Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR

Skinner, Thomas E.; Reiss, Timo O.; Luy, Burkhard; Khaneja, Navin; Glaser, Steffen J.

doi:10.1016/s1090-7807(03)00153-8

Cited by 270 publications

(328 citation statements)

References 13 publications

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“…In contrast, the number of pulse parameters that can be optimized by optimal control based algorithms can be several orders of magnitude larger compared to conventional approaches. In NMR, this approach has been used so far to design bandselective pulses (9,(15)(16)(17), robust broadband excitation and inversion pulses (18)(19)(20)(21) and to explore the physical limits of pulse performance (20). Here, we demonstrate the design of pulses which create arbitrary patterns as a function of offset and rf amplitude.…”

Section: Introductionmentioning

confidence: 99%

Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset

Kobzar

Luy

Khaneja

et al. 2005

Journal of Magnetic Resonance

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115

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Section: Introductionmentioning

confidence: 99%

Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset

Kobzar

Luy

Khaneja

et al. 2005

Journal of Magnetic Resonance

Self Cite

107

115

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“…With relatively coarse discretization (N ¼ 30) and sampling (N ω ¼ 8) chosen with the LGL nodes, the PS method achieves a performance of 0.98. In the commonly used gradient methods, optimizations are usually performed in 0.5-μs steps over time (corresponding to N ¼ 200) and 0.5 kHz over the resonance offset space (N ω ¼ 80), which may achieve a comparable performance (13). Increasing the number of discre-tizations or samples in the PS method, as shown in the convergence section, would yield an increased objective value.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…However, these approaches have a number of shortcomings, such as slow convergence rates and being easily trapped into local optima. In recent years, there have been attempts to look at pulse design problems from a control theory perspective (11)(12)(13)(14). In particular, state-of-the-art methods such as gradient ascent and Krotov algorithms are based on principles of optimal control theory (15, 16) and have been used successfully to design broadband and relaxation-optimized pulses that maximize the performance of quantum systems in the presence of relaxation (17)(18)(19).…”

mentioning

confidence: 99%

Optimal pulse design in quantum control: A unified computational method

Ruths

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

134

109

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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 π 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.pseudospectral methods | ensemble control | Lie algebra | broadband excitation C ompelling applications for quantum control have received particular attention and have motivated seminal studies in wide-ranging areas from coherent spectroscopy and MRI to quantum optics. Designing and implementing time-varying excitations (rf pulses) to manipulate complex dynamics of a large quantum ensemble on the order of Avogadro's number is a long-standing problem and an indispensable step that enables every application of quantum control (1). For example, magnetic resonance applications often suffer from imperfections such as inhomogeneity in the static magnetic field (B 0 inhomogeneity) and in the applied rf field (rf inhomogeneity). In addition, there is dispersion in the Larmor frequency of spins due to chemical shifts. A good pulse design strategy must be robust to these effects, and such variations need to be considered in the modeling and pulse design stages in order to match theoretical predictions to experimental outcomes. As difficult experiments with more demanding performance specifications have emerged, the complexity of finding optimal pulse sequences has drastically increased. For example, as high-field NMR spectrometers are increasingly more accessible and required, broadband excitation pulses are needed to cover a wide 13 C chemical-shift range (e.g., up to 40 kHz). In addition, to design excitation and inversion pulses that are practical for a typical NMR spectrometer, methods must accommodate realistic maximum rf power and pulse duration while accomplishing the desired spin evolution. In the majority of cases, the length of an rf pulse is constrained by the fixed delays that dictate a certain coherence transfer. S...

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“…Nowadays, Optimal Control Theory (OCT) reveals to be a highly efficient and versatile tool to bring answers to the different issues raised by the experimental setups [2,[10][11][12][13][14][15][16][17][18][19][20][21][22]. For the past few years, there has been an intense theoretical activity in developing new optimal control procedures able to build high quality control fields in presence of some experimental imperfections and constraints [2,13,[23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Discrete-valued-pulse optimal control algorithms: Application to spin systems

et al. 2015

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This article is aimed at extending the framework of optimal control techniques to the situation where the control field values are restricted to a finite set. We propose a generalization of the standard GRAPE algorithm suited to this constraint. We test the validity and the efficiency of this approach for the inversion of an inhomogeneous ensemble of spin systems with different offset frequencies. It is shown that a remarkable efficiency can be achieved even for a very limited number of discrete values. Some applications in Nuclear Magnetic Resonance are discussed.

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Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR

Cited by 270 publications

References 13 publications

Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset

Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset

Optimal pulse design in quantum control: A unified computational method

Discrete-valued-pulse optimal control algorithms: Application to spin systems

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