Time-Minimal Control of Dissipative Two-Level Quantum Systems: The Generic Case

Bonnard, Bernard; Chyba, Monique; Sugny, Dominique

doi:10.1109/tac.2009.2031212

Cited by 71 publications

(51 citation statements)

References 16 publications

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“…Typically, this requires understanding of the geometry of the control problem from which one can deduce the structure of the optimal solution, a proof of global optimality and physical limits, such as the minimal time to reach the target [5]. Mathematical tools that were developed recently [11][12][13][68][69][70] could tackle problems of increasing difficulty, including fundamental control problems for closed [14,[71][72][73][74][75] and open quantum systems [76][77][78][79][80][81]. This method is able to treat quantum control problems ranging from two and three level quantum systems or two and three coupled spins to two-level dissipative quantum systems with dynamics governed by the Lindblad equation.…”

Section: Geometric Optimal Control -State Of the Artmentioning

confidence: 99%

“…Both analytical and numerical methods have proven very effective for two-and three-level systems [72,[74][75][76][77]80,159,[336][337][338][339][340][341][342][343][344][345][346][347][348], two uncoupled spins [349,350], and two coupled spins [83,85,89,[351][352][353][354][355]. Significant progress has been made in understanding of how to optimally control coupled spin systems with more than two spins [65,71,86,87,[313][314][315][356][357][358][359][360][361][362][363][364][365][366]…”

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: Geometric 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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“…M 0 is the magnitude of the Bloch vector at thermal equilibrium. Using the symmetry of revolution of the system around the z-axis, we can restrict the problem to only one control field [19,20]. In the following of the paper, we will assume without loss of generality that ω y = 0, which implies that the x-coordinate of the Bloch vector is not coupled to the other components.…”

Section: The Model Systemmentioning

confidence: 99%

Optimal control of the signal-to-noise ratio per unit time for a spin-1/2 particle

et al. 2014

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We investigate the maximum signal to noise ratio per unit time that can be achieved for a spin 1/2 particle subjected to a periodic pulse sequence. Optimal control techniques are applied to design the control field and the position of the steady state, leading to the best signal to noise performance. A complete geometric description of the optimal control problem is given in the unbounded case. We show the optimality of the well-known Ernst angle solution, which is widely used in spectroscopic and medical imaging applications, over a large control space allowing use of shaped pulses.

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“…In recent years, significant progress has been made in quantum control for both numerical [24][25][26][27][28][29][30][31][32][33][34][35][36][37] and analytical [38][39][40][41] methods. Extensive knowledge has been gained on optimal pulse sequences for two-and three-level systems [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], two uncoupled spins [57,58], and two coupled spins [59][60][61][62][63][64][65]. Further advances have been made on how to optimally control multiple coupled spins .…”

Section: Introductionmentioning

confidence: 99%