Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Control Conference (CCC)

A Numerical Quantum Optimal Control with Grover Iteration

Ming Li, Qiyu Yang, Hui Zhang

Published Jul 1, 2018• 0 citations
Publisher

Abstract

This paper proposes a new numerical quantum optimal control method with Grover Iteration for two-level quantum systems. We show that our treatment of using the piecewise constant controls with desired control structure is implementable for laboratory laser experiments. And then, the robustness of the algorithm is also considered when parameter perturbations of quantum systems exist. The performance of the system is enhanced using the combination of the quantum optimal control and the Grover Iteration. In particular, the feasibility, effectiveness and priority of the new control scheme are presented by a comparison between our algorithm and the traditional quantum optimal control.

DOI
10.23919/chicc.2018.8483175

Related papers

Quantum Control With Piecewise Constant Control Functions

Ilan Degani, Antonella Zanna, L. Sælen +1 more

One of the long-standing problems in the field of computational quantum control is to devise algorithms that converge to high yield controls with a desired structure; particularly, controls that can be reproduced by laboratory laser pulse shapers. In this paper we propose an approach that is a considerable step forward toward the solution of this problem. Our treatment employs piecewise constant controls. For these, the concept of “desired structure” is addressed by including appropriate quadratic forms in the performance functionals. Thereafter, correct extremal control equations are derived, whereas the equations appearing in the literature are correct only to first or second order. We illustrate numerically that our approach can give extremely high yield controls with a desired structure. Our results are valid not only in the context of quantum control, but also for similiar bilinear systems arising in different areas. In particular, they are suitable for controlling linear flows with drift on unitary matrix groups.

SIAM Journal on Scientific Computing•Jan 1, 2009•18 citations

Quantum Optimal Control Based on the Constrained Control Field

Ze-Xia Huang, You-Hong Yu

According to the specialty of quantum systems, the reliability or the efficiency of a general optimal control scheme leave much to be desired. In this paper, we develop a special improved quantum optimal control method for using dynamic control field, which can be implemented as fast convergent algorithms. The relations among, convergence speed and iteration step parameters are analyzed in detail through a three-level ¦® system simulation experiments. Theoretical analysis show that this new algorithm exhibits significantly superior to the classical quantum optimal control method and the Krotov method in reliability and convergence rate.

International Conference on Electronics, Communications and Control•Oct 16, 2012•0 citations

Algebraic and computational aspects of quantum control and applications.

I. C. H. Pullen

We investigate the problem of control of quantum systems. Various notions of controllability of quantum systems are discussed and Lie algebraic techniques are employed to derive necessary and sufficient conditions for the resulting degrees of controllability. The results are employed to study the degree of controllability for various model systems. The problem of optimal control is formulated as a problem of maximisation of the expectation value of an observable of the system subject to dynamical constraints and costs. A class of iterative algorithms is discussed, and shown to converge to a solution of the Euler-Lagrange equations, which is a necessary condition for optimality of a solution. A numerical realisation of the algorithm is presented and potential implementation of the resulting control fields in the laboratory is discussed. The algorithm is applied to find optimal control fields for a variety of applications including selective and simultaneous excitation of individual quantum dots in a globally addressed ensemble, creation of superposition states, and selective excitation of certain vibrational modes of a simple molecule such as Hydrogen Fluoride. In each case we systematically explore the parameter space of the algorithm to select solutions with desirable physical features from the multitude of possible choices. As there are many possible optimal control fields which give similar yields the question of whether some are more robust than others is investigated. A number of optimal fields are analysed quantitatively in terms of robustness with regard to temporal and spectral noise affecting the fields, uncertainty in the model parameters and the effect of experimental limitations such as restrictions on the bandwidth of the fields. It is shown that whilst the solutions tend to be sensitive to uncertainty in the energy levels chosen for the model, they appear to be surprisingly tolerant to even severe bandwidth limitations.

•Jan 1, 2006•0 citations

Robust Quantum Control via a Model Predictive Control Strategy

Yunyan Lee, Ian R. Petersen, Daoyi Dong

This article presents a robust control strategy using Time-Optimal Model Predictive Control (TOMPC) for a two-level quantum system subject to bounded uncertainties. In this method, the control field is optimized over a finite horizon using a nominal quantum system as the reference and then the optimal control for the first time interval is applied and a projective measurement is implemented on the uncertain system. The new control field for the next time interval will be iteratively optimized based on the measurement result. We present theoretical results to guarantee the stability of the TOMPC algorithm. We also characterize the robustness and the convergence rate of the TOMPC strategy for the control of two-level systems. Numerical simulations further demonstrate that, in the presence of uncertainties, our quantum TOMPC algorithm enhances robustness and steers the state to the desired state with high fidelity. This work contributes to the progress of Model Predictive Control in quantum control and explores its potential in practical applications of quantum technology.

arXiv:2402.07396•IEEE Transactions on Automatic Control•Jan 1, 2026•1 citation

Optimal Quantum Control Using Ensemble Quantization

Jr-Shin Li, Yuan-Hung Kuan, Wei Zhang

Abstract. The robust manipulation of ensembles of quantum systems exhibiting variations or uncertainties in the system parameters and dynamics has been a long-standing problem in the field of quantum control. Existing methods for addressing quantum ensemble control primarily rely on the use of state-space models that describe the time evolution of quantum states. In this paper, we introduce a distinctive quantum control paradigm by mapping the quantum ensemble control problem to a dual problem defined on a coordinate system established by a moment transform. This transformation introduces a new type of quantization in quantum systems, enabling tractable systems-theoretic analysis and effective optimal control design, which are typically opaque. Subsequently, we develop an iterative computational algorithm to solve the transformed optimal moment control problems. We conduct a convergence analysis for the proposed algorithm and demonstrate its applicability and effectiveness on various challenging pulse design problems in quantum control.

SIAM Journal on Control and Optimization•Jan 8, 2025•3 citations

A Numerical Approximation Approach for Quantum Optimal Control of Two-Level Systems

Cutberto Romero-Meléndez, Leopoldo González-Santos

In this paper, we discuss a quantum control algorithm, devised by the authors, inspired in Rabitz and Krotov algorithms and applied to Nuclear Magnetic Resonance (NMR) That algorithm is based on a numerical method for iterative optimization.Specifically, we address the determination of external optimal pulses (controls) to minimal cost, over a two-level quantum system.We use the numerical approximation to find the optimal controls in the case of two external electromagnetic fields, integrating the associated equations of the Pontryagin Maximum Principle.That algorithm unifies and generalizes the Rabitz and Krotov algorithms.We compare the efficiency of these algorithms with the solutions found by analytical methods.

International Journal of Applied Physics and Mathematics•Jan 1, 2017•1 citation
This paper proposes a new numerical quantum optimal control method with Grover Iteration for two-level quantum systems. We show that our treatment of using the piecewise constant controls with desired control structure is implementable for laboratory laser experiments. And then, the robustness of the algorithm is also considered when parameter perturbations of quantum systems exist. The performance of the system is enhanced using the combination of the quantum optimal control and the Grover Iteration. In particular, the feasibility, effectiveness and priority of the new control scheme are presented by a comparison between our algorithm and the traditional quantum optimal control.
One of the long-standing problems in the field of computational quantum control is to devise algorithms that converge to high yield controls with a desired structure; particularly, controls that can be reproduced by laboratory laser pulse shapers. In this paper we propose an approach that is a considerable step forward toward the solution of this problem. Our treatment employs piecewise constant controls. For these, the concept of “desired structure” is addressed by including appropriate quadratic forms in the performance functionals. Thereafter, correct extremal control equations are derived, whereas the equations appearing in the literature are correct only to first or second order. We illustrate numerically that our approach can give extremely high yield controls with a desired structure. Our results are valid not only in the context of quantum control, but also for similiar bilinear systems arising in different areas. In particular, they are suitable for controlling linear flows with drift on unitary matrix groups.
According to the specialty of quantum systems, the reliability or the efficiency of a general optimal control scheme leave much to be desired. In this paper, we develop a special improved quantum optimal control method for using dynamic control field, which can be implemented as fast convergent algorithms. The relations among, convergence speed and iteration step parameters are analyzed in detail through a three-level ¦® system simulation experiments. Theoretical analysis show that this new algorithm exhibits significantly superior to the classical quantum optimal control method and the Krotov method in reliability and convergence rate.
We investigate the problem of control of quantum systems. Various notions of controllability of quantum systems are discussed and Lie algebraic techniques are employed to derive necessary and sufficient conditions for the resulting degrees of controllability. The results are employed to study the degree of controllability for various model systems. The problem of optimal control is formulated as a problem of maximisation of the expectation value of an observable of the system subject to dynamical constraints and costs. A class of iterative algorithms is discussed, and shown to converge to a solution of the Euler-Lagrange equations, which is a necessary condition for optimality of a solution. A numerical realisation of the algorithm is presented and potential implementation of the resulting control fields in the laboratory is discussed. The algorithm is applied to find optimal control fields for a variety of applications including selective and simultaneous excitation of individual quantum dots in a globally addressed ensemble, creation of superposition states, and selective excitation of certain vibrational modes of a simple molecule such as Hydrogen Fluoride. In each case we systematically explore the parameter space of the algorithm to select solutions with desirable physical features from the multitude of possible choices. As there are many possible optimal control fields which give similar yields the question of whether some are more robust than others is investigated. A number of optimal fields are analysed quantitatively in terms of robustness with regard to temporal and spectral noise affecting the fields, uncertainty in the model parameters and the effect of experimental limitations such as restrictions on the bandwidth of the fields. It is shown that whilst the solutions tend to be sensitive to uncertainty in the energy levels chosen for the model, they appear to be surprisingly tolerant to even severe bandwidth limitations.
This article presents a robust control strategy using Time-Optimal Model Predictive Control (TOMPC) for a two-level quantum system subject to bounded uncertainties. In this method, the control field is optimized over a finite horizon using a nominal quantum system as the reference and then the optimal control for the first time interval is applied and a projective measurement is implemented on the uncertain system. The new control field for the next time interval will be iteratively optimized based on the measurement result. We present theoretical results to guarantee the stability of the TOMPC algorithm. We also characterize the robustness and the convergence rate of the TOMPC strategy for the control of two-level systems. Numerical simulations further demonstrate that, in the presence of uncertainties, our quantum TOMPC algorithm enhances robustness and steers the state to the desired state with high fidelity. This work contributes to the progress of Model Predictive Control in quantum control and explores its potential in practical applications of quantum technology.
Abstract. The robust manipulation of ensembles of quantum systems exhibiting variations or uncertainties in the system parameters and dynamics has been a long-standing problem in the field of quantum control. Existing methods for addressing quantum ensemble control primarily rely on the use of state-space models that describe the time evolution of quantum states. In this paper, we introduce a distinctive quantum control paradigm by mapping the quantum ensemble control problem to a dual problem defined on a coordinate system established by a moment transform. This transformation introduces a new type of quantization in quantum systems, enabling tractable systems-theoretic analysis and effective optimal control design, which are typically opaque. Subsequently, we develop an iterative computational algorithm to solve the transformed optimal moment control problems. We conduct a convergence analysis for the proposed algorithm and demonstrate its applicability and effectiveness on various challenging pulse design problems in quantum control.
In this paper, we discuss a quantum control algorithm, devised by the authors, inspired in Rabitz and Krotov algorithms and applied to Nuclear Magnetic Resonance (NMR) That algorithm is based on a numerical method for iterative optimization.Specifically, we address the determination of external optimal pulses (controls) to minimal cost, over a two-level quantum system.We use the numerical approximation to find the optimal controls in the case of two external electromagnetic fields, integrating the associated equations of the Pontryagin Maximum Principle.That algorithm unifies and generalizes the Rabitz and Krotov algorithms.We compare the efficiency of these algorithms with the solutions found by analytical methods.