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A proof that almost all quantum systems have trap free (that is, free from local optima) landscapes is presented for a large and physically general class of quantum system.
The measure of the critical values of differentiable maps
Arthur Sard · 1942
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Representation Theory: A First Course
W. Fulton and J. Harris · 1991
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Teaching lasers to control molecules
Richard S. Judson and Herschel Rabitz · 1992
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Differential Topology
M.W. Hirsch · 1997
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Geometric Control Theory
V. Jurdjevic · 1997
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The Convenient Setting of Global Analysis
A. Kriegl and P.W. Michor · 1997
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Geometric quantum mechanics
Dorje C. Brody and Lane P. Hughston · 2001
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Controllability of quantum mechanical systems by root space decomposition of su(n)
Claudio Altafini · 2002
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
B. Hall · 2003
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A geometric approach to quantum circuit lower bounds
M. A. Nielsen · 2005
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Time-optimal quantum evolution
Alberto Carlini, Akio Hosoya, Tatsuhiko Koike, and Yosuke Okudaira · 2006
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Quantum control landscapes
Raj Chakrabarti and Herschel Rabitz · 2007
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On the relationship between quantum control landscape structure and optimization complexity
Katharine Moore, Michael Hsieh, and Herschel Rabitz · 2008
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Gradient algorithm applied to laboratory quantum control
Jonathan Roslund and Herschel Rabitz · 2009
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Experimental quantum control landscapes: Inherent monotonicity and artificial structure
Jonathan Roslund and Herschel Rabitz · 2009
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A (terse) Introduction to Lebesgue Integration
J.M. Franks · 2009
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Landscape of unitary transformations in controlled quantum dynamics
Tak-San Ho, Jason Dominy, and Herschel Rabitz · 2009
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Control of quantum phenomena: past, present and future
Constantin Brif, Raj Chakrabarti, and Herschel Rabitz · 2010
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Exploring quantum control landscapes: Topology, features, and optimization scaling
Katharine W. Moore and Herschel Rabitz · 2011
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Search complexity and resource scaling for the quantum optimal control of unitary transformations
Katharine W. Moore, Raj Chakrabarti, Gregory Riviello, and Herschel Rabitz · 2011
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Are there traps in quantum control landscapes?
Alexander N. Pechen and David J. Tannor · 2011
Searching for quantum optimal control fields in the presence of singular critical points
Gregory Riviello, Constantin Brif, Ruixing Long, Re-Bing Wu, Katharine Moore Tibbetts, Tak-San Ho, and Herschel Rabitz · 2014
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Experimental exploration over a quantum control landscape through nuclear magnetic resonance
Qiuyang Sun, István Pelczer, Gregory Riviello, Re-Bing Wu, and Herschel Rabitz · 2014
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Control of open quantum systems: case study of the central spin model
Christian Arenz, Giulia Gualdi, and Daniel Burgarth · 2014
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applications of finsler geometry to speed limits to quantum information processing
Benjamin Russell and Susan Stepney · 2014
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Zermelo navigation in the quantum brachistochrone
Benjamin Russell and Susan Stepney · 2015
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Generalized euler-poincaré equations on lie groups and homogeneous spaces, orbit invariants and applications
Feride Tiglay and Cornelia Vizman · 2011
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Comment on “are there traps in quantum control landscapes?”
Herschel Rabitz, Tak-San Ho, Ruixing Long, Rebing Wu, and Constantin Brif · 2012
Cited alongside, same era.
Singularities of quantum control landscapes
Re-Bing Wu, Ruixing Long, Jason Dominy, Tak-San Ho, and Herschel Rabitz · 2012
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a closer look at quantum control landscapes and their implication for control optimization
Pierre De Fouquieres and Sophie G. Schirmer · 2013
Cited alongside, same era.
The gradient flow for control of closed quantum systems
Ruixing Long, G. Riviello, and H. Rabitz · 2013
Cited alongside, same era.
Zermelo navigation and a speed limit to quantum information processing
Benjamin Russell and Susan Stepney · 2014
Cited alongside, same era.
Quantum brachistochrone curves as geodesics: Obtaining accurate minimum-time protocols for the control of quantum systems
Xiaoting Wang, Michele Allegra, Kurt Jacobs, Seth Lloyd, Cosmo Lupo, and Masoud Mohseni · 2015
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Elementary solution to the time-independent quantum navigation problem
Dorje C Brody and David M Meier · 2015
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Time-optimal navigation through quantum wind
Dorje C Brody, Gary W Gibbons, and David M Meier · 2015
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Solution to the quantum zermelo navigation problem
Dorje C. Brody and David M. Meier · 2015
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Searching for quantum optimal controls under severe constraints
Gregory Riviello, Katharine Moore Tibbetts, Constantin Brif, Ruixing Long, Re-Bing Wu, Tak-San Ho, and Herschel Rabitz · 2015
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On choosing the form of the objective functional for optimal control of molecules
T.-S. Ho C. Joe-Wong and H. Rabitz · 2015
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Optimization: Algorithms and Applications
R.K. Arora · 2015
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Experimental observation of saddle points over the quantum control landscape of a two-spin system
Qiuyang Sun, István Pelczer, Gregory Riviello, Re-Bing Wu, and Herschel Rabitz · 2015
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Quantum Control Landscapes Beyond the Dipole Approximation
B. Russell, H. Rabitz, and R. Wu · 2016
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