Tunable, Flexible, and Efficient Optimization of Control Pulses for Practical Qubits

Machnes, Shai; Assémat, Elie; Tannor, David J.; Wilhelm, Frank K.

doi:10.1103/physrevlett.120.150401

Cited by 171 publications

(142 citation statements)

References 55 publications

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“…We note that this particular formula has been observed in [46] in the context of pulse finding for derivative evaluation.…”

Section: Methodsmentioning

confidence: 62%

“…This method has found application in unitary engineering [45], as it provides an accurate and efficient tool for evaluating partial derivatives of U(T). We also note that the first order version the method outlined here has been observed in [46,47] for evaluating functional derivatives of U(T) with respect to control amplitudes.…”

Section: T T T U T a T U T U T A T U Tmentioning

confidence: 95%

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Engineering effective Hamiltonians

et al. 2019

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In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilizes perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we provide a general framework for computing arbitrary timedependent perturbation theory terms, as well as their gradients with respect to control variations, enabling the use of gradient methods for optimizing these terms. In particular, we show that effective Hamiltonian engineering is an instance of a bilinear control problem-the same general problem class as that of standard unitary design-and hence the same optimization algorithms apply. We demonstrate this method in various examples, including decoupling, recoupling, and robustness to control errors and stochastic errors. We also present a control engineering example that was used in experiment, demonstrating the practical feasibility of this approach.

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“…We note that this particular formula has been observed in [46] in the context of pulse finding for derivative evaluation.…”

Section: Methodsmentioning

confidence: 62%

Section: T T T U T a T U T U T A T U Tmentioning

confidence: 95%

Engineering effective Hamiltonians

et al. 2019

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show abstract

“…[29]) and implemented [30]. Recently, an optimized algorithm has been developed for the control pulses for practical qubits [31].…”

Section: G Gmentioning

confidence: 99%

High-fidelity non-adiabatic cutting and stitching of a spin chain via local control

et al. 2018

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We propose and analyze, focusing on non-adiabatic effects, a technique of manipulating quantum spin systems based on local 'cutting' and 'stitching' of the Heisenberg exchange coupling between the spins. This first operation is cutting of a bond separating a single spin from a linear chain, or of two neighboring bonds for a ring-shaped array of spins. We show that the disconnected spin can be in the ground state with a high-fidelity even after a non-adiabatic process. Next, we consider inverse operation of stitching these bonds to increase the system size. We show that the optimal control algorithm can be found by using common numerical procedures with a simple twoparametric control function able to produce a high-fidelity cutting and stitching. These results can be applied for manipulating ensembles of quantum dots, considered as prospective elements for quantum information technologies, and for design of machines based on quantum thermodynamics.

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“…Optimization with amplitude constraints can be done using GRAPE or analytically in some cases. Bandwidth constraints can be implemented in GOAT [52] or approximately, using filtered optimal pulses [56]. Our approach is physically motivated by the observation that even in the strong driving regime the dynamics can be simply described in terms of three unitaries, for the rise, central, and fall parts of the pulses.…”

Section: Comparison With Other Pulse Optimization Methodsmentioning

confidence: 99%

“…With sufficient discretization, continuously varying control parameters can be approximated with good accuracy. Other control methods, including chopped random-basis quantum optimization (CRAB) [51] and Gradient Optimization of Analytic conTrols (GOAT) [52] assume the Hamiltonian to be expressed in terms of analytic functions, with a set of parameters entering these functions to be optimized. Derivative Removal by Adiabatic Gate (DRAG) [53] is concerned with the reduction of state leakage in a weakly anharmonic system, providing an approximate analytical solution to this problem.…”

Section: Comparison With Other Pulse Optimization Methodsmentioning

confidence: 99%

Dynamics of a two-level system under strong driving: Quantum-gate optimization based on Floquet theory

et al. 2016

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We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is non-adiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet Interference Efficient Suppression of Transitions in the Adiabatic basis (FIESTA), that can be used to design ultra-fast high-fidelity single-qubit quantum gates.

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Tunable, Flexible, and Efficient Optimization of Control Pulses for Practical Qubits

Cited by 171 publications

References 55 publications

Engineering effective Hamiltonians

Engineering effective Hamiltonians

High-fidelity non-adiabatic cutting and stitching of a spin chain via local control

Dynamics of a two-level system under strong driving: Quantum-gate optimization based on Floquet theory

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