Optimal Control Methods in NMR Spectroscopy

Nielsen, Niels Chr.; Kehlet, Cindie; Glaser, Steffen J.; Khaneja, Navin

doi:10.1002/9780470034590.emrstm1043

Cited by 50 publications

(42 citation statements)

References 75 publications

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“…While in spin systems optimal control methods are well established (as has become obvious by several other contributions in this issue; see also the review in Nielsen et al [88]), here we have focused on wider applicability by examples from Josephson elements and cavity grids, and further implementations in ion traps and nitrogen vacancy centres of diamonds are in progress. Most often standard decompositions into local gates plus CNOT gates are far less robust and less efficient than the assembly of effective multi-qubit gates compiled via optimal control.…”

Section: Discussionmentioning

confidence: 99%

Control aspects of quantum computing using pure and mixed states

Schulte‐Herbrüggen

Marx

Fahmy

et al. 2012

Phil. Trans. R. Soc. A.

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Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

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Section: Discussionmentioning

confidence: 99%

Control aspects of quantum computing using pure and mixed states

Schulte‐Herbrüggen

Marx

Fahmy

et al. 2012

Phil. Trans. R. Soc. A.

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“…Further advances have been made on how to optimally control multiple coupled spins . These methods have been successfully applied in NMR [92,93] to designing broad-band [94][95][96] and decoupling pulse sequences [97][98][99][100][101][102]. They have also been utilized in magnetic resonance imaging [25,[103][104][105] and electron paramagnetic resonance [106].…”

Section: Introductionmentioning

confidence: 99%

Time-optimal polarization transfer from an electron spin to a nuclear spin

et al. 2015

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“…[1,2] During the past decade or so, optimal-control-based methods have been increasingly used for a development of new experiments within optical spectroscopy, [3][4][5][6][7][8] quantum information processing, [9][10][11][12][13][14] liquid-and solid-state nuclear magnetic resonance (NMR) spectroscopy, [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] magnetic resonance imaging (MRI), [30][31][32][33][34][35][36] and dynamic nuclear polarization (DNP) hybrids between electron and nuclear magnetic resonance. [37][38][39][40] Such applications have not only been useful for the specific disciplines taking advantage of new efficient design procedures and improved experimental methods, but it has also stimulated mathematical investigations in quantum optimal control theory.…”

Section: Introductionmentioning

confidence: 99%

“…For example, looking at the many optimal control pulse sequences proposed so far, 3 it appears that many of these display quite wild oscillations in phase and amplitude of the rf control fields (see, e.g., Refs. [18,[20][21][22][23][24][25][26][27][28][29]) which may complicate implementation on available instrumentation with limitations on the speed and accuracy of phase and amplitude switching. Furthermore, it turns out that GRAPE displays a quite strong dependence on the initial guess of the pulse sequence, dependence on the applied time discretization (i.e., the number of pulse variables, and their duration), as well as unpredictable convergence to local extremum points.…”

Section: Introductionmentioning

confidence: 99%

A smoothing monotonic convergent optimal control algorithm for nuclear magnetic resonance pulse sequence design

Maximov

Salomon

Turinici

et al. 2010

The Journal of Chemical Physics

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The past decade has demonstrated increasing interests in using optimal control based methods within coherent quantum controllable systems. The versatility of such methods has been demonstrated with particular elegance within nuclear magnetic resonance (NMR) where natural separation between coherent and dissipative spin dynamics processes has enabled coherent quantum control over long periods of time to shape the experiment to almost ideal adoption to the spin system and external manipulations. This has led to new design principles as well as powerful new experimental methods within magnetic resonance imaging, liquid-state and solid-state NMR spectroscopy. For this development to continue and expand, it is crucially important to constantly improve the underlying numerical algorithms to provide numerical solutions which are optimally compatible with implementation on current instrumentation and at same time are numerically stable and offer fast monotonic convergence towards the target. Addressing such aims, we here present a smoothing monotonically convergent algorithm for pulse sequence design in magnetic resonance which with improved optimization stability lead to smooth pulse sequence easier to implement experimentally and potentially understand within the analytical framework of modern NMR spectroscopy.

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Optimal Control Methods in NMR Spectroscopy

Cited by 50 publications

References 75 publications

Control aspects of quantum computing using pure and mixed states

Control aspects of quantum computing using pure and mixed states

Time-optimal polarization transfer from an electron spin to a nuclear spin

A smoothing monotonic convergent optimal control algorithm for nuclear magnetic resonance pulse sequence design

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