{"paper":{"title":"Time-dependent Hamiltonian simulation with $L^1$-norm scaling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","cs.DS","physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Andrew M. Childs, Dominic W. Berry, Nathan Wiebe, Xin Wang, Yuan Su","submitted_at":"2019-06-17T16:31:56Z","abstract_excerpt":"The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For sparse Hamiltonian simulation, the gate complexity scales with the $L^1$ norm $\\int_{0}^{t}\\mathrm{d}\\tau\\left\\lVert H(\\tau)\\right\\lVert_{\\max}$, whereas the best previous results scale with $t\\max_{\\tau\\in[0,t]}\\left\\lVert H(\\tau)\\right\\lVert_{\\max}$. We also show analogous results for Hamiltonians that are linear combi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07115","kind":"arxiv","version":2},"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/1906.07115/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"}