{"paper":{"title":"Characterization of the Critical Sets of Quantum Unitary Control Landscapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Herschel Rabitz, Jason Dominy, Tak-San Ho","submitted_at":"2011-02-17T06:04:04Z","abstract_excerpt":"This work considers various families of quantum control landscapes (i.e. objective functions for optimal control) for obtaining target unitary transformations as the general solution of the controlled Schr\\\"odinger equation. We examine the critical point structure of the kinematic landscapes J_F (U) = ||(U-W)A||^2 and J_P (U) = ||A||^4 - |Tr(AA'W'U)|^2 defined on the unitary group U(H) of a finite-dimensional Hilbert space H. The parameter operator A in B(H) is allowed to be completely arbitrary, yielding an objective function that measures the difference in the actions of U and the target W o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3502","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":""},"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"}