id":"71541"}],"year":"2025","user_id":"71541","date_created":"2025-06-27T06:56:35Z","status":"public","abstract":[{"lang":"eng","text":"The Quantum k-SAT problem is the quantum generalization of the k-SAT problem.\r\nIt is the problem whether a given local Hamiltonian is frustration-free.\r\nFrustration-free means that the ground state of the k-local Hamiltonian\r\nminimizes the energy of every local interaction term simultaneously. This is a\r\ncentral question in quantum physics and a canonical QMA_1-complete problem. The\r\nQuantum k-SAT problem is not as well studied as the classical k-SAT problem in\r\nterms of special tractable cases, approximation algorithms and parameterized\r\ncomplexity. In this paper, we will give a graph-theoretic study of the Quantum\r\nk-SAT problem with the structures core and radius. These hypergraph structures\r\nare important to solve the Quantum k-SAT problem. We can solve a Quantum k-SAT\r\ninstance in polynomial time if the derived hypergraph has a core of size n-m+a,\r\nwhere a is a constant, and the radius is at most logarithmic. If it exists, we\r\ncan find a core of size n-m+a with the best possible radius in polynomial time,\r\nwhereas finding a general minimum core with minimal radius is NP-hard."}],"external_id":{"arxiv":["2506.17066"]}}