Optimizing for an arbitrary perfect entangler. II. Application

Goerz, Michael H.; Gualdi, Giulia; Reich, Daniel M.; Koch, Christiane P.; Motzoi, Felix; Whaley, K. Birgitta; Vala, Jiří; Müller, Matthias; Montangero, Simone; Calarco, Tommaso

doi:10.1103/physreva.91.062307

Cited by 41 publications

(36 citation statements)

References 58 publications

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“…While the additional computational effort for evaluating the control update is negligible, storage of allρ (i) j is necessary and may become a limiting factor when scaling up the system size. Such extensions of the optimization algorithm to control targets other than a specific state or unitary have been applied to coherent dynamics [29,[97][98][99]. For open quantum systems, they are still under exploration.…”

Section: A Optimal Control Theory Applied To Open Quantum Systemsmentioning

confidence: 99%

“…The corresponding figure of merit is based on the so-called local invariants [29,97]. Similarly, one can formulate a figure of merit for targeting an arbitrary perfect entangler [98,99]. Since these figures of merit are based on the local invariants which in turn are calculated from the unitary evolution, extension to non-unitary dynamics requires to first determine the unitary part of the overall evolution.…”

Section: B Measuring Success Of Control In Open Quantum Systemsmentioning

confidence: 99%

“…Moreover, weights may be introduced inσ j (t = T ) to speed up convergence by attaching different importance to different basis stateŝ ρ j (t = 0) [39]. Extension of the optimization algorithm to more flexible control targets, such as an arbitrary perfect entangler [98,99] instead of a specific unitary, requires two steps. First, a modified target functional results in a modification of Eq.…”

Section: A Optimal Control Theory Applied To Open Quantum Systemsmentioning

confidence: 99%

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Controlling open quantum systems: tools, achievements, and limitations

Koch

2016

J. Phys.: Condens. Matter

251

222

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The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge to preserve the relevant nonclassical features at the level of device operation. A major obstacle is decoherence which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. We review here recent advances in optimal control methodology that allow for tackling typical tasks in device operation for open quantum systems and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions.

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Section: A Optimal Control Theory Applied To Open Quantum Systemsmentioning

confidence: 99%

Section: B Measuring Success Of Control In Open Quantum Systemsmentioning

confidence: 99%

Section: A Optimal Control Theory Applied To Open Quantum Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Controlling open quantum systems: tools, achievements, and limitations

Koch

2016

J. Phys.: Condens. Matter

251

222

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“…Optimization algorithms had to be derived for specific quantum gates [470][471][472], dissipative evolution as seen in the reduced system dynamics [56,113,114,461,473], or exploiting invariants in system-bath models [474], optimization up to local equivalence classes [475], which can also be used for arbitrary perfect entanglers [476,477] or optimizing for many-body entanglement [478]. Moreover, control techniques were adapted to non-linear dynamics as found in a BEC [479][480][481] and to general dynamics, functionals and couplings to be controlled [98].…”

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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“…We illustrate this with an analysis of the reachable set of local equivalence classes, considering a generic two-qubit Hamiltonian including controls that models superconducting qubits. The application of our optimization approach to specific physical examples is presented in the companion to this paper [10]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Optimizing for an arbitrary perfect entangler. I. Functionals

Watts

Vala²,

Müller

et al. 2015

Phys. Rev. A

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Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally entangled state out of some initial product state. The functional depends on easily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.

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Optimizing for an arbitrary perfect entangler. II. Application

Cited by 41 publications

References 58 publications

Controlling open quantum systems: tools, achievements, and limitations

Controlling open quantum systems: tools, achievements, and limitations

Training Schrödinger’s cat: quantum optimal control

Optimizing for an arbitrary perfect entangler. I. Functionals

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