Unitary Control in Quantum Ensembles: Maximizing Signal Intensity in Coherent Spectroscopy

Glaser, Steffen J.; Schulte‐Herbrüggen, Thomas; Sieveking, Malte; Schedletzky, O.; Nielsen, Niels Chr.; Sørensen, Ole W.; Griesinger, Christian

doi:10.1126/science.280.5362.421

Cited by 202 publications

(192 citation statements)

References 17 publications

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“…These results were applied to a variety of NMR problems, including polarization transfer between spin species [1,2,3,4,5,6], and cross-polarization in solids [7,8,6]. Extensions to non-Hermitian operators and non-unitary dissipative evolution were developed [9,10,11].…”

Section: Introductionmentioning

confidence: 99%

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Symmetry constraints on spin dynamics: Application to hyperpolarized NMR

Levitt

2016

Journal of Magnetic Resonance

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Spin dynamical evolution is constrained by the symmetries of the spin Hamiltonians that generate the quantum dynamics. The consequences of symmetry-induced constraints are examined for some common hyperpolarized NMR experiments, including the excitation of singlet order in spin-pair systems, and the transfer of parahydrogen-induced hyperpolarized singlet order to magnetization in systems displaying chemical and magnetic equivalence.

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Section: Introductionmentioning

confidence: 99%

“…To facilitate discussion of this topic, the theory of unitary bounds in the presence of symmetry, as developed by Sørensen and co-workers [1,2,3,4,5,6,7,8,9,10,12] is reviewed and reformulated with a revised notation, and combined with a more detailed discussion of spin permutation symmetry.…”

Section: Introductionmentioning

confidence: 99%

Symmetry constraints on spin dynamics: Application to hyperpolarized NMR

Levitt

2016

Journal of Magnetic Resonance

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“…Many areas of spectroscopic fields, such as nuclear magnetic resonance (NMR), electron magnetic resonance and optical spectroscopy rely on a limited set of control variables in order to create desired unitary transformations [5,6,7]. In NMR, unitary transformations are used to manipulate an ensemble of nuclear spins, e.g.…”

Section: Introductionmentioning

confidence: 99%

Time optimal control in spin systems

2001

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In this paper, we study the design of pulse sequences for NMR 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 of state. 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. Moreover, the general proofs are no more difficult than the specific problems of current interest. 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 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 systems.

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“…Concomitantly, progress has been made in applying optimal control techniques to steer quantum systems [5] in a robust, relaxation-minimising [6] or timeoptimal way [7]. Spin systems are a particularly powerful paradigm of quantum systems [8]: under mild conditions they are fully controllable, i.e., local and universal quantum gates can be implemented. In N spins-1 2 it suffices that (i) all spins can be addressed selectively by rf-pulses and (ii) that the spins form an arbitrary connected graph of weak coupling interactions.…”

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confidence: 99%

Optimal control of coupled Josephson qubits

et al. 2007

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This paper is dedicated to the memory of Martti Salomaa.Quantum optimal control theory is applied to two and three coupled Josephson charge qubits. It is shown that by using shaped pulses a cnot gate can be obtained with a trace fidelity > 0.99999 for the two qubits, and even when including higher charge states, the leakage is below 1%. Yet, the required time is only a fifth of the pioneering experiment [1] for otherwise identical parameters. The controls have palindromic smooth time courses representable by superpositions of a few harmonics. We outline schemes to generate these shaped pulses such as simple network synthesis. The approach is easy to generalise to larger systems as shown by a fast realisation of Toffoli's gate in three linearly coupled charge qubits. Thus it is to be anticipated that this method will find wide application in coherent quantum control of systems with finite degrees of freedom whose dynamics are Liealgebraically closed.PACS numbers: 85.25. Cp, 82.65.Jn, 03.67.Lx, 85.35.Gv In view of Hamiltonian simulation and quantum computation recent years have seen an increasing amount of quantum systems that can be coherently controlled. Next to natural microscopic quantum systems, a particular attractive candidate for scalable setups are superconducting devices based on Josephson junctions [2]. Due to the ubiquitous bath degrees of freedom in the solid-state environment, the time over which quantum coherence can be maintained remains limited, although significant progress has been achieved [3,4]. Yet, it is a challenge how to produce accurate quantum gates, and how to minimize their duration such that the number of possible operations within T 2 meets the error correction threshold. Concomitantly, progress has been made in applying optimal control techniques to steer quantum systems [5] in a robust, relaxation-minimising [6] or timeoptimal way [7]. Spin systems are a particularly powerful paradigm of quantum systems [8]: under mild conditions they are fully controllable, i.e., local and universal quantum gates can be implemented. In N spins-1 2 it suffices that (i) all spins can be addressed selectively by rf-pulses and (ii) that the spins form an arbitrary connected graph of weak coupling interactions. The optimal control techniques of spin systems can be extended to pseudo-spin systems, such as charge or flux states in superconducting setups, provided their Hamiltonian dynamics can be approximated to sufficient accuracy by a closed Lie algebra, e.g., in a system of N qubits su(2 N ).As a practically relevant and illustrative example, we consider two capacitively coupled charge qubits controlled by DC pulses as in Ref. [1]. The infinitedimensional Hilbert space of charge states in the device can be projected to its low-energy part defined by zero or one excess charge on the respective islands [2]. Identifying these charges as pseudo-spin states, the Hamiltonian can be written as H tot = H drift + H control , where the drift or static part reads (for the constants see caption to Fig. 1)while...

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Unitary Control in Quantum Ensembles: Maximizing Signal Intensity in Coherent Spectroscopy

Cited by 202 publications

References 17 publications

Symmetry constraints on spin dynamics: Application to hyperpolarized NMR

Symmetry constraints on spin dynamics: Application to hyperpolarized NMR

Time optimal control in spin systems

Optimal control of coupled Josephson qubits

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