TY - GEN
T1 - Level sets of quantum control landscapes
AU - Beltrani, Vincent
AU - Dominy, Jason
AU - Ho, Tak San
AU - Rabitz, Herschel
PY - 2010
Y1 - 2010
N2 - A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable value. This paper focuses on level sets of the transition probability P i→f. For transition probabilities 0 < Pi→f < 1, a first order diffeomorphic modulation observable response preserving homotopy (D-MORPH) algorithm is utilized to investigate level sets. At the top of the control landscape, Pi→f = 1, a second order D-MORPH algorithm is presented that can explore the perfect control level set. D-MORPH is utilized to identify level set members that exhibit certain desirable secondary characteristics, e.g., minimal pulse ftuence. Numerical simulations for finite level systems are presented to illustrate the variety of control behavior found across level set members.
AB - A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable value. This paper focuses on level sets of the transition probability P i→f. For transition probabilities 0 < Pi→f < 1, a first order diffeomorphic modulation observable response preserving homotopy (D-MORPH) algorithm is utilized to investigate level sets. At the top of the control landscape, Pi→f = 1, a second order D-MORPH algorithm is presented that can explore the perfect control level set. D-MORPH is utilized to identify level set members that exhibit certain desirable secondary characteristics, e.g., minimal pulse ftuence. Numerical simulations for finite level systems are presented to illustrate the variety of control behavior found across level set members.
UR - http://www.scopus.com/inward/record.url?scp=77953818752&partnerID=8YFLogxK
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U2 - 10.1109/ISCCSP.2010.5463443
DO - 10.1109/ISCCSP.2010.5463443
M3 - Conference contribution
AN - SCOPUS:77953818752
SN - 9781424462858
T3 - Final Program and Abstract Book - 4th International Symposium on Communications, Control, and Signal Processing, ISCCSP 2010
BT - Final Program and Abstract Book - 4th International Symposium on Communications, Control, and Signal Processing, ISCCSP 2010
T2 - 4th International Symposium on Communications, Control, and Signal Processing, ISCCSP-2010
Y2 - 3 March 2010 through 5 March 2010
ER -