{"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/variational-quantum-state-diagonalization","title":"Variational Quantum State Diagonalization","arxiv_id":"1810.10506","date":"2018-10-24","proceeding":null,"authors":["Ryan LaRose","Arkin Tikku","Étude O'Neel-Judy","Lukasz Cincio","Patrick J. Coles"],"abstract":"Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost evaluation), and a classical computer uses this information to adjust the parameters of the gate sequence. Here we present such an algorithm for quantum state diagonalization. State diagonalization has applications in condensed matter physics (e.g., entanglement spectroscopy) as well as in machine learning (e.g., principal component analysis). For a quantum state $\\rho$ and gate sequence $U$, our cost function quantifies how far $ U\\rho U^{\\dagger}$ is from being diagonal. We introduce novel short-depth quantum circuits to quantify our cost. Minimizing this cost returns a gate sequence that approximately diagonalizes $\\rho$. One can then read out approximations of the largest eigenvalues, and the associated eigenvectors, of $\\rho$. As a proof-of-principle, we implement our algorithm on Rigetti's quantum computer to diagonalize one-qubit states and on a simulator to find the entanglement spectrum of the Heisenberg model ground state.","url_abs":"https://arxiv.org/abs/1810.10506v2","url_pdf":"https://arxiv.org/pdf/1810.10506v2.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":"variational-quantum-state-diagonalization","repo_url":"https://github.com/rmlarose/vqsd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}