[{"title":"Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture","date_updated":"2023-10-09T04:17:29Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2111.09079"}],"citation":{"apa":"Gharibian, S., & Gall, F. L. (2022). Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture. *Proceedings of the 54th ACM Symposium on Theory of Computing (STOC)*, 19–32.","chicago":"Gharibian, Sevag, and François Le Gall. “Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture.” In *Proceedings of the 54th ACM Symposium on Theory of Computing (STOC)*, 19–32, 2022.","ieee":"S. Gharibian and F. L. Gall, “Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture,” in *Proceedings of the 54th ACM Symposium on Theory of Computing (STOC)*, 2022, pp. 19–32.","mla":"Gharibian, Sevag, and François Le Gall. “Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture.” *Proceedings of the 54th ACM Symposium on Theory of Computing (STOC)*, 2022, pp. 19–32.","ama":"Gharibian S, Gall FL. Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture. In: *Proceedings of the 54th ACM Symposium on Theory of Computing (STOC)*. ; 2022:19-32.","short":"S. Gharibian, F.L. Gall, in: Proceedings of the 54th ACM Symposium on Theory of Computing (STOC), 2022, pp. 19–32.","bibtex":"@inproceedings{Gharibian_Gall_2022, title={Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture}, booktitle={Proceedings of the 54th ACM Symposium on Theory of Computing (STOC)}, author={Gharibian, Sevag and Gall, François Le}, year={2022}, pages={19–32} }"},"user_id":"71541","oa":"1","publication_status":"published","department":[{"_id":"623"},{"_id":"7"}],"publication":"Proceedings of the 54th ACM Symposium on Theory of Computing (STOC)","year":"2022","abstract":[{"lang":"eng","text":"The Quantum Singular Value Transformation (QSVT) is a recent technique that\r\ngives a unified framework to describe most quantum algorithms discovered so\r\nfar, and may lead to the development of novel quantum algorithms. In this paper\r\nwe investigate the hardness of classically simulating the QSVT. A recent result\r\nby Chia, Gily\\'en, Li, Lin, Tang and Wang (STOC 2020) showed that the QSVT can\r\nbe efficiently \"dequantized\" for low-rank matrices, and discussed its\r\nimplication to quantum machine learning. In this work, motivated by\r\nestablishing the superiority of quantum algorithms for quantum chemistry and\r\nmaking progress on the quantum PCP conjecture, we focus on the other main class\r\nof matrices considered in applications of the QSVT, sparse matrices.\r\n We first show how to efficiently \"dequantize\", with arbitrarily small\r\nconstant precision, the QSVT associated with a low-degree polynomial. We apply\r\nthis technique to design classical algorithms that estimate, with constant\r\nprecision, the singular values of a sparse matrix. We show in particular that a\r\ncentral computational problem considered by quantum algorithms for quantum\r\nchemistry (estimating the ground state energy of a local Hamiltonian when\r\ngiven, as an additional input, a state sufficiently close to the ground state)\r\ncan be solved efficiently with constant precision on a classical computer. As a\r\ncomplementary result, we prove that with inverse-polynomial precision, the same\r\nproblem becomes BQP-complete. This gives theoretical evidence for the\r\nsuperiority of quantum algorithms for chemistry, and strongly suggests that\r\nsaid superiority stems from the improved precision achievable in the quantum\r\nsetting. We also discuss how this dequantization technique may help make\r\nprogress on the central quantum PCP conjecture."}],"page":"19-32","external_id":{"arxiv":["2111.09079"]},"type":"conference","language":[{"iso":"eng"}],"date_created":"2021-11-18T07:32:56Z","status":"public","_id":"27531","author":[{"orcid":"0000-0002-9992-3379","first_name":"Sevag","last_name":"Gharibian","id":"71541","full_name":"Gharibian, Sevag"},{"full_name":"Gall, François Le","last_name":"Gall","first_name":"François Le"}]}]