Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

Tošner, Zdeněk; Vosegaard, Thomas; Kehlet, Cindie; Khaneja, Navin; Glaser, Steffen J.; Nielsen, Niels Chr.

doi:10.1016/j.jmr.2008.11.020

Cited by 195 publications

(195 citation statements)

References 64 publications

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“…The algorithms are comparatively easy to use and several program packages include optimal control modules, e.g. SIMPSON [100], SPINACH [101], DYNAMO [94], and QuTiP [102]. Modifications to account for experimental imperfections and limitations and to ensure robustness of the solution have been introduced [53,[103][104][105][106][107][108][109][110][111], and numerical optimal control theory has been extended to open quantum systems [112][113][114][115][116][117].…”

Section: Numerical Optimal Control -State Of the Artmentioning

confidence: 99%

“…In the solidstate NMR community, the SIMPSON software package (SIMulation Program for SOlid state Nuclear magnetic resonance) has been the most extensively used generalpurpose software. It also includes an optimal control toolbox to facilitate robust experiment design [100]. MAT-PULSE [329,330], DYNAMO [94] and QuTiP [102] are versatile Matlab and Python based simulation and optimization programs.…”

Section: State Of the Artmentioning

confidence: 99%

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Training Schrödinger’s cat: quantum optimal control

et al. 2015

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Abstract. It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantumenhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments. ForewordThe authors of this paper represent the QUAINT consortium, a European Coordination Action on Optimal Control of Quantum Systems, funded by the European Commission Framework Programme 7, Future Emerging Technologies FET-OPEN programme and the Virtual Facility for Quantum Control (VF-QC). This consortium has considerable expertise in optimal control theory and its applications to quantum systems, both in existing areas, such as spectroscopy and imaging, and in emerging quantum technologies, such as quantum information processing, quantum communication, quantum simulation a e-mail: fwm@lusi.uni-sb.de and quantum sensing. The list of challenges for quantum control has been gathered by a broad poll of leading researchers across the communities of general and mathematical control theory, atomic, molecular-, and chemical physics, electron and nuclear magnetic resonance spectroscopy, as well as medical imaging, quantum information, communication and simulation. 144 experts in these fields have provided feedback and specific input on the state of the art, mid-term and long-term goals. Those have been summarized in this document, which can be viewed as a perspectives paper, providing a roadmap for the future development of quantum control. Because such an endeavour can hardly ever be complete (there are many additional areas of quantum control applications, such as spintronics, nano-optomechanical technologies etc.), this roadmap

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Section: Numerical Optimal Control -State Of the Artmentioning

confidence: 99%

Section: State Of the Artmentioning

confidence: 99%

Training Schrödinger’s cat: quantum optimal control

et al. 2015

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“…Several optimization techniques have been successfully developed for quantum control such as strongly modulated pulses [34], GRAPE optimization [35,36], sequential convex programming [37] and optimal dynamical discrimination [38]. A novel set of optimization techniques broadly categorized as 'Genetic Algorithms (GAs)', have also been proposed as a means to achieve a global minimum for the optimization [39].…”

Section: Introductionmentioning

confidence: 99%

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

Devra

Prabhu

Singh

et al. 2018

Quantum Inf Process

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We have designed efficient quantum circuits for the three-qubit Toffoli (controlled-controlled NOT) and the Fredkin (controlled-SWAP) gate, optimized via genetic programming methods. The gates thus obtained were experimentally implemented on a three-qubit NMR quantum information processor, with a high fidelity. Toffoli and Fredkin gates in conjunction with the single-qubit Hadamard gates form a universal gate set for quantum computing, and are an essential component of several quantum algorithms. Genetic algorithms are stochastic search algorithms based on the logic of natural selection and biological genetics and have been widely used for quantum information processing applications. The numerically optimized rf pulse profiles of the three-qubit quantum gates achieve > 99% fidelity. The optimization was performed under the constraint that the experimentally implemented pulses are of short duration and can be implemented with high fidelity. Therefore the gate implementations do not suffer from the drawbacks of rf offset errors or debilitating effects of decoherence during gate action. We demonstrate the advantage of our pulse sequences by comparing our results with existing experimental schemes.

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“…Examples include perturbative relaxation theories [1][2][3] , reaction yield expressions in radical pair dynamics [4][5][6] , average Hamiltonian theory 7 , fidelity functional derivatives in optimal control theory 8,9 and pulsed field gradient propagators in nuclear magnetic resonance 10 . Their common feature is the complexity of evaluation: expensive matrix factorizations * are usually required 3,11,12 .…”

Section: Introductionmentioning

confidence: 99%

Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories

Goodwin

2015

The Journal of Chemical Physics

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Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.3

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Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

Cited by 195 publications

References 64 publications

Training Schrödinger’s cat: quantum optimal control

Training Schrödinger’s cat: quantum optimal control

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation theories

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