{"language":[{"iso":"eng"}],"user_id":"71541","department":[{"_id":"7"},{"_id":"623"}],"_id":"61778","external_id":{"arxiv":["2510.06796"]},"status":"public","abstract":[{"text":"Understanding the entanglement structure of local Hamiltonian ground spaces\r\nis a physically motivated problem, with applications ranging from tensor\r\nnetwork design to quantum error-correcting codes. To this end, we study the\r\ncomplexity of estimating ground state entanglement, and more generally entropy\r\nestimation for low energy states and Gibbs states. We find, in particular, that\r\nthe classes qq-QAM [Kobayashi, le Gall, Nishimura, SICOMP 2019] (a quantum\r\nanalogue of public-coin AM) and QMA(2) (QMA with unentangled proofs) play a\r\ncrucial role for such problems, showing: (1) Detecting a high-entanglement\r\nground state is qq-QAM-complete, (2) computing an additive error approximation\r\nto the Helmholtz free energy (equivalently, a multiplicative error\r\napproximation to the partition function) is in qq-QAM, (3) detecting a\r\nlow-entanglement ground state is QMA(2)-hard, and (4) detecting low energy\r\nstates which are close to product states can range from QMA-complete to\r\nQMA(2)-complete. Our results make progress on an open question of [Bravyi,\r\nChowdhury, Gosset and Wocjan, Nature Physics 2022] on free energy, and yield\r\nthe first QMA(2)-complete Hamiltonian problem using local Hamiltonians (cf. the\r\nsparse QMA(2)-complete Hamiltonian problem of [Chailloux, Sattath, CCC 2012]).","lang":"eng"}],"type":"preprint","publication":"arXiv:2510.06796","title":"On the complexity of estimating ground state entanglement and free  energy","date_created":"2025-10-10T13:45:28Z","author":[{"first_name":"Sevag","full_name":"Gharibian, Sevag","last_name":"Gharibian"},{"first_name":"Jonas","last_name":"Kamminga","full_name":"Kamminga, Jonas"}],"date_updated":"2026-04-20T13:53:47Z","citation":{"ieee":"S. Gharibian and J. Kamminga, “On the complexity of estimating ground state entanglement and free  energy,” <i>arXiv:2510.06796</i>. 2025.","chicago":"Gharibian, Sevag, and Jonas Kamminga. “On the Complexity of Estimating Ground State Entanglement and Free  Energy.” <i>ArXiv:2510.06796</i>, 2025.","ama":"Gharibian S, Kamminga J. On the complexity of estimating ground state entanglement and free  energy. <i>arXiv:251006796</i>. Published online 2025.","apa":"Gharibian, S., &#38; Kamminga, J. (2025). On the complexity of estimating ground state entanglement and free  energy. In <i>arXiv:2510.06796</i>.","short":"S. Gharibian, J. Kamminga, ArXiv:2510.06796 (2025).","bibtex":"@article{Gharibian_Kamminga_2025, title={On the complexity of estimating ground state entanglement and free  energy}, journal={arXiv:2510.06796}, author={Gharibian, Sevag and Kamminga, Jonas}, year={2025} }","mla":"Gharibian, Sevag, and Jonas Kamminga. “On the Complexity of Estimating Ground State Entanglement and Free  Energy.” <i>ArXiv:2510.06796</i>, 2025."},"year":"2025"}