A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator

Zhu, Wenhui; Rabitz, Herschel

doi:10.1063/1.476575

Cited by 304 publications

(328 citation statements)

References 9 publications

Supporting

Mentioning

325

Contrasting

Order By: Relevance

“…For the parameter choice σ = 1 and τ = 0, the original Krotov method [21] is obtained and, for σ = τ = 1, the algorithm corresponds to the one proposed by Zhu et al [28,29]. We propose to restrict the space of possible pulses by Fourier transforming and truncating the expansion.…”

Section: Comparison With the Krotov Methodsmentioning

confidence: 99%

“…We design a pulse of length 100 fs using both the Krotov-like method by Zhu and Rabitz [29] and our Fourier-based BFGS method. We use a step size of ∆t = 0.01 fs.…”

Section: Comparison With Krotov-like Methodsmentioning

confidence: 99%

“…The idea of the Krotov scheme is to solve the first-order optimality condition for the control parameter and solve the resulting equation by fixed-point iteration. Zhu et al [28,29] refined this ansatz in a similar fashion as Gauss-Seidel iteration improves Jacobi's method. Maday and Turinici [13] generalized this further and formulated a framework of Krotov-like methods where the old and the new field are combined in various ways.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Fourier-Coefficient Based Solution of an Optimal Control Problem in Quantum Chemistry

Kormann

Holmgren

Karlsson

2010

J Optim Theory Appl

View full text Add to dashboard Cite

We consider an optimal control problem for the time-dependent Schrödinger equation modeling molecular dynamics. Given a molecule in its ground state, the interaction with a tuned laser pulse can result in an excitation to a state of interest. By these means, one can optimize the yield of chemical reactions. The problem of designing an optimal laser pulse can be posed as an optimal control problem. We reformulate the optimization problem by Fourier-transforming the electric field of the laser and narrow the frequency band. In this way, we reduce the dimensionality of the control variable. This allows for storing an approximate Hessian and, thereby, we can solve the optimization problem with a quasi-Newton method. Such an implementation provides superlinear convergence. We show computational results for a Raman-transition example and give numerical evidence that our algorithm can outperform the standard Krotovlike method which does not employ approximative second derivatives.

show abstract

Section: Comparison With the Krotov Methodsmentioning

confidence: 99%

“…We design a pulse of length 100 fs using both the Krotov-like method by Zhu and Rabitz [29] and our Fourier-based BFGS method. We use a step size of ∆t = 0.01 fs.…”

Section: Comparison With Krotov-like Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Fourier-Coefficient Based Solution of an Optimal Control Problem in Quantum Chemistry

Kormann

Holmgren

Karlsson

2010

J Optim Theory Appl

View full text Add to dashboard Cite

show abstract

“…[7]) there exists U T ∈ S U (5) such that U T ψ 0 = ψ T and by the Theorem 4 there exists a time T and a control u : [0, T ] → R such that u(t), u(t) − 0.1 and u(t) + 0.1 all drive Id to U T in equation (1) thus all drive the initial state ψ 0 to the final state ψ T in equation (10). We searched numerically the control u(t) using a so-called monotonic procedure, see [44][45][46][47][48][49] for details. For T = 500, we obtain the control presented in Figure 1.…”

Section: Application To the Control Of A Quantum Systemmentioning

confidence: 99%

Ensemble controllability and discrimination of perturbed bilinear control systems on connected, simple, compact Lie groups

Belhadj

Salomon

Turinici

2015

European Journal of Control

View full text Add to dashboard Cite

The controllability of bilinear systems is well understood for finite dimensional isolated systems where the control can be implemented exactly. However when perturbations are present some interesting theoretical questions are raised. We consider in this paper a control system whose control cannot be implemented exactly but is shifted by a time independent constant in a discrete list of possibilities. We prove under general hypothesis that the collection of possible systems (one for each possible perturbation) is simultaneously controllable with a common control. The result is extended to the situations where the perturbations are constant over a common, long enough, time frame. We apply the result to the controllability of quantum systems. Furthermore, some examples and a convergence result are presented for the situation where an infinite number of perturbations occur. In addition, the techniques invoked in the proof allow to obtain generic necessary and sufficient conditions for ensemble controllability.

show abstract

“…A great effort has been invested in recent years in the development of different methods in order to solve the optimal equations [26,27,28,29,30]. Monotonically convergent iterative schemes proposed by Tannor et al [31] and Rabitz et al [32] have been successfully applied to the control of different quantum phenomena, mainly related to chemical process [33,34]. In the last years, optimal control theory became a research area that has received increasing interest from the scientists studying emerging fields within quantum information science [35,36].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a charge qubit in a double quantum dot with a Coulomb impurity

Coden

Romero

Ferrón

et al. 2017

Physica E: Low-dimensional Systems and Nanostructures

View full text Add to dashboard Cite

Abstract. We study the efficiency of modulated laser pulses to produce efficient and fast charge localization transitions in a two-electron double quantum dot. We use a configuration interaction method to calculate the electronic structure of a quantum dot model within the effective mass approximation. The interaction with the electric field of the laser is considered within the dipole approximation and optimal control theory is applied to design high-fidelity ultrafast pulses in pristine samples. We assessed the influence of the presence of Coulomb charged impurities on the efficiency and speed of the pulses. A protocol based on a two-step optimization is proposed for preserving both advantages of the original pulse. The processes affecting the charge localization is explained from the dipole transitions of the lowest lying two-electron states, as described by a discrete model with an effective electron-electron interaction.

show abstract

A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator

Cited by 304 publications

References 9 publications

A Fourier-Coefficient Based Solution of an Optimal Control Problem in Quantum Chemistry

A Fourier-Coefficient Based Solution of an Optimal Control Problem in Quantum Chemistry

Ensemble controllability and discrimination of perturbed bilinear control systems on connected, simple, compact Lie groups

Optimal control of a charge qubit in a double quantum dot with a Coulomb impurity

Contact Info

Product

Resources

About