{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-square-root-speedup-for-finding-the","title":"A square-root speedup for finding the smallest eigenvalue","arxiv_id":"2311.04379","date":"2023-11-07","proceeding":null,"authors":["Alex Kerzner","Vlad Gheorghiu","Michele Mosca","Thomas Guilbaud","Federico Carminati","Fabio Fracas","Luca Dellantonio"],"abstract":"We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical algorithm in terms of matrix dimensionality, i.e., $\\widetilde{\\mathcal{O}}(\\sqrt{N}/\\epsilon)$ black-box queries to an oracle encoding the matrix, where $N$ is the matrix dimension and $\\epsilon$ is the desired precision. In contrast, the best classical algorithm for the same task requires $\\Omega(N)\\text{polylog}(1/\\epsilon)$ queries. In addition, this algorithm allows the user to select any constant success probability. We also provide a similar algorithm with the same runtime that allows us to prepare a quantum state lying mostly in the matrix's low-energy subspace. We implement simulations of both algorithms and demonstrate their application to problems in quantum chemistry and materials science.","url_abs":"https://arxiv.org/abs/2311.04379v2","url_pdf":"https://arxiv.org/pdf/2311.04379v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-square-root-speedup-for-finding-the","repo_url":"https://github.com/softwareqinc/eigenvaluefinding","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}