Time optimal control in spin systems
By Navin Khaneja, Roger W. Brockett, Steffen J. Glaser. 2000
386 citations recorded by the source corpus.
In this paper, we study the design of pulse sequences for nuclear magnetic resonance spectroscopy as a problem of time optimal control of the unitary propagator. Radio-frequency pulses are used in coherent spectroscopy to implement a unitary transfer between states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group. What is the minimum time required to steer the system from some initial point to a specified final point? In nuclear magnetic resonance (NMR) spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two-spin system.
Subfields: Atomic and Molecular Physics, and Optics, Spectroscopy
View Paper: https://www.semanticscholar.org/paper/ba622a20a19b852b6e66f63bd7fa856123f64338
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In Spectroscopy
Citations in the corpus
- Quantum control theory and applications: A survey (2009, neutral): “ptimal in some sense to accomplish a specified quantum control task. In some applications, it is desirable to accomplish the control task as soon as possible in order to minimize the relaxation effects [35]. For example, it is desirable to perform a quantum computation task with a minimum time using a”
- Time-optimal Control of Spin Systems (2006, background): “In Section 2.5 we are then specializing to the situation where the Lie algebra g has the additional property of being semisimple and belonging to a symmetric Lie algebra pair (g, k) (cf. Definition 1.2.5).”
- Reinforcement Learning in Different Phases of Quantum Control (2017, background): “[25] Navin Khaneja, Roger Brockett, and Steffen J.”