Exploring the limits of broadband excitation and inversion: II. Rf-power optimized pulses

Kobzar, Kyryl; Skinner, Thomas E.; Khaneja, Navin; Glaser, Steffen J.; Luy, Burkhard

doi:10.1016/j.jmr.2008.05.023

Cited by 126 publications

(147 citation statements)

References 46 publications

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“…Approximate and exact controllability results have been obtained recently in this direction [47][48][49][50]. This analysis is important for designing control fields which are robust to experimental imperfections [51][52][53][54][55][56]. Adiabatic techniques could be very useful to this purpose, see Section 2.2.3.…”

Section: State Of the Artmentioning

confidence: 99%

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: State Of the Artmentioning

confidence: 99%

Training Schrödinger’s cat: quantum optimal control

et al. 2015

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“…[ 16 ]. The solution for tan φ max then occurs for cotψ = (− cosθ) −1/2 , giving the same bound for φ max as in Eq.…”

Section: Euler Anglesmentioning

confidence: 72%

“…Although a great deal of effort has been devoted to increasing the bandwidth of inversion pulses, most broadband inversion pulses [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] execute only a point-to-point (PP) rotation for one specific initial state, magnetization M z → −M z , and are not UR pulses. However, two PP inversion pulses with suitable interpulse delays can be used to construct a refocusing sequence [17,18], which is effectively a 360…”

Section: Introductionmentioning

confidence: 99%

New strategies for designing robust universal rotation pulses: Application to broadband refocusing at low power

Skinner

Gershenzon

Nimbalkar

et al. 2012

Journal of Magnetic Resonance

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Broadband inversion pulses that rotate all magnetization components 180• about a given fixed axis are necessary for refocusing and mixing in highresolution NMR spectroscopy. The relative merits of various methodologies for generating pulses suitable for broadband refocusing are considered. The de novo design of 180• universal rotation pulses (180 • U R ) using optimal control can provide improved performance compared to schemes which construct refocusing pulses as composites of existing pulses. The advantages of broadband universal rotation by optimized pulses (BURBOP) are most evident for pulse design that includes tolerance to RF inhomogeneity or miscalibration. We present new modifications of the optimal control algorithm that incorporate symmetry principles and relax conservative limits on peak RF pulse amplitude for short time periods that pose no threat to the probe. We apply them to generate a set of 180• BU RBOP pulses suitable for widespread use in 13 C spectroscopy on the majority of available probes.

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“…Penalties can be added to this basic objective function in order to demand that the solution admit certain properties. For instance, penalty functions have been used to ensure robustness to control noise and limited pulse fluence [13,[27][28][29] or to ensure that undesired subspaces are avoided [30,31]. Now we include the effect of our hardware by modifying the objective function to compose with the distortion operator,…”

Section: Pacs Numbersmentioning

confidence: 99%

Controlling Quantum Devices with Nonlinear Hardware

et al. 2015

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High fidelity coherent control of quantum systems is critical to building quantum devices and quantum computers. We provide a general optimal control framework for designing control sequences that account for hardware control distortions while maintaining robustness to environmental noise. We demonstrate the utility of our algorithm by presenting examples of robust quantum gates optimized in the presence of nonlinear distortions. We show that nonlinear classical controllers do not necessarily incur additional computational cost to pulse optimization, enabling more powerful quantum devices. PACS numbers:The ability to coherently control the dynamics of quantum systems with high fidelity is a critical component of the development of modern quantum devices, including quantum computers [1], actuators [2,3], and sensors [4][5][6] that push beyond the capabilities of classical computation and metrology. In recent years, quantum computation has presented a compelling application for quantum control, as high-fidelity control is essential to implement quantum information processors that achieve fault-tolerance [7][8][9].The performance of numerically optimized quantum gates in laboratory applications strongly depends on the accuracy of the system model used to approximate the response of the experimental system to the applied control sequence. Here we develop a general framework whereby classical control hardware components are modelled explicitly, such that their effect on a quantum system can be computed and compensated for using numerical optimal control theory (OCT) [10] algorithms to optimize control sequences. Control sequences designed using OCT algorithms, such as the GRadient Ascent Pulse Engineering (GRAPE) [11] algorithm, can be made robust to a wide variety of inhomogenities, pulse errors and noise processes [12][13][14]. These methods are also easily extended [15][16][17][18] to other applications and may be integrated into other protocols [19]. Recently, it was demonstrated how a model of linear distortions of the control sequence, such as those arising from finite bandwidth of the classical control hardware, may also be integrated into OCT algorithms [20][21][22].Here, we improve and generalize those results beyond linear kernels to any operation that smoothly maps a list of control steps to a classical field seen by the quantum system. Importantly, our framework naturally allows for robustness against uncertainties and errors due to classical control hardware. We begin developing our method generally, without making assumptions about the device of interest, so that our results may be broadly applicable to a wide range of quantum devices. We briefly discuss how our theory is easily applied to any linear distortion, and then in more detail, demonstrate with numerics how nonlinearities in control hardware, such as those found in strongly-driven superconducting resonators used for pulsed electron spin resonance (PESR) [23][24][25], may be included in OCT algorithms.With this goal in mind, we briefly review th...

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Exploring the limits of broadband excitation and inversion: II. Rf-power optimized pulses

Cited by 126 publications

References 46 publications

Training Schrödinger’s cat: quantum optimal control

Training Schrödinger’s cat: quantum optimal control

New strategies for designing robust universal rotation pulses: Application to broadband refocusing at low power

Controlling Quantum Devices with Nonlinear Hardware

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