{"paper":{"title":"State $k$-designs from Hamiltonian evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"quant-ph","authors_text":"Shengxian Hou, Zhi-Cheng Yang, Zong-Yue Hou","submitted_at":"2026-07-20T22:04:54Z","abstract_excerpt":"We study the generation of state $k$-designs from time evolution under a fixed Hamiltonian. Specifically, we consider the ensemble $\\mathcal{E}=\\left\\{e^{-iHt}|\\psi_0\\rangle | \\ t\\sim \\mathrm{Unif}[0,T],\\, |\\psi_0\\rangle\\sim \\mathcal{E}'\\right\\}$, where the initial states are sampled from an ensemble $\\mathcal{E}'$. For Hamiltonians drawn from the Gaussian unitary ensemble, we derive a simple relation between the frame potential of the evolved ensemble $\\mathcal{E}$ and that of the initial ensemble $\\mathcal{E}'$ in the large evolution time limit. This relation shows that $\\mathcal{E}$ forms a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18537","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.18537/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}