TY - JOUR
T1 - Optimal pulse design in quantum control
T2 - A unified computational method
AU - Li, Shin
AU - Ruths, Justin
AU - Yu, Tsyr Yan
AU - Arthanari, Haribabu
AU - Wagner, Gerhard
N1 - Funding Information:
The authors are grateful to Research Management Centre (RMC), International Islamic University Malaysia (IIUM) for partially funding this research project entitled ´Fisheries Conservation Towards Sustainable Development in Tropical Environmentµ through Research Grant (RIGS16-106-0270) during their study period.
PY - 2011/2/1
Y1 - 2011/2/1
N2 - Many key aspects of control of quantum systems involve manipulating a large quantum ensemble exhibiting variation in the value of parameters characterizing the system dynamics. Developing electromagnetic pulses to produce a desired evolution in the presence of such variation is a fundamental and challenging problem in this research area. We present such robust pulse designs as an optimal control problem of a continuum of bilinear systems with a common control function. We map this control problem of infinite dimension to a problem of polynomial approximation employing tools from geometric control theory. We then adopt this new notion and develop a unified computational method for optimal pulse design using ideas from pseudospectral approximations, by which a continuous-time optimal control problem of pulse design can be discretized to a constrained optimization problem with spectral accuracy. Furthermore, this is a highly flexible and efficient numerical method that requires low order of discretization and yields inherently smooth solutions. We demonstrate this method by designing effective broadband π/2 and ? pulses with reduced rf energy and pulse duration, which show significant sensitivity enhancement at the edge of the spectrum over conventional pulses in 1D and 2D NMR spectroscopy experiments.
AB - Many key aspects of control of quantum systems involve manipulating a large quantum ensemble exhibiting variation in the value of parameters characterizing the system dynamics. Developing electromagnetic pulses to produce a desired evolution in the presence of such variation is a fundamental and challenging problem in this research area. We present such robust pulse designs as an optimal control problem of a continuum of bilinear systems with a common control function. We map this control problem of infinite dimension to a problem of polynomial approximation employing tools from geometric control theory. We then adopt this new notion and develop a unified computational method for optimal pulse design using ideas from pseudospectral approximations, by which a continuous-time optimal control problem of pulse design can be discretized to a constrained optimization problem with spectral accuracy. Furthermore, this is a highly flexible and efficient numerical method that requires low order of discretization and yields inherently smooth solutions. We demonstrate this method by designing effective broadband π/2 and ? pulses with reduced rf energy and pulse duration, which show significant sensitivity enhancement at the edge of the spectrum over conventional pulses in 1D and 2D NMR spectroscopy experiments.
KW - Broadband excitation
KW - Ensemble control
KW - Lie algebra
KW - Pseudospectral methods
UR - http://www.scopus.com/inward/record.url?scp=79952119589&partnerID=8YFLogxK
U2 - 10.1073/pnas.1009797108
DO - 10.1073/pnas.1009797108
M3 - Article
AN - SCOPUS:79952119589
SN - 0027-8424
VL - 108
SP - 1879
EP - 1884
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 5
ER -