{"publication_status":"published","volume":261,"external_id":{"arxiv":["2207.10250"]},"issue":"32","department":[{"_id":"623"},{"_id":"7"}],"doi":"10.4230/LIPIcs.ICALP.2023.32","language":[{"iso":"eng"}],"abstract":[{"text":"Estimating the ground state energy of a local Hamiltonian is a central\r\nproblem in quantum chemistry. In order to further investigate its complexity\r\nand the potential of quantum algorithms for quantum chemistry, Gharibian and Le\r\nGall (STOC 2022) recently introduced the guided local Hamiltonian problem\r\n(GLH), which is a variant of the local Hamiltonian problem where an\r\napproximation of a ground state is given as an additional input. Gharibian and\r\nLe Gall showed quantum advantage (more precisely, BQP-completeness) for GLH\r\nwith $6$-local Hamiltonians when the guiding vector has overlap\r\n(inverse-polynomially) close to 1/2 with a ground state. In this paper, we\r\noptimally improve both the locality and the overlap parameters: we show that\r\nthis quantum advantage (BQP-completeness) persists even with 2-local\r\nHamiltonians, and even when the guiding vector has overlap\r\n(inverse-polynomially) close to 1 with a ground state. Moreover, we show that\r\nthe quantum advantage also holds for 2-local physically motivated Hamiltonians\r\non a 2D square lattice. This makes a further step towards establishing\r\npractical quantum advantage in quantum chemistry.","lang":"eng"}],"citation":{"bibtex":"@inproceedings{Gharibian_Hayakawa_Gall_Morimae_2023, title={Improved Hardness Results for the Guided Local Hamiltonian Problem}, volume={261}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.32\">10.4230/LIPIcs.ICALP.2023.32</a>}, number={32}, booktitle={Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP)}, author={Gharibian, Sevag and Hayakawa, Ryu and Gall, François Le and Morimae, Tomoyuki}, year={2023}, pages={1–19} }","ama":"Gharibian S, Hayakawa R, Gall FL, Morimae T. Improved Hardness Results for the Guided Local Hamiltonian Problem. In: <i>Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>. Vol 261. ; 2023:1-19. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.32\">10.4230/LIPIcs.ICALP.2023.32</a>","apa":"Gharibian, S., Hayakawa, R., Gall, F. L., &#38; Morimae, T. (2023). Improved Hardness Results for the Guided Local Hamiltonian Problem. <i>Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>, <i>261</i>(32), 1–19. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.32\">https://doi.org/10.4230/LIPIcs.ICALP.2023.32</a>","mla":"Gharibian, Sevag, et al. “Improved Hardness Results for the Guided Local Hamiltonian Problem.” <i>Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>, vol. 261, no. 32, 2023, pp. 1–19, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.32\">10.4230/LIPIcs.ICALP.2023.32</a>.","chicago":"Gharibian, Sevag, Ryu Hayakawa, François Le Gall, and Tomoyuki Morimae. “Improved Hardness Results for the Guided Local Hamiltonian Problem.” In <i>Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>, 261:1–19, 2023. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.32\">https://doi.org/10.4230/LIPIcs.ICALP.2023.32</a>.","ieee":"S. Gharibian, R. Hayakawa, F. L. Gall, and T. Morimae, “Improved Hardness Results for the Guided Local Hamiltonian Problem,” in <i>Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>, 2023, vol. 261, no. 32, pp. 1–19, doi: <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2023.32\">10.4230/LIPIcs.ICALP.2023.32</a>.","short":"S. Gharibian, R. Hayakawa, F.L. Gall, T. Morimae, in: Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP), 2023, pp. 1–19."},"year":"2023","_id":"32407","publication":"Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP)","date_created":"2022-07-22T12:32:40Z","status":"public","author":[{"first_name":"Sevag","last_name":"Gharibian","id":"71541","orcid":"0000-0002-9992-3379","full_name":"Gharibian, Sevag"},{"full_name":"Hayakawa, Ryu","first_name":"Ryu","last_name":"Hayakawa"},{"first_name":"François Le","last_name":"Gall","full_name":"Gall, François Le"},{"last_name":"Morimae","first_name":"Tomoyuki","full_name":"Morimae, Tomoyuki"}],"intvolume":"       261","page":"1-19","type":"conference","user_id":"71541","title":"Improved Hardness Results for the Guided Local Hamiltonian Problem","date_updated":"2023-10-09T04:17:10Z"}