{"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/ground-state-preparation-via-qubitization","title":"Ground State Preparation via Qubitization","arxiv_id":"2306.14993","date":"2023-06-26","proceeding":null,"authors":["Charles Marteau"],"abstract":"We describe a protocol for preparing the ground state of a Hamiltonian $H$ on a quantum computer. This is done by designing a quantum algorithm that implements the imaginary time evolution operator: $e^{-\\tau H}$. The method relies on the so-called ``qubitization'' procedure of Low and Chuang which, assuming the existence of a unitary encoding of the Hamiltonian $H = \\langle G| U_H |G\\rangle$, produces a new operator $W_H$ whose moments are the Chebyshev polynomials of $H$ when projected on $|G\\rangle$. Using this result and the expansion of $e^{-\\tau H}$ in terms of Chebyshev polynomials we construct a circuit that implements an approximation of the imaginary time evolution operator which, at large time, projects any state on the ground state, provided a non-trivial initial overlap between the two. We illustrate our method on two models: the transverse field Ising model and a single qubit toy model.","url_abs":"https://arxiv.org/abs/2306.14993v1","url_pdf":"https://arxiv.org/pdf/2306.14993v1.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":"ground-state-preparation-via-qubitization","repo_url":"https://github.com/charles-marteau/ground-state-preparation-via-qubitization","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}