{"publication":"arXiv:2411.04874","date_created":"2024-11-08T07:58:24Z","user_id":"71541","title":"Hardness of approximation for ground state problems","citation":{"ama":"Gharibian S, Hecht C. Hardness of approximation for ground state problems. <i>arXiv:241104874</i>. Published online 2024.","apa":"Gharibian, S., &#38; Hecht, C. (2024). Hardness of approximation for ground state problems. In <i>arXiv:2411.04874</i>.","ieee":"S. Gharibian and C. Hecht, “Hardness of approximation for ground state problems,” <i>arXiv:2411.04874</i>. 2024.","short":"S. Gharibian, C. Hecht, ArXiv:2411.04874 (2024).","mla":"Gharibian, Sevag, and Carsten Hecht. “Hardness of Approximation for Ground State Problems.” <i>ArXiv:2411.04874</i>, 2024.","bibtex":"@article{Gharibian_Hecht_2024, title={Hardness of approximation for ground state problems}, journal={arXiv:2411.04874}, author={Gharibian, Sevag and Hecht, Carsten}, year={2024} }","chicago":"Gharibian, Sevag, and Carsten Hecht. “Hardness of Approximation for Ground State Problems.” <i>ArXiv:2411.04874</i>, 2024."},"date_updated":"2024-11-08T07:58:44Z","language":[{"iso":"eng"}],"author":[{"full_name":"Gharibian, Sevag","orcid":"0000-0002-9992-3379","first_name":"Sevag","id":"71541","last_name":"Gharibian"},{"last_name":"Hecht","first_name":"Carsten","full_name":"Hecht, Carsten"}],"external_id":{"arxiv":["2411.04874"]},"_id":"56950","type":"preprint","year":"2024","status":"public","abstract":[{"text":"After nearly two decades of research, the question of a quantum PCP theorem\r\nfor quantum Constraint Satisfaction Problems (CSPs) remains wide open. As a\r\nresult, proving QMA-hardness of approximation for ground state energy\r\nestimation has remained elusive. Recently, it was shown [Bittel, Gharibian,\r\nKliesch, CCC 2023] that a natural problem involving variational quantum\r\ncircuits is QCMA-hard to approximate within ratio N^(1-eps) for any eps > 0 and\r\nN the input size. Unfortunately, this problem was not related to quantum CSPs,\r\nleaving the question of hardness of approximation for quantum CSPs open. In\r\nthis work, we show that if instead of focusing on ground state energies, one\r\nconsiders computing properties of the ground space, QCMA-hardness of computing\r\nground space properties can be shown. In particular, we show that it is (1)\r\nQCMA-complete within ratio N^(1-eps) to approximate the Ground State\r\nConnectivity problem (GSCON), and (2) QCMA-hard within the same ratio to\r\nestimate the amount of entanglement of a local Hamiltonian's ground state,\r\ndenoted Ground State Entanglement (GSE). As a bonus, a simplification of our\r\nconstruction yields NP-completeness of approximation for a natural k-SAT\r\nreconfiguration problem, to be contrasted with the recent PCP-based PSPACE\r\nhardness of approximation results for a different definition of k-SAT\r\nreconfiguration [Karthik C.S. and Manurangsi, 2023, and Hirahara, Ohsaka, STOC\r\n2024].","lang":"eng"}]}