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Searching for quantum optimal control fields in the presence of singular critical points

Author(s): Riviello, Gregory; Brif, Constantin; Long, Ruixing; Wu, Re-Bing; Tibbetts, Katharine Moore; et al

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dc.contributor.authorRiviello, Gregory-
dc.contributor.authorBrif, Constantin-
dc.contributor.authorLong, Ruixing-
dc.contributor.authorWu, Re-Bing-
dc.contributor.authorTibbetts, Katharine Moore-
dc.contributor.authorHo, Tak-San-
dc.contributor.authorRabitz, Herschel-
dc.date.accessioned2020-10-30T18:35:46Z-
dc.date.available2020-10-30T18:35:46Z-
dc.date.issued2014-07-07en_US
dc.identifier.citationRiviello, Gregory, Brif, Constantin, Long, Ruixing, Wu, Re-Bing, Tibbetts, Katharine Moore, Ho, Tak-San, Rabitz, Herschel. (2014). Searching for quantum optimal control fields in the presence of singular critical points. PHYSICAL REVIEW A, 90 (10.1103/PhysRevA.90.013404en_US
dc.identifier.issn1050-2947-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1zv4h-
dc.description.abstractQuantum optimal control has enjoyed wide success for a variety of theoretical and experimental objectives. These favorable results have been attributed to advantageous properties of the corresponding control landscapes, which are free from local optima if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is full rank, and (3) the control field is not constrained. This paper explores how gradient searches for globally optimal control fields are affected by deviations from assumption (2). In some quantum control problems, so-called singular critical points, at which the Jacobian is rank deficient, may exist on the landscape. Using optimal control simulations, we show that search failure is only observed when a singular critical point is also a second-order trap, which occurs if the control problem meets additional conditions involving the system Hamiltonian and/or the control objective. All known second-order traps occur at constant control fields, and we also show that they only affect searches that originate very close to them. As a result, even when such traps exist on the control landscape, they are unlikely to affect well-designed gradient optimizations under realistic searching conditions.en_US
dc.format.extent013404-1 - 013404-12en_US
dc.language.isoen_USen_US
dc.relation.ispartofPHYSICAL REVIEW Aen_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleSearching for quantum optimal control fields in the presence of singular critical pointsen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1103/PhysRevA.90.013404-
dc.identifier.eissn1094-1622-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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